Daily Papers

The ability to understand and work with numbers (numeracy) is critical for many complex reasoning tasks. Currently, most NLP models treat numbers in text in the same way as other tokens---they embed them as distributed vectors. Is this enough to capture numeracy? We begin by investigating the numerical reasoning capabilities of a state-of-the-art question answering model on the DROP dataset. We find this model excels on questions that require numerical reasoning, i.e., it already captures numeracy. To understand how this capability emerges, we probe token embedding methods (e.g., BERT, GloVe) on synthetic list maximum, number decoding, and addition tasks. A surprising degree of numeracy is naturally present in standard embeddings. For example, GloVe and word2vec accurately encode magnitude for numbers up to 1,000. Furthermore, character-level embeddings are even more precise---ELMo captures numeracy the best for all pre-trained methods---but BERT, which uses sub-word units, is less exact.

Diffusion language models (DLMs) have recently emerged as an alternative to autoregressive approaches, offering parallel sequence generation and flexible token orders. However, their inference remains slower than that of autoregressive models, primarily due to the cost of bidirectional attention and the large number of refinement steps required for high quality outputs. In this work, we highlight and leverage an overlooked property of DLMs early answer convergence: in many cases, the correct answer can be internally identified by half steps before the final decoding step, both under semi-autoregressive and random remasking schedules. For example, on GSM8K and MMLU, up to 97% and 99% of instances, respectively, can be decoded correctly using only half of the refinement steps. Building on this observation, we introduce Prophet, a training-free fast decoding paradigm that enables early commit decoding. Specifically, Prophet dynamically decides whether to continue refinement or to go "all-in" (i.e., decode all remaining tokens in one step), using the confidence gap between the top-2 prediction candidates as the criterion. It integrates seamlessly into existing DLM implementations, incurs negligible overhead, and requires no additional training. Empirical evaluations of LLaDA-8B and Dream-7B across multiple tasks show that Prophet reduces the number of decoding steps by up to 3.4x while preserving high generation quality. These results recast DLM decoding as a problem of when to stop sampling, and demonstrate that early decode convergence provides a simple yet powerful mechanism for accelerating DLM inference, complementary to existing speedup techniques. Our code is publicly available at https://github.com/pixeli99/Prophet.

The inference process in Large Language Models (LLMs) is often limited due to the absence of parallelism in the auto-regressive decoding process, resulting in most operations being restricted by the memory bandwidth of accelerators. While methods such as speculative decoding have been suggested to address this issue, their implementation is impeded by the challenges associated with acquiring and maintaining a separate draft model. In this paper, we present Medusa, an efficient method that augments LLM inference by adding extra decoding heads to predict multiple subsequent tokens in parallel. Using a tree-based attention mechanism, Medusa constructs multiple candidate continuations and verifies them simultaneously in each decoding step. By leveraging parallel processing, Medusa introduces only minimal overhead in terms of single-step latency while substantially reducing the number of decoding steps required. We present two levels of fine-tuning procedures for Medusa to meet the needs of different use cases: Medusa-1: Medusa is directly fine-tuned on top of a frozen backbone LLM, enabling lossless inference acceleration. Medusa-2: Medusa is fine-tuned together with the backbone LLM, enabling better prediction accuracy of Medusa heads and higher speedup but needing a special training recipe that preserves the backbone model's capabilities. Moreover, we propose several extensions that improve or expand the utility of Medusa, including a self-distillation to handle situations where no training data is available and a typical acceptance scheme to boost the acceptance rate while maintaining generation quality. We evaluate Medusa on models of various sizes and training procedures. Our experiments demonstrate that Medusa-1 can achieve over 2.2x speedup without compromising generation quality, while Medusa-2 further improves the speedup to 2.3-3.6x.

Recent theoretical work has identified surprisingly simple reasoning problems, such as checking if two nodes in a graph are connected or simulating finite-state machines, that are provably unsolvable by standard transformers that answer immediately after reading their input. However, in practice, transformers' reasoning can be improved by allowing them to use a "chain of thought" or "scratchpad", i.e., generate and condition on a sequence of intermediate tokens before answering. Motivated by this, we ask: Does such intermediate generation fundamentally extend the computational power of a decoder-only transformer? We show that the answer is yes, but the amount of increase depends crucially on the amount of intermediate generation. For instance, we find that transformer decoders with a logarithmic number of decoding steps (w.r.t. the input length) push the limits of standard transformers only slightly, while a linear number of decoding steps, assuming a slight generalization to standard pre-norm, adds a clear new ability (under standard complexity conjectures): recognizing all regular languages. Our results also imply that linear steps keep transformer decoders within context-sensitive languages, and polynomial steps with generalized pre-norm make them recognize exactly the class of polynomial-time solvable problems -- the first exact characterization of a type of transformers in terms of standard complexity classes. Together, our results provide a nuanced framework for understanding how the length of a transformer's chain of thought or scratchpad impacts its reasoning power.

Recent advancements in large language models have facilitated the execution of complex language tasks, not only in English but also in non-English languages. However, the tokenizers of most language models, such as Llama, trained on English-centric corpora, tend to excessively fragment tokens in non-English languages. This issue is especially pronounced in non-roman alphabetic languages, which are often divided at a character or even Unicode level, leading to slower text generation. To address this, our study introduces a novel framework designed to expedite text generation in these languages. This framework predicts larger linguistic units than those of conventional multilingual tokenizers and is specifically tailored to the target language, thereby reducing the number of decoding steps required. Our empirical results demonstrate that the proposed framework increases the generation speed by a factor of 1.9 compared to standard decoding while maintaining the performance of a pre-trained multilingual model on monolingual tasks.

Autoregressive decoding of large language models (LLMs) is memory bandwidth bounded, resulting in high latency and significant wastes of the parallel processing power of modern accelerators. Existing methods for accelerating LLM decoding often require a draft model (e.g., speculative decoding), which is nontrivial to obtain and unable to generalize. In this paper, we introduce Lookahead decoding, an exact, parallel decoding algorithm that accelerates LLM decoding without needing auxiliary models or data stores. It allows trading per-step log(FLOPs) to reduce the number of total decoding steps, is more parallelizable on single or multiple modern accelerators, and is compatible with concurrent memory-efficient attention (e.g., FlashAttention). Our implementation of Lookahead decoding can speed up autoregressive decoding by up to 1.8x on MT-bench and 4x with strong scaling on multiple GPUs in code completion tasks. Our code is avialable at https://github.com/hao-ai-lab/LookaheadDecoding

We present TURJUMAN, a neural toolkit for translating from 20 languages into Modern Standard Arabic (MSA). TURJUMAN exploits the recently-introduced text-to-text Transformer AraT5 model, endowing it with a powerful ability to decode into Arabic. The toolkit offers the possibility of employing a number of diverse decoding methods, making it suited for acquiring paraphrases for the MSA translations as an added value. To train TURJUMAN, we sample from publicly available parallel data employing a simple semantic similarity method to ensure data quality. This allows us to prepare and release AraOPUS-20, a new machine translation benchmark. We publicly release our translation toolkit (TURJUMAN) as well as our benchmark dataset (AraOPUS-20).

While language models have exceptional capabilities at text generation, they lack a natural inductive bias for emitting numbers and thus struggle in tasks involving reasoning over quantities, especially arithmetics. This has particular relevance in scientific datasets where combinations of text and numerical data are abundant. One fundamental limitation is the nature of the CE loss, which assumes a nominal (categorical) scale and thus cannot convey proximity between generated number tokens. As a remedy, we here present two versions of a number token loss. The first is based on an L_p loss between the ground truth token value and the weighted sum of the predicted class probabilities. The second loss minimizes the Wasserstein-1 distance between the distribution of the predicted output probabilities and the ground truth distribution. These regression-like losses can easily be added to any language model and extend the CE objective during training. We compare the proposed schemes on a mathematics dataset against existing tokenization, encoding, and decoding schemes for improving number representation in language models. Our results reveal a significant improvement in numerical accuracy when equipping a standard T5 model with the proposed loss schemes.

Decoding methods play an indispensable role in converting language models from next-token predictors into practical task solvers. Prior research on decoding methods, primarily focusing on task-specific models, may not extend to the current era of general-purpose large language models (LLMs). Moreover, the recent influx of decoding strategies has further complicated this landscape. This paper provides a comprehensive and multifaceted analysis of various decoding methods within the context of LLMs, evaluating their performance, robustness to hyperparameter changes, and decoding speeds across a wide range of tasks, models, and deployment environments. Our findings reveal that decoding method performance is notably task-dependent and influenced by factors such as alignment, model size, and quantization. Intriguingly, sensitivity analysis exposes that certain methods achieve superior performance at the cost of extensive hyperparameter tuning, highlighting the trade-off between attaining optimal results and the practicality of implementation in varying contexts.

Inference-time optimization scales computation to derive deliberate reasoning steps for effective performance. While previous search-based strategies address the short-sightedness of auto-regressive generation, the vast search space leads to excessive exploration and insufficient exploitation. To strike an efficient balance to derive the optimal step, we frame the decoding strategy as foresight sampling, leveraging simulated future steps to obtain globally optimal step estimation. Built on it, we propose a novel decoding strategy, named phi-Decoding. To provide a precise and expressive estimation of step value, phi-Decoding approximates two distributions via foresight and clustering. Sampling from the joint distribution, the optimal steps can be selected for exploitation. To support adaptive computation allocation, we propose in-width and in-depth pruning strategies, featuring a light-weight solution to achieve inference efficiency. Extensive experiments across seven benchmarks show phi-Decoding outperforms strong baselines in both performance and efficiency. Additional analysis demonstrates its generalization across various LLMs and scalability across a wide range of computing budgets. The code will be released at https://github.com/xufangzhi/phi-Decoding, and the open-source PyPI package is coming soon.

Transformers, central to the successes in modern Natural Language Processing, often falter on arithmetic tasks despite their vast capabilities --which paradoxically include remarkable coding abilities. We observe that a crucial challenge is their naive reliance on positional information to solve arithmetic problems with a small number of digits, leading to poor performance on larger numbers. Herein, we delve deeper into the role of positional encoding, and propose several ways to fix the issue, either by modifying the positional encoding directly, or by modifying the representation of the arithmetic task to leverage standard positional encoding differently. We investigate the value of these modifications for three tasks: (i) classical multiplication, (ii) length extrapolation in addition, and (iii) addition in natural language context. For (i) we train a small model on a small dataset (100M parameters and 300k samples) with remarkable aptitude in (direct, no scratchpad) 15 digits multiplication and essentially perfect up to 12 digits, while usual training in this context would give a model failing at 4 digits multiplication. In the experiments on addition, we use a mere 120k samples to demonstrate: for (ii) extrapolation from 10 digits to testing on 12 digits numbers while usual training would have no extrapolation, and for (iii) almost perfect accuracy up to 5 digits while usual training would be correct only up to 3 digits (which is essentially memorization with a training set of 120k samples).

Large Language Models (LLMs) typically represent numbers using multiple tokens, which requires the model to aggregate these tokens to interpret numerical values. This fragmentation makes both training and inference less efficient and adversely affects the model's performance on number-related tasks. Inspired by the observation that pre-trained LLMs internally learn Fourier-like features for number tokens, we propose Fourier Number Embedding (FoNE), a novel method that directly maps numbers into the embedding space with their Fourier features. FoNE encodes each number as a single token with only two embedding dimensions per digit, effectively capturing numerical values without fragmentation. This compact representation accelerates both training and inference. Compared to traditional subword and digit-wise embeddings, FoNE not only reduces computational overhead but also achieves higher accuracy across various numerical tasks including addition, subtraction and multiplication. On 6-digit decimal addition, FoNE requires 64times less data to achieve 99% accuracy than subword and digit-wise embeddings while using 3times and 6times fewer tokens per number, respectively. Furthermore, FoNE is the only method that yields 100% accuracy on over 100,000 test examples for addition, subtraction, and multiplication. The codes and visualization are available at https://fouriernumber.github.io/.

Self-consistency-based approaches, which involve repeatedly sampling multiple outputs and selecting the most consistent one as the final response, prove to be remarkably effective in improving the factual accuracy of large language models. Nonetheless, existing methods usually have strict constraints on the task format, largely limiting their applicability. In this paper, we present Integrative Decoding (ID), to unlock the potential of self-consistency in open-ended generation tasks. ID operates by constructing a set of inputs, each prepended with a previously sampled response, and then processes them concurrently, with the next token being selected by aggregating of all their corresponding predictions at each decoding step. In essence, this simple approach implicitly incorporates self-consistency in the decoding objective. Extensive evaluation shows that ID consistently enhances factuality over a wide range of language models, with substantial improvements on the TruthfulQA (+11.2%), Biographies (+15.4%) and LongFact (+8.5%) benchmarks. The performance gains amplify progressively as the number of sampled responses increases, indicating the potential of ID to scale up with repeated sampling.

Due to the large number of parameters, the inference phase of Large Language Models (LLMs) is resource-intensive. Unlike traditional model compression, which needs retraining, recent dynamic computation methods show that not all components are required for inference, enabling a training-free pipeline. In this paper, we focus on the dynamic depth of LLM generation. A token-position aware layer skipping framework is proposed to save 1.5x times operations efficiently while maintaining performance. We first observed that tokens predicted later have lower perplexity and thus require less computation. Then, we propose a training-free algorithm called Position-Aware Depth Decay Decoding (D^3), which leverages a power-law decay function, leftlfloor L times (alpha^i) rightrfloor, to determine the number of layers to retain when generating token T_i. Remarkably, without any retraining, the D^3 achieves success across a wide range of generation tasks for the first time. Experiments on large language models (\ie the Llama) with 7 sim 70 billion parameters show that D^3 can achieve an average 1.5x speedup compared with the full-inference pipeline while maintaining comparable performance with nearly no performance drop (<1%) on the GSM8K and BBH benchmarks.

The growth in the number of parameters of Large Language Models (LLMs) has led to a significant surge in computational requirements, making them challenging and costly to deploy. Speculative decoding (SD) leverages smaller models to efficiently propose future tokens, which are then verified by the LLM in parallel. Small models that utilise activations from the LLM currently achieve the fastest decoding speeds. However, we identify several limitations of SD models including the lack of on-policyness during training and partial observability. To address these shortcomings, we propose a more grounded architecture for small models by introducing a Mixture of Attentions for SD. Our novel architecture can be applied in two scenarios: a conventional single device deployment and a novel client-server deployment where the small model is hosted on a consumer device and the LLM on a server. In a single-device scenario, we demonstrate state-of-the-art speedups improving EAGLE-2 by 9.5% and its acceptance length by 25%. In a client-server setting, our experiments demonstrate: 1) state-of-the-art latencies with minimal calls to the server for different network conditions, and 2) in the event of a complete disconnection, our approach can maintain higher accuracy compared to other SD methods and demonstrates advantages over API calls to LLMs, which would otherwise be unable to continue the generation process.

Large language models (LLMs) have recently shown remarkable performance across a wide range of tasks. However, the substantial number of parameters in LLMs contributes to significant latency during model inference. This is particularly evident when utilizing autoregressive decoding methods, which generate one token in a single forward process, thereby not fully capitalizing on the parallel computing capabilities of GPUs. In this paper, we propose a novel parallel decoding approach, namely hidden transfer, which decodes multiple successive tokens simultaneously in a single forward pass. The idea is to transfer the intermediate hidden states of the previous context to the pseudo hidden states of the future tokens to be generated, and then the pseudo hidden states will pass the following transformer layers thereby assimilating more semantic information and achieving superior predictive accuracy of the future tokens. Besides, we use the novel tree attention mechanism to simultaneously generate and verify multiple candidates of output sequences, which ensure the lossless generation and further improves the generation efficiency of our method. Experiments demonstrate the effectiveness of our method. We conduct a lot of analytic experiments to prove our motivation. In terms of acceleration metrics, we outperform all the single-model acceleration techniques, including Medusa and Self-Speculative decoding.

Recent studies have revealed a number of pathologies of neural machine translation (NMT) systems. Hypotheses explaining these mostly suggest there is something fundamentally wrong with NMT as a model or its training algorithm, maximum likelihood estimation (MLE). Most of this evidence was gathered using maximum a posteriori (MAP) decoding, a decision rule aimed at identifying the highest-scoring translation, i.e. the mode. We argue that the evidence corroborates the inadequacy of MAP decoding more than casts doubt on the model and its training algorithm. In this work, we show that translation distributions do reproduce various statistics of the data well, but that beam search strays from such statistics. We show that some of the known pathologies and biases of NMT are due to MAP decoding and not to NMT's statistical assumptions nor MLE. In particular, we show that the most likely translations under the model accumulate so little probability mass that the mode can be considered essentially arbitrary. We therefore advocate for the use of decision rules that take into account the translation distribution holistically. We show that an approximation to minimum Bayes risk decoding gives competitive results confirming that NMT models do capture important aspects of translation well in expectation.

Conditional neural text generation models generate high-quality outputs, but often concentrate around a mode when what we really want is a diverse set of options. We present a search algorithm to construct lattices encoding a massive number of generation options. First, we restructure decoding as a best-first search, which explores the space differently than beam search and improves efficiency by avoiding pruning paths. Second, we revisit the idea of hypothesis recombination: we can identify pairs of similar generation candidates during search and merge them as an approximation. On both summarization and machine translation, we show that our algorithm encodes thousands of diverse options that remain grammatical and high-quality into one lattice. This algorithm provides a foundation for building downstream generation applications on top of massive-scale diverse outputs.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

Speculative decoding is a promising method for reducing the inference latency of large language models. The effectiveness of the method depends on the speculation length (SL) - the number of tokens generated by the draft model at each iteration. The vast majority of speculative decoding approaches use the same SL for all iterations. In this work, we show that this practice is suboptimal. We introduce DISCO, a DynamIc SpeCulation length Optimization method that uses a classifier to dynamically adjust the SL at each iteration, while provably preserving the decoding quality. Experiments with four benchmarks demonstrate average speedup gains of 10.3% relative to our best baselines.

The end-to-end nature of neural machine translation (NMT) removes many ways of manually guiding the translation process that were available in older paradigms. Recent work, however, has introduced a new capability: lexically constrained or guided decoding, a modification to beam search that forces the inclusion of pre-specified words and phrases in the output. However, while theoretically sound, existing approaches have computational complexities that are either linear (Hokamp and Liu, 2017) or exponential (Anderson et al., 2017) in the number of constraints. We present a algorithm for lexically constrained decoding with a complexity of O(1) in the number of constraints. We demonstrate the algorithms remarkable ability to properly place these constraints, and use it to explore the shaky relationship between model and BLEU scores. Our implementation is available as part of Sockeye.

Large language models have demonstrated exceptional capability in natural language understanding and generation. However, their generation speed is limited by the inherently sequential nature of their decoding process, posing challenges for real-time applications. This paper introduces Lexical Unit Decoding (LUD), a novel decoding methodology implemented in a data-driven manner, accelerating the decoding process without sacrificing output quality. The core of our approach is the observation that a pre-trained language model can confidently predict multiple contiguous tokens, forming the basis for a lexical unit, in which these contiguous tokens could be decoded in parallel. Extensive experiments validate that our method substantially reduces decoding time while maintaining generation quality, i.e., 33\% speed up on natural language generation with no quality loss, and 30\% speed up on code generation with a negligible quality loss of 3\%. Distinctively, LUD requires no auxiliary models and does not require changes to existing architectures. It can also be integrated with other decoding acceleration methods, thus achieving an even more pronounced inference efficiency boost. We posit that the foundational principles of LUD could define a new decoding paradigm for future language models, enhancing their applicability for a broader spectrum of applications. All codes are be publicly available at https://github.com/tjunlp-lab/Lexical-Unit-Decoding-LUD-. Keywords: Parallel Decoding, Lexical Unit Decoding, Large Language Model

The poor performance of transformers on arithmetic tasks seems to stem in large part from their inability to keep track of the exact position of each digit inside of a large span of digits. We mend this problem by adding an embedding to each digit that encodes its position relative to the start of the number. In addition to the boost these embeddings provide on their own, we show that this fix enables architectural modifications such as input injection and recurrent layers to improve performance even further. With positions resolved, we can study the logical extrapolation ability of transformers. Can they solve arithmetic problems that are larger and more complex than those in their training data? We find that training on only 20 digit numbers with a single GPU for one day, we can reach state-of-the-art performance, achieving up to 99% accuracy on 100 digit addition problems. Finally, we show that these gains in numeracy also unlock improvements on other multi-step reasoning tasks including sorting and multiplication.

In this work, we propose Dimple, the first Discrete Diffusion Multimodal Large Language Model (DMLLM). We observe that training with a purely discrete diffusion approach leads to significant training instability, suboptimal performance, and severe length bias issues. To address these challenges, we design a novel training paradigm that combines an initial autoregressive phase with a subsequent diffusion phase. This approach yields the Dimple-7B model, trained on the same dataset and using a similar training pipeline as LLaVA-NEXT. Dimple-7B ultimately surpasses LLaVA-NEXT in performance by 3.9%, demonstrating that DMLLM can achieve performance comparable to that of autoregressive models. To improve inference efficiency, we propose a decoding strategy termed confident decoding, which dynamically adjusts the number of tokens generated at each step, significantly reducing the number of generation iterations. In autoregressive models, the number of forward iterations during generation equals the response length. With confident decoding, however, the number of iterations needed by Dimple is even only text{response length}{3}. We also re-implement the prefilling technique in autoregressive models and demonstrate that it does not significantly impact performance on most benchmark evaluations, while offering a speedup of 1.5x to 7x. Additionally, we explore Dimple's capability to precisely control its response using structure priors. These priors enable structured responses in a manner distinct from instruction-based or chain-of-thought prompting, and allow fine-grained control over response format and length, which is difficult to achieve in autoregressive models. Overall, this work validates the feasibility and advantages of DMLLM and enhances its inference efficiency and controllability. Code and models are available at https://github.com/yu-rp/Dimple.

Due to the high resource demands of Large Language Models (LLMs), achieving widespread deployment on consumer-grade devices presents significant challenges. Typically, personal or consumer-grade devices, including servers configured prior to the era of large-scale models, generally have relatively weak GPUs and relatively strong CPUs. However, most current methods primarily depend on GPUs for computation. Therefore, we propose Dovetail, an approach that deploys the draft model on the GPU to generate draft tokens while allowing the target model to perform parallel verification on the CPU, thereby improving the utilization of all available hardware resources and occupying less inter-device communication bandwidth. Accordingly, we have redesigned the draft model to better align with heterogeneous hardware characteristics. To this end, we implemented several optimizations: reducing the number of draft tokens to mitigate latency in parallel verification, increasing the depth of the draft model to enhance its predictive capacity, and introducing DGF (Dynamic Gating Fusion) to improve the integration of features and token embeddings. In the HumanEval benchmark, Dovetail achieved an inference speed of 5.86 tokens per second for LLaMA2-Chat-7B using 3GB of VRAM, representing an approximately 2.77x improvement over CPU-only inference. Furthermore, the inference speed was increased to 8 tokens per second when utilizing 7GB of VRAM.

Speculative Decoding (SD) is a popular lossless technique for accelerating the inference of Large Language Models (LLMs). We show that the decoding speed of SD frameworks with static draft structures can be significantly improved by incorporating context-aware adaptive draft structures. However, current studies on adaptive draft structures are limited by their performance, modeling approaches, and applicability. In this paper, we introduce AdaEAGLE, the first SD framework that explicitly models adaptive draft structures. AdaEAGLE leverages the Lightweight Draft Length Predictor (LDLP) module to explicitly predict the optimal number of draft tokens during inference to guide the draft model. It achieves comparable speedup results without manual thresholds and allows for deeper, more specialized optimizations. Moreover, together with threshold-based strategies, AdaEAGLE achieves a 1.62times speedup over the vanilla AR decoding and outperforms fixed-length SotA baseline while maintaining output quality.

Speculative decoding emerges as a pivotal technique for enhancing the inference speed of Large Language Models (LLMs). Despite recent research aiming to improve prediction efficiency, multi-sample speculative decoding has been overlooked due to varying numbers of accepted tokens within a batch in the verification phase. Vanilla method adds padding tokens in order to ensure that the number of new tokens remains consistent across samples. However, this increases the computational and memory access overhead, thereby reducing the speedup ratio. We propose a novel method that can resolve the issue of inconsistent tokens accepted by different samples without necessitating an increase in memory or computing overhead. Furthermore, our proposed method can handle the situation where the prediction tokens of different samples are inconsistent without the need to add padding tokens. Sufficient experiments demonstrate the efficacy of our method. Our code is available at https://github.com/niyunsheng/EMS-SD.

Autoregressive next token prediction language models offer powerful capabilities but face significant challenges in practical deployment due to the high computational and memory costs of inference, particularly during the decoding stage. We introduce Set Block Decoding (SBD), a simple and flexible paradigm that accelerates generation by integrating standard next token prediction (NTP) and masked token prediction (MATP) within a single architecture. SBD allows the model to sample multiple, not necessarily consecutive, future tokens in parallel, a key distinction from previous acceleration methods. This flexibility allows the use of advanced solvers from the discrete diffusion literature, offering significant speedups without sacrificing accuracy. SBD requires no architectural changes or extra training hyperparameters, maintains compatibility with exact KV-caching, and can be implemented by fine-tuning existing next token prediction models. By fine-tuning Llama-3.1 8B and Qwen-3 8B, we demonstrate that SBD enables a 3-5x reduction in the number of forward passes required for generation while achieving same performance as equivalent NTP training.

When reading, we often have specific information that interests us in a text. For example, you might be reading this paper because you are curious about LLMs for eye movements in reading, the experimental design, or perhaps you only care about the question ``but does it work?''. More broadly, in daily life, people approach texts with any number of text-specific goals that guide their reading behavior. In this work, we ask, for the first time, whether open-ended reading goals can be automatically decoded from eye movements in reading. To address this question, we introduce goal classification and goal reconstruction tasks and evaluation frameworks, and use large-scale eye tracking for reading data in English with hundreds of text-specific information seeking tasks. We develop and compare several discriminative and generative multimodal LLMs that combine eye movements and text for goal classification and goal reconstruction. Our experiments show considerable success on both tasks, suggesting that LLMs can extract valuable information about the readers' text-specific goals from eye movements.

The generation speed of LLMs are bottlenecked by autoregressive decoding, where tokens are predicted sequentially one by one. Alternatively, diffusion large language models (dLLMs) theoretically allow for parallel token generation, but in practice struggle to achieve the speed of autoregressive models without significantly sacrificing quality. We therefore introduce adaptive parallel decoding (APD), a novel method that dynamically adjusts the number of tokens sampled in parallel. We achieve this by defining a multiplicative mixture between the dLLM marginal probabilities and the joint probability of sequences under a small auxiliary autoregressive model. This inverts the standard setup of speculative decoding, where the goal is to sample from a large autoregressive verifier by drafting from a smaller model. We further optimize APD by enabling KV caching and limiting the size of the masked input. Altogether, our method puts forward three tunable parameters to flexibly tradeoff throughput and quality. We show that APD provides markedly higher throughput with minimal quality degradations on downstream benchmarks.

Fast Automatic Speech Recognition (ASR) is critical for latency-sensitive applications such as real-time captioning and meeting transcription. However, truly parallel ASR decoding remains challenging due to the sequential nature of autoregressive (AR) decoders and the context limitations of non-autoregressive (NAR) methods. While modern ASR encoders can process up to 30 seconds of audio at once, AR decoders still generate tokens sequentially, creating a latency bottleneck. We propose Whisfusion, the first framework to fuse a pre-trained Whisper encoder with a text diffusion decoder. This NAR architecture resolves the AR latency bottleneck by processing the entire acoustic context in parallel at every decoding step. A lightweight cross-attention adapter trained via parameter-efficient fine-tuning (PEFT) bridges the two modalities. We also introduce a batch-parallel, multi-step decoding strategy that improves accuracy by increasing the number of candidates with minimal impact on speed. Fine-tuned solely on LibriSpeech (960h), Whisfusion achieves a lower WER than Whisper-tiny (8.3% vs. 9.7%), and offers comparable latency on short audio. For longer utterances (>20s), it is up to 2.6x faster than the AR baseline, establishing a new, efficient operating point for long-form ASR. The implementation and training scripts are available at https://github.com/taeyoun811/Whisfusion.

Though Large Language Models (LLMs) have shown remarkable abilities in mathematics reasoning, they are still struggling with performing numeric operations accurately, such as addition and multiplication. Numbers can be tokenized into tokens in various ways by different LLMs and affect the numeric operations performance. Currently, there are two representatives: 1) Tokenize into 1-digit, and 2) Tokenize into 1sim 3 digit. The difference is roughly equivalent to using different numeral systems (namely base 10 or base 10^{3}). In light of this, we study the scaling behavior of different numeral systems in the context of transformer-based large language models. We empirically show that a base 10 system is consistently more data-efficient than a base 10^{2} or 10^{3} system across training data scale, model sizes under from-scratch training settings, while different number systems have very similar fine-tuning performances. We attribute this to higher token frequencies of a base 10 system. Additionally, we reveal extrapolation behavior patterns on addition and multiplication. We identify that base 100 and base 1000 systems struggle on token-level discernment and token-level operations. We also sheds light on the mechanism learnt by the models.

Autoregressive Large Language Models (LLMs) have achieved impressive performance in language tasks but face two significant bottlenecks: (1) quadratic complexity in the attention module as the number of tokens increases, and (2) limited efficiency due to the sequential processing nature of autoregressive LLMs during generation. While linear attention and speculative decoding offer potential solutions, their applicability and synergistic potential for enhancing autoregressive LLMs remain uncertain. We conduct the first comprehensive study on the efficacy of existing linear attention methods for autoregressive LLMs, integrating them with speculative decoding. We introduce an augmentation technique for linear attention that ensures compatibility with speculative decoding, enabling more efficient training and serving of LLMs. Extensive experiments and ablation studies involving seven existing linear attention models and five encoder/decoder-based LLMs consistently validate the effectiveness of our augmented linearized LLMs. Notably, our approach achieves up to a 6.67 reduction in perplexity on the LLaMA model and up to a 2times speedup during generation compared to prior linear attention methods. Codes and models are available at https://github.com/GATECH-EIC/Linearized-LLM.

Self-ensembling techniques with diverse reasoning paths such as Self-Consistency have demonstrated remarkable performance gains in text generation with Large Language Models (LLMs). However, such techniques depend on the availability of an accurate answer extraction process to aggregate across multiple outputs. Moreover, they acquire higher inference cost, in comparison to Greedy Decoding, due to generation of relatively higher number of output tokens. Research has shown that the free form text outputs from Self-Consistency can be aggregated reliably using LLMs to produce the final output. Additionally, recent advancements in LLM inference have demonstrated that usage of diverse exemplars in prompts have the ability to induce diversity in the LLM outputs. Such proven techniques can be easily extended to self-ensembling based approaches to achieve enhanced results in text generation. In this paper, we introduce PEDAL (Prompts based on Exemplar Diversity Aggregated using LLMs), a hybrid self-ensembling approach, that combines the strengths of diverse exemplar based prompts and LLM based aggregation to achieve improvement in overall performance. On the publicly available SVAMP and ARC datasets, our experiments reveal that PEDAL can achieve better accuracy than Greedy Decoding based strategies with lower inference cost compared to Self Consistency based approaches.

Speculative decoding reduces the inference latency of a target large language model via utilizing a smaller and faster draft model. Its performance depends on a hyperparameter K -- the candidate length, i.e., the number of candidate tokens for the target model to verify in each round. However, previous methods often use simple heuristics to choose K, which may result in sub-optimal performance. We study the choice of the candidate length K and formulate it as a Markov Decision Process. We theoretically show that the optimal policy of this Markov decision process takes the form of a threshold policy, i.e., the current speculation should stop and be verified when the probability of getting a rejection exceeds a threshold value. Motivated by this theory, we propose SpecDec++, an enhanced version of speculative decoding that adaptively determines the candidate length on the fly. We augment the draft model with a trained acceptance prediction head to predict the conditional acceptance probability of the candidate tokens. SpecDec++ will stop the current speculation when the predicted probability that at least one token gets rejected exceeds a threshold. We implement SpecDec++ and apply it to the llama-2-chat 7B & 70B model pair. Our adaptive method achieves a 2.04x speedup on the Alpaca dataset (an additional 7.2% improvement over the baseline speculative decoding). On the GSM8K and HumanEval datasets, our method achieves a 2.26x speedup (9.4% improvement) and 2.23x speedup (11.1% improvement), respectively.

Vision-Language-Action (VLA) models adapt large vision-language backbones to map images and instructions to robot actions. However, prevailing VLA decoders either generate actions autoregressively in a fixed left-to-right order or attach continuous diffusion or flow matching heads outside the backbone, demanding specialized training and iterative sampling that hinder a unified, scalable architecture. We present Discrete Diffusion VLA, a single-transformer policy that models discretized action chunks with discrete diffusion and is trained with the same cross-entropy objective as the VLM backbone. The design retains diffusion's progressive refinement paradigm while remaining natively compatible with the discrete token interface of VLMs. Our method achieves an adaptive decoding order that resolves easy action elements before harder ones and uses secondary remasking to revisit uncertain predictions across refinement rounds, which improves consistency and enables robust error correction. This unified decoder preserves pretrained vision language priors, supports parallel decoding, breaks the autoregressive bottleneck, and reduces the number of function evaluations. Discrete Diffusion VLA achieves 96.3% avg. SR on LIBERO, 71.2% visual matching on SimplerEnv Fractal and 49.3% overall on SimplerEnv Bridge, improving over both autoregressive and continuous diffusion baselines. These findings indicate that discrete-diffusion action decoder supports precise action modeling and consistent training, laying groundwork for scaling VLA to larger models and datasets.

In arbitrary-order language models, it is an open question how to sample tokens in parallel from the correct joint distribution. With discrete diffusion models, the more tokens they generate in parallel, the less their predicted distributions adhere to the originally learned data distribution, as they rely on a conditional independence assumption that only works with infinitesimally small timesteps. We find that a different class of models, any-subset autoregressive models (AS-ARMs), holds the solution. As implied by the name, AS-ARMs can generate tokens in any order, and in parallel. Moreover, AS-ARMs support parallelized joint probability density estimation, allowing them to correct their own parallel-generated token distributions, via our Any-Subset Speculative Decoding (ASSD) algorithm. ASSD provably enables generation of tokens from the correct joint distribution, with the number of neural network calls upper bounded by the number of tokens predicted. We empirically verify that ASSD speeds up language generation, without sacrificing quality. Furthermore, we provide a mathematically justified scheme for training AS-ARMs for generation, and show that AS-ARMs achieve state-of-the-art performance among sub-200M parameter models on infilling benchmark tasks, and nearly match the performance of models 50X larger on code generation. Our theoretical and empirical results indicate that the once-forgotten AS-ARMs are a promising direction of language modeling.

The massive adoption of large language models (LLMs) demands efficient deployment strategies. However, the auto-regressive decoding process, which is fundamental to how most LLMs generate text, poses challenges to achieve efficient serving. In this work, we introduce a parallel auto-regressive generation method. By instruct-tuning on general domain data that contains hierarchical structures, we enable LLMs to independently plan their generation process and perform auto-parallel auto-regressive (APAR) generation, significantly reducing the number of generation steps. APAR alone can achieve up to 2x speed-up, and when combined with speculative decoding, the speed-up can reach up to 4x. In addition, APAR reduces the key-value cache consumption and attention computation during generation. This leads to a throughput increase of 20-70% and a latency reduce of 20-35% in high-throughput scenarios, compared to state-of-the-art serving frameworks.

Large language models (LLMs) have shown promising capabilities in using external tools to solve complex problems. However, existing approaches either involve fine-tuning on tool demonstrations, which do not generalize to new tools without additional training, or providing tool documentation in context, limiting the number of tools. Both approaches often generate syntactically invalid tool calls. In this paper, we propose ToolDec, a finite-state machine-guided decoding algorithm for tool-augmented LLMs. ToolDec eliminates tool-related errors for any tool-augmented LLMs by ensuring valid tool names and type-conforming arguments. Furthermore, ToolDec enables LLM to effectively select tools using only the information contained in their names, with no need for fine-tuning or in-context documentation. We evaluated multiple prior methods and their ToolDec-enhanced versions on a variety of tasks involving tools like math functions, knowledge graph relations, and complex real-world RESTful APIs. Our experiments show that ToolDec reduces syntactic errors to zero, consequently achieving significantly better performance and as much as a 2x speedup. We also show that ToolDec achieves superior generalization performance on unseen tools, performing up to 8x better than the baselines.

Speculative Decoding (SD) is a widely used approach to accelerate the inference of large language models (LLMs) without reducing generation quality. It operates by first using a compact model to draft multiple tokens efficiently, followed by parallel verification using the target LLM. This approach leads to faster inference compared to auto-regressive decoding. While there are multiple approaches to create a draft model, one promising approach is to use early-exit methods. These methods draft candidate tokens by using a subset of layers of the primary model and applying the remaining layers for verification, allowing a single model to handle both drafting and verification. While this technique reduces memory usage and computational cost, its performance relies on the choice of the exit layer for drafting and the number of tokens drafted (speculation length) in each SD round. Prior works use hyperparameter exploration to statically select these values. However, our evaluations show that these hyperparameter values are task-specific, and even within a task they are dependent on the current sequence context. We introduce DEL, a plug-and-play method that adaptively selects the exit layer and speculation length during inference. DEL dynamically tracks the token acceptance rate if the tokens are drafted at each layer of an LLM and uses that knowledge to heuristically select the optimal exit layer and speculation length. Our experiments across a broad range of models and downstream tasks show that DEL achieves overall speedups of 2.16timessim2.50times over vanilla auto-regressive decoding and improves upon the state-of-the-art SD methods by up to 0.27times.

Computationally intensive decoding procedures--including search, reranking, and self-critique--can improve the quality of language model (LM) outputs in problems spanning code generation, numerical reasoning, and dialog. Existing work typically applies the same decoding procedure for every input to an LM. But not all inputs require the same amount of computation to process. Can we allocate decoding computation adaptively, using more resources to answer questions whose answers will be harder to compute? We present an approach that predicts the distribution of rewards given an input and computation budget, then allocates additional computation to inputs for which it is predicted to be most useful. We apply this approach in two decoding procedures: first, an adaptive best-of-k procedure that dynamically selects the number of samples to generate as input to a reranker; second, a routing procedure that dynamically responds to a query using a decoding procedure that is expensive but accurate, or one that is cheaper but less capable. Across a suite of programming, mathematics, and dialog tasks, we show that accurate computation-allocation procedures can be learned, and reduce computation by up to 50% at no cost to response quality, or improve quality by up to 10% at a fixed computational budget.

Striking an optimal balance between minimal drafting latency and high speculation accuracy to enhance the inference speed of Large Language Models remains a significant challenge in speculative decoding. In this paper, we introduce Falcon, an innovative semi-autoregressive speculative decoding framework fashioned to augment both the drafter's parallelism and output quality. Falcon incorporates the Coupled Sequential Glancing Distillation technique, which fortifies inter-token dependencies within the same block, leading to increased speculation accuracy. We offer a comprehensive theoretical analysis to illuminate the underlying mechanisms. Additionally, we introduce a Custom-Designed Decoding Tree, which permits the drafter to generate multiple tokens in a single forward pass and accommodates multiple forward passes as needed, thereby boosting the number of drafted tokens and significantly improving the overall acceptance rate. Comprehensive evaluations on benchmark datasets such as MT-Bench, HumanEval, and GSM8K demonstrate Falcon's superior acceleration capabilities. The framework achieves a lossless speedup ratio ranging from 2.91x to 3.51x when tested on the Vicuna and LLaMA2-Chat model series. These results outstrip existing speculative decoding methods for LLMs, including Eagle, Medusa, Lookahead, SPS, and PLD, while maintaining a compact drafter architecture equivalent to merely two Transformer layers.

Large language model (LLM) decoding involves generating a sequence of tokens based on a given context, where each token is predicted one at a time using the model's learned probabilities. The typical autoregressive decoding method requires a separate forward pass through the model for each token generated, which is computationally inefficient and poses challenges for deploying LLMs in latency-sensitive scenarios. The main limitations of current decoding methods stem from their inefficiencies and resource demands. Existing approaches either necessitate fine-tuning smaller models, which is resource-intensive, or rely on fixed retrieval schemes to construct drafts for the next tokens, which lack adaptability and fail to generalize across different models and contexts. To address these issues, we introduce a novel methodology called ADED, which accelerates LLM decoding without requiring fine-tuning. Our approach involves an adaptive draft-verification process that evolves over time to improve efficiency. We utilize a tri-gram matrix-based LLM representation to dynamically approximate the output distribution of the LLM, allowing the model to adjust to changing token probabilities during the decoding process. Additionally, we implement a draft construction mechanism that effectively balances exploration and exploitation, ensuring that the drafts generated are both diverse and close to the true output distribution of the LLM. The importance of this design lies in its ability to optimize the draft distribution adaptively, leading to faster and more accurate decoding. Through extensive experiments on various benchmark datasets and LLM architectures, we demonstrate that ADED significantly accelerates the decoding process while maintaining high accuracy, making it suitable for deployment in a wide range of practical applications.

A critical component of a successful language generation pipeline is the decoding algorithm. However, the general principles that should guide the choice of decoding algorithm remain unclear. Previous works only compare decoding algorithms in narrow scenarios and their findings do not generalize across tasks. To better structure the discussion, we introduce a taxonomy that groups decoding strategies based on their implicit assumptions about how well the model's likelihood is aligned with the task-specific notion of utility. We argue that this taxonomy allows a broader view of the decoding problem and can lead to generalizable statements because it is grounded on the interplay between the decoding algorithms and the likelihood-utility misalignment. Specifically, by analyzing the correlation between the likelihood and the utility of predictions across a diverse set of tasks, we provide the first empirical evidence supporting the proposed taxonomy, and a set of principles to structure reasoning when choosing a decoding algorithm. Crucially, our analysis is the first one to relate likelihood-based decoding strategies with strategies that rely on external information such as value-guided methods and prompting, and covers the most diverse set of tasks up-to-date.

Numerical reasoning over natural language has been a long-standing goal for the research community. However, cutting-edge language models have proven difficult to reliably generalize to a broad range of numbers, although they have shown proficiency in reasoning over common and simple numbers. In this paper, we propose a novel method to elicit and exploit the numerical reasoning knowledge hidden in pre-trained language models using simple anchor numbers. Concretely, we first leverage simple numbers as anchors to probe the implicitly inferred arithmetic expressions from language models, and then explicitly apply the expressions on complex numbers to get corresponding answers. To inversely elicit arithmetic expressions, we transform and formulate the task as an analytically solvable linear system. Experimental results on several numerical reasoning benchmarks demonstrate that our approach significantly improves numerical reasoning capabilities of existing LMs. More importantly, our approach is training-free and simply works in the inference phase, making it highly portable and achieving consistent performance benefits across a variety of language models (GPT-3, T5, BART, etc) in all zero-shot, few-shot, and fine-tuning scenarios.

This paper introduces a novel training methodology that enables a small Transformer model to generalize the addition of two-digit numbers to numbers with unseen lengths of digits. The proposed approach employs an autoregressive generation technique, processing from right to left, which mimics a common manual method for adding large numbers. To the best of my knowledge, this methodology has not been previously explored in the literature. All results are reproducible, and the corresponding R code is available at: https://github.com/AGPatriota/ALGA-R/.

Length generalization, the ability to generalize from small training context sizes to larger ones, is a critical challenge in the development of Transformer-based language models. Positional encoding (PE) has been identified as a major factor influencing length generalization, but the exact impact of different PE schemes on extrapolation in downstream tasks remains unclear. In this paper, we conduct a systematic empirical study comparing the length generalization performance of decoder-only Transformers with five different position encoding approaches including Absolute Position Embedding (APE), T5's Relative PE, ALiBi, and Rotary, in addition to Transformers without positional encoding (NoPE). Our evaluation encompasses a battery of reasoning and mathematical tasks. Our findings reveal that the most commonly used positional encoding methods, such as ALiBi, Rotary, and APE, are not well suited for length generalization in downstream tasks. More importantly, NoPE outperforms other explicit positional encoding methods while requiring no additional computation. We theoretically demonstrate that NoPE can represent both absolute and relative PEs, but when trained with SGD, it mostly resembles T5's relative PE attention patterns. Finally, we find that scratchpad is not always helpful to solve length generalization and its format highly impacts the model's performance. Overall, our work suggests that explicit position embeddings are not essential for decoder-only Transformers to generalize well to longer sequences.

This work aims to predict channels in wireless communication systems based on noisy observations, utilizing sequence-to-sequence models with attention (Seq2Seq-attn) and transformer models. Both models are adapted from natural language processing to tackle the complex challenge of channel prediction. Additionally, a new technique called reverse positional encoding is introduced in the transformer model to improve the robustness of the model against varying sequence lengths. Similarly, the encoder outputs of the Seq2Seq-attn model are reversed before applying attention. Simulation results demonstrate that the proposed ordering techniques allow the models to better capture the relationships between the channel snapshots within the sequence, irrespective of the sequence length, as opposed to existing methods.

This work introduces a general code generation framework that incorporates infilling operations into auto-regressive decoding. Our approach capitalizes on the observation that recent code language models with infilling capabilities can perform self-infilling: whereas infilling operations aim to fill in the middle based on a predefined prefix and suffix, self-infilling sequentially generates both such surrounding context and the infilled content. We utilize this feature to develop an infilling-augmented decoding process that facilitates non-monotonic generation. This approach allows for postponing the generation of uncertain code snippets until a definitive suffix is established, leading to improved control over the generation sequence. In addition, it facilitates a looping mechanism, which can iteratively update and synchronize each piece of generation in a cyclic manner. Extensive experiments are conducted to demonstrate that our proposed decoding process is effective in enhancing regularity and quality across several code generation benchmarks.

Standard Neural Networks can learn mathematical operations, but they do not extrapolate. Extrapolation means that the model can apply to larger numbers, well beyond those observed during training. Recent architectures tackle arithmetic operations and can extrapolate; however, the equally important problem of quantitative reasoning remains unaddressed. In this work, we propose a novel architectural element, the Neural Status Register (NSR), for quantitative reasoning over numbers. Our NSR relaxes the discrete bit logic of physical status registers to continuous numbers and allows end-to-end learning with gradient descent. Experiments show that the NSR achieves solutions that extrapolate to numbers many orders of magnitude larger than those in the training set. We successfully train the NSR on number comparisons, piecewise discontinuous functions, counting in sequences, recurrently finding minimums, finding shortest paths in graphs, and comparing digits in images.

Code search is crucial for code reuse, enabling developers to efficiently locate relevant snippets. Current methods rely on encoder-based models, which suffer from limitations such as poor generalization and restricted input lengths. Decoder-only large language models (LLMs), with their extensive pre-training, larger size, and longer input capabilities, offer potential solutions to these issues, yet their effectiveness in code search remains underexplored. To fill this gap, our study presents the first systematic exploration of decoder-only LLMs for code search. We evaluate nine state-of-the-art decoder-only models using two fine-tuning methods, two datasets (CSN and CoSQA^+), and three model sizes. Our findings reveal that fine-tuned CodeGemma significantly outperforms encoder-only models like UniXcoder, achieving a 5.57% improvement in MRR on CSN and a 49.6% increase in MAP on CoSQA^+ compared to zero-shot UniXcoder. These results highlight the superior performance and adaptability of decoder-only models. Additionally, we provide valuable insights into optimizing these models for code search, covering aspects such as model selection, fine-tuning methods, training data, and model size, and discussing their strengths and limitations.

We examine how transformers cope with two challenges: learning basic integer arithmetic, and generalizing to longer sequences than seen during training. We find that relative position embeddings enable length generalization for simple tasks, such as addition: models trained on 5-digit numbers can perform 15-digit sums. However, this method fails for multiplication, and we propose train set priming: adding a few (10 to 50) long sequences to the training set. We show that priming allows models trained on 5-digit times 3-digit multiplications to generalize to 35times 3 examples. We also show that models can be primed for different generalization lengths, and that the priming sample size scales as the logarithm of the training set size. Finally, we discuss potential applications of priming beyond arithmetic.

Large Language Models (LLMs) have demonstrated impressive capabilities in natural language processing tasks, such as text generation and semantic understanding. However, their performance on numerical reasoning tasks, such as basic arithmetic, numerical retrieval, and magnitude comparison, remains surprisingly poor. This gap arises from their reliance on surface-level statistical patterns rather than understanding numbers as continuous magnitudes. Existing benchmarks primarily focus on either linguistic competence or structured mathematical problem-solving, neglecting fundamental numerical reasoning required in real-world scenarios. To bridge this gap, we propose NumericBench, a comprehensive benchmark to evaluate six fundamental numerical capabilities: number recognition, arithmetic operations, contextual retrieval, comparison, summary, and logical reasoning. NumericBench includes datasets ranging from synthetic number lists to the crawled real-world data, addressing challenges like long contexts, noise, and multi-step reasoning. Extensive experiments on state-of-the-art LLMs, including GPT-4 and DeepSeek, reveal persistent weaknesses in numerical reasoning, highlighting the urgent need to improve numerically-aware language modeling. The benchmark is released in: https://github.com/TreeAI-Lab/NumericBench.

Advances in hardware and language model architecture have spurred a revolution in natural language generation. However, autoregressive models compute probability distributions over next-token choices, and sampling from these distributions, known as decoding, has received significantly less attention than other design choices. Existing decoding strategies are largely based on heuristics, resulting in methods that are hard to apply or improve in a principled manner. We develop the theory of decoding strategies for language models by expressing popular decoding algorithms as equilibrium states in the language of ergodic theory and stating the functions they optimize. Using this, we analyze the effect of the local normalization step of top-k, nucleus, and temperature sampling, used to make probabilities sum to one. We argue that local normalization distortion is a fundamental defect of decoding strategies and quantify the size of this distortion and its effect on mathematical proxies for the quality and diversity of generated text. Contrary to the prevailing explanation, we argue that the major cause of the under-performance of top-k sampling relative to nucleus sampling is local normalization distortion. This yields conclusions for the future design of decoding algorithms and the detection of machine-generated text.

Large language models (LLMs) have achieved impressive performance across various domains. However, the substantial hardware resources required for their training present a significant barrier to efficiency and scalability. To mitigate this challenge, low-precision training techniques have been widely adopted, leading to notable advancements in training efficiency. Despite these gains, low-precision training involves several componentsx2013such as weights, activations, and gradientsx2013each of which can be represented in different numerical formats. The resulting diversity has created a fragmented landscape in low-precision training research, making it difficult for researchers to gain a unified overview of the field. This survey provides a comprehensive review of existing low-precision training methods. To systematically organize these approaches, we categorize them into three primary groups based on their underlying numerical formats, which is a key factor influencing hardware compatibility, computational efficiency, and ease of reference for readers. The categories are: (1) fixed-point and integer-based methods, (2) floating-point-based methods, and (3) customized format-based methods. Additionally, we discuss quantization-aware training approaches, which share key similarities with low-precision training during forward propagation. Finally, we highlight several promising research directions to advance this field. A collection of papers discussed in this survey is provided in https://github.com/Hao840/Awesome-Low-Precision-Training.

Recently, most handwritten mathematical expression recognition (HMER) methods adopt the encoder-decoder networks, which directly predict the markup sequences from formula images with the attention mechanism. However, such methods may fail to accurately read formulas with complicated structure or generate long markup sequences, as the attention results are often inaccurate due to the large variance of writing styles or spatial layouts. To alleviate this problem, we propose an unconventional network for HMER named Counting-Aware Network (CAN), which jointly optimizes two tasks: HMER and symbol counting. Specifically, we design a weakly-supervised counting module that can predict the number of each symbol class without the symbol-level position annotations, and then plug it into a typical attention-based encoder-decoder model for HMER. Experiments on the benchmark datasets for HMER validate that both joint optimization and counting results are beneficial for correcting the prediction errors of encoder-decoder models, and CAN consistently outperforms the state-of-the-art methods. In particular, compared with an encoder-decoder model for HMER, the extra time cost caused by the proposed counting module is marginal. The source code is available at https://github.com/LBH1024/CAN.

Large Language Models (LLMs) do not differentially represent numbers, which are pervasive in text. In contrast, neuroscience research has identified distinct neural representations for numbers and words. In this work, we investigate how well popular LLMs capture the magnitudes of numbers (e.g., that 4 < 5) from a behavioral lens. Prior research on the representational capabilities of LLMs evaluates whether they show human-level performance, for instance, high overall accuracy on standard benchmarks. Here, we ask a different question, one inspired by cognitive science: How closely do the number representations of LLMscorrespond to those of human language users, who typically demonstrate the distance, size, and ratio effects? We depend on a linking hypothesis to map the similarities among the model embeddings of number words and digits to human response times. The results reveal surprisingly human-like representations across language models of different architectures, despite the absence of the neural circuitry that directly supports these representations in the human brain. This research shows the utility of understanding LLMs using behavioral benchmarks and points the way to future work on the number representations of LLMs and their cognitive plausibility.

Previous studies have typically assumed that large language models are unable to accurately perform arithmetic operations, particularly multiplication of >8 digits, and operations involving decimals and fractions, without the use of calculator tools. This paper aims to challenge this misconception. With sufficient training data, a 2 billion-parameter language model can accurately perform multi-digit arithmetic operations with almost 100% accuracy without data leakage, significantly surpassing GPT-4 (whose multi-digit multiplication accuracy is only 4.3%). We also demonstrate that our MathGLM, fine-tuned from GLM-10B on a dataset with additional multi-step arithmetic operations and math problems described in text, achieves similar performance to GPT-4 on a 5,000-samples Chinese math problem test set.

Hierarchical classification offers an approach to incorporate the concept of mistake severity by leveraging a structured, labeled hierarchy. However, decoding in such settings frequently relies on heuristic decision rules, which may not align with task-specific evaluation metrics. In this work, we propose a framework for the optimal decoding of an output probability distribution with respect to a target metric. We derive optimal decision rules for increasingly complex prediction settings, providing universal algorithms when candidates are limited to the set of nodes. In the most general case of predicting a subset of nodes, we focus on rules dedicated to the hierarchical hF_{beta} scores, tailored to hierarchical settings. To demonstrate the practical utility of our approach, we conduct extensive empirical evaluations, showcasing the superiority of our proposed optimal strategies, particularly in underdetermined scenarios. These results highlight the potential of our methods to enhance the performance and reliability of hierarchical classifiers in real-world applications. The code is available at https://github.com/RomanPlaud/hierarchical_decision_rules

Understanding the inner workings of machine learning models like Transformers is vital for their safe and ethical use. This paper provides a comprehensive analysis of a one-layer Transformer model trained to perform n-digit integer addition. Our findings suggest that the model dissects the task into parallel streams dedicated to individual digits, employing varied algorithms tailored to different positions within the digits. Furthermore, we identify a rare scenario characterized by high loss, which we explain. By thoroughly elucidating the model's algorithm, we provide new insights into its functioning. These findings are validated through rigorous testing and mathematical modeling, thereby contributing to the broader fields of model understanding and interpretability. Our approach opens the door for analyzing more complex tasks and multi-layer Transformer models.

We present MIPS, a novel method for program synthesis based on automated mechanistic interpretability of neural networks trained to perform the desired task, auto-distilling the learned algorithm into Python code. We test MIPS on a benchmark of 62 algorithmic tasks that can be learned by an RNN and find it highly complementary to GPT-4: MIPS solves 32 of them, including 13 that are not solved by GPT-4 (which also solves 30). MIPS uses an integer autoencoder to convert the RNN into a finite state machine, then applies Boolean or integer symbolic regression to capture the learned algorithm. As opposed to large language models, this program synthesis technique makes no use of (and is therefore not limited by) human training data such as algorithms and code from GitHub. We discuss opportunities and challenges for scaling up this approach to make machine-learned models more interpretable and trustworthy.

Tokenization, the division of input text into input tokens, is an often overlooked aspect of the large language model (LLM) pipeline and could be the source of useful or harmful inductive biases. Historically, LLMs have relied on byte pair encoding, without care to specific input domains. With the increased use of LLMs for reasoning, various number-specific tokenization schemes have been adopted, with popular models like LLaMa and PaLM opting for single-digit tokenization while GPT-3.5 and GPT-4 have separate tokens for each 1-, 2-, and 3-digit numbers. In this work, we study the effect this choice has on numerical reasoning through the use of arithmetic tasks. We consider left-to-right and right-to-left tokenization for GPT-3.5 and -4, finding that right-to-left tokenization (enforced by comma separating numbers at inference time) leads to largely improved performance. Furthermore, we find that model errors when using standard left-to-right tokenization follow stereotyped error patterns, suggesting that model computations are systematic rather than approximate. We show that the model is able to convert between tokenizations easily, thus allowing chain-of-thought-inspired approaches to recover performance on left-to-right tokenized inputs. We also find the gap between tokenization directions decreases when models are scaled, possibly indicating that larger models are better able to override this tokenization-dependent inductive bias. In summary, our work performs the first study of how number tokenization choices lead to differences in model performance on arithmetic tasks, accompanied by a thorough analysis of error patterns. We hope this work inspires practitioners to more carefully ablate number tokenization-related choices when working towards general models of numerical reasoning.

Efficient inference in large language models (LLMs) has become a critical focus as their scale and complexity grow. Traditional autoregressive decoding, while effective, suffers from computational inefficiencies due to its sequential token generation process. Speculative decoding addresses this bottleneck by introducing a two-stage framework: drafting and verification. A smaller, efficient model generates a preliminary draft, which is then refined by a larger, more sophisticated model. This paper provides a comprehensive survey of speculative decoding methods, categorizing them into draft-centric and model-centric approaches. We discuss key ideas associated with each method, highlighting their potential for scaling LLM inference. This survey aims to guide future research in optimizing speculative decoding and its integration into real-world LLM applications.

To advance the neural decoding of Portuguese, in this paper we present a fully open Transformer-based, instruction-tuned decoder model that sets a new state of the art in this respect. To develop this decoder, which we named Gerv\'asio PT*, a strong LLaMA~2 7B model was used as a starting point, and its further improvement through additional training was done over language resources that include new instruction data sets of Portuguese prepared for this purpose, which are also contributed in this paper. All versions of Gerv\'asio are open source and distributed for free under an open license, including for either research or commercial usage, and can be run on consumer-grade hardware, thus seeking to contribute to the advancement of research and innovation in language technology for Portuguese.

We show that autoregressive decoding of a transformer-based language model can realize universal computation, without external intervention or modification of the model's weights. Establishing this result requires understanding how a language model can process arbitrarily long inputs using a bounded context. For this purpose, we consider a generalization of autoregressive decoding where, given a long input, emitted tokens are appended to the end of the sequence as the context window advances. We first show that the resulting system corresponds to a classical model of computation, a Lag system, that has long been known to be computationally universal. By leveraging a new proof, we show that a universal Turing machine can be simulated by a Lag system with 2027 production rules. We then investigate whether an existing large language model can simulate the behaviour of such a universal Lag system. We give an affirmative answer by showing that a single system-prompt can be developed for gemini-1.5-pro-001 that drives the model, under deterministic (greedy) decoding, to correctly apply each of the 2027 production rules. We conclude that, by the Church-Turing thesis, prompted gemini-1.5-pro-001 with extended autoregressive (greedy) decoding is a general purpose computer.

Recent research in decoding methods for Natural Language Generation (NLG) tasks has shown that MAP decoding is not optimal, because model probabilities do not always align with human preferences. Stronger decoding methods, including Quality Estimation (QE) reranking and Minimum Bayes' Risk (MBR) decoding, have since been proposed to mitigate the model-perplexity-vs-quality mismatch. While these decoding methods achieve state-of-the-art performance, they are prohibitively expensive to compute. In this work, we propose MBR finetuning and QE finetuning which distill the quality gains from these decoding methods at training time, while using an efficient decoding algorithm at inference time. Using the canonical NLG task of Neural Machine Translation (NMT), we show that even with self-training, these finetuning methods significantly outperform the base model. Moreover, when using an external LLM as a teacher model, these finetuning methods outperform finetuning on human-generated references. These findings suggest new ways to leverage monolingual data to achieve improvements in model quality that are on par with, or even exceed, improvements from human-curated data, while maintaining maximum efficiency during decoding.

The large number of parameters of some prominent language models, such as BERT, makes their fine-tuning on downstream tasks computationally intensive and energy hungry. Previously researchers were focused on lower bit-width integer data types for the forward propagation of language models to save memory and computation. As for the backward propagation, however, only 16-bit floating-point data type has been used for the fine-tuning of BERT. In this work, we use integer arithmetic for both forward and back propagation in the fine-tuning of BERT. We study the effects of varying the integer bit-width on the model's metric performance. Our integer fine-tuning uses integer arithmetic to perform forward propagation and gradient computation of linear, layer-norm, and embedding layers of BERT. We fine-tune BERT using our integer training method on SQuAD v1.1 and SQuAD v2., and GLUE benchmark. We demonstrate that metric performance of fine-tuning 16-bit integer BERT matches both 16-bit and 32-bit floating-point baselines. Furthermore, using the faster and more memory efficient 8-bit integer data type, integer fine-tuning of BERT loses an average of 3.1 points compared to the FP32 baseline.

Decoding for many NLP tasks requires an effective heuristic algorithm for approximating exact search since the problem of searching the full output space is often intractable, or impractical in many settings. The default algorithm for this job is beam search -- a pruned version of breadth-first search. Quite surprisingly, beam search often returns better results than exact inference due to beneficial search bias for NLP tasks. In this work, we show that the standard implementation of beam search can be made up to 10x faster in practice. Our method assumes that the scoring function is monotonic in the sequence length, which allows us to safely prune hypotheses that cannot be in the final set of hypotheses early on. We devise effective monotonic approximations to popular nonmonontic scoring functions, including length normalization and mutual information decoding. Lastly, we propose a memory-reduced variant of Best-First Beam Search, which has a similar beneficial search bias in terms of downstream performance, but runs in a fraction of the time.

In this paper, we propose a novel neural network model called RNN Encoder-Decoder that consists of two recurrent neural networks (RNN). One RNN encodes a sequence of symbols into a fixed-length vector representation, and the other decodes the representation into another sequence of symbols. The encoder and decoder of the proposed model are jointly trained to maximize the conditional probability of a target sequence given a source sequence. The performance of a statistical machine translation system is empirically found to improve by using the conditional probabilities of phrase pairs computed by the RNN Encoder-Decoder as an additional feature in the existing log-linear model. Qualitatively, we show that the proposed model learns a semantically and syntactically meaningful representation of linguistic phrases.

Speculative Decoding is a widely used technique to speed up inference for Large Language Models (LLMs) without sacrificing quality. When performing inference, speculative decoding uses a smaller draft model to generate speculative tokens and then uses the target LLM to verify those draft tokens. The speedup provided by speculative decoding heavily depends on the choice of the draft model. In this work, we perform a detailed study comprising over 350 experiments with LLaMA-65B and OPT-66B using speculative decoding and delineate the factors that affect the performance gain provided by speculative decoding. Our experiments indicate that the performance of speculative decoding depends heavily on the latency of the draft model, and the draft model's capability in language modeling does not correlate strongly with its performance in speculative decoding. Based on these insights we explore a new design space for draft models and design hardware-efficient draft models for speculative decoding. Our newly designed draft model for LLaMA-65B can provide 60% higher throughput than existing draft models and can generalize further to the LLaMA-2 model family and supervised fine-tuned models.

To mitigate the high inference latency stemming from autoregressive decoding in Large Language Models (LLMs), Speculative Decoding has emerged as a novel decoding paradigm for LLM inference. In each decoding step, this method first efficiently drafts several future tokens and then verifies them in parallel. Unlike autoregressive decoding, Speculative Decoding facilitates the simultaneous decoding of multiple tokens per step, thereby accelerating inference. This paper presents a comprehensive overview and analysis of this promising decoding paradigm. We begin by providing a formal definition and formulation of Speculative Decoding. Then, we organize in-depth discussions on its key facets, including current leading techniques, the challenges faced, and potential future directions in this field. We aim for this work to serve as a catalyst for further research on Speculative Decoding, ultimately contributing to more efficient LLM inference.

Recent advances with large language models (LLM) illustrate their diverse capabilities. We propose a novel algorithm, staged speculative decoding, to accelerate LLM inference in small-batch, on-device scenarios. We address the low arithmetic intensity of small-batch inference by improving upon previous work in speculative decoding. First, we restructure the speculative batch as a tree, which reduces generation costs and increases the expected tokens per batch. Second, we add a second stage of speculative decoding. Taken together, we reduce single-batch decoding latency by 3.16x with a 762M parameter GPT-2-L model while perfectly preserving output quality.

Deep autoregressive sequence-to-sequence models have demonstrated impressive performance across a wide variety of tasks in recent years. While common architecture classes such as recurrent, convolutional, and self-attention networks make different trade-offs between the amount of computation needed per layer and the length of the critical path at training time, generation still remains an inherently sequential process. To overcome this limitation, we propose a novel blockwise parallel decoding scheme in which we make predictions for multiple time steps in parallel then back off to the longest prefix validated by a scoring model. This allows for substantial theoretical improvements in generation speed when applied to architectures that can process output sequences in parallel. We verify our approach empirically through a series of experiments using state-of-the-art self-attention models for machine translation and image super-resolution, achieving iteration reductions of up to 2x over a baseline greedy decoder with no loss in quality, or up to 7x in exchange for a slight decrease in performance. In terms of wall-clock time, our fastest models exhibit real-time speedups of up to 4x over standard greedy decoding.

FP8 is a natural progression for accelerating deep learning training inference beyond the 16-bit formats common in modern processors. In this paper we propose an 8-bit floating point (FP8) binary interchange format consisting of two encodings - E4M3 (4-bit exponent and 3-bit mantissa) and E5M2 (5-bit exponent and 2-bit mantissa). While E5M2 follows IEEE 754 conventions for representatio of special values, E4M3's dynamic range is extended by not representing infinities and having only one mantissa bit-pattern for NaNs. We demonstrate the efficacy of the FP8 format on a variety of image and language tasks, effectively matching the result quality achieved by 16-bit training sessions. Our study covers the main modern neural network architectures - CNNs, RNNs, and Transformer-based models, leaving all the hyperparameters unchanged from the 16-bit baseline training sessions. Our training experiments include large, up to 175B parameter, language models. We also examine FP8 post-training-quantization of language models trained using 16-bit formats that resisted fixed point int8 quantization.

Transformers' ability to generalize to longer sequences than they have been trained on, known as length extrapolation, degrades as sequence length increases. Most of Relative Positional Encoding (RPE) methods address this problem by either adding constant linear biases or learning general biases, lacking the ability to specialize for different sequences. In this work, inspired by ALiBi, we propose Context-aware Biases for Length Extrapolation (Cable), that learns token-specific biases for each head in decoder-based transformers. Cable learns adaptive, context-aware biases, overcoming the limitations of fixed patterns by adding dynamic biases specific to each token in the sequence. Results show that when tested on a sequence length of 1024, a GPT-3 Medium (334M parameters) with our positional encoding, trained on a sequence length of 512, achieves better perplexity (-0.65) than a similar network with sinusoidal positional encoding trained on a sequence length of 1024. This is achieved with 48% lower memory usage, and only 3.5% higher training time. Furthermore, our method notably improves the extrapolation ability of existing RPE methods on the Edu-FineWeb10B and WikiText-103 datasets. Code is available at: https://github.com/axiomlab/Cable

We introduce a frustratingly simple, super efficient and surprisingly effective decoding method, which we call Frustratingly Simple Decoding (FSD), for neural text generation. The idea behind FSD is straightforward: we build an anti-LM based on previously generated text and use this anti-LM to penalize future generation of what has been generated. The anti-LM can be implemented as simple as an n-gram language model or a vectorized variant. In this way, FSD introduces no extra model parameters and negligible computational overhead (FSD can be as fast as greedy search). Despite the simplicity, FSD is surprisingly effective; Experiments show that FSD can outperform the canonical methods to date (i.e., nucleus sampling) as well as several strong baselines that were proposed recently.

In language modeling based music generation, a generated waveform is represented by a sequence of hierarchical token stacks that can be decoded either in an auto-regressive manner or in parallel, depending on the codebook patterns. In particular, flattening the codebooks represents the highest quality decoding strategy, while being notoriously slow. To this end, we propose a novel stack-and-delay style of decoding strategy to improve upon the flat pattern decoding where generation speed is four times faster as opposed to vanilla flat decoding. This brings the inference time close to that of the delay decoding strategy, and allows for faster inference on GPU for small batch sizes. For the same inference efficiency budget as the delay pattern, we show that the proposed approach performs better in objective evaluations, almost closing the gap with the flat pattern in terms of quality. The results are corroborated by subjective evaluations which show that samples generated by the new model are slightly more often preferred to samples generated by the competing model given the same text prompts.

Quantization techniques can reduce the size of Deep Neural Networks and improve inference latency and throughput by taking advantage of high throughput integer instructions. In this paper we review the mathematical aspects of quantization parameters and evaluate their choices on a wide range of neural network models for different application domains, including vision, speech, and language. We focus on quantization techniques that are amenable to acceleration by processors with high-throughput integer math pipelines. We also present a workflow for 8-bit quantization that is able to maintain accuracy within 1% of the floating-point baseline on all networks studied, including models that are more difficult to quantize, such as MobileNets and BERT-large.

One of the most striking findings in modern research on large language models (LLMs) is that scaling up compute during training leads to better results. However, less attention has been given to the benefits of scaling compute during inference. This survey focuses on these inference-time approaches. We explore three areas under a unified mathematical formalism: token-level generation algorithms, meta-generation algorithms, and efficient generation. Token-level generation algorithms, often called decoding algorithms, operate by sampling a single token at a time or constructing a token-level search space and then selecting an output. These methods typically assume access to a language model's logits, next-token distributions, or probability scores. Meta-generation algorithms work on partial or full sequences, incorporating domain knowledge, enabling backtracking, and integrating external information. Efficient generation methods aim to reduce token costs and improve the speed of generation. Our survey unifies perspectives from three research communities: traditional natural language processing, modern LLMs, and machine learning systems.

This paper presents RevOrder, a novel technique aimed at improving arithmetic operations in large language models (LLMs) by reversing the output digits in addition, subtraction, and n-digit by 1-digit (nD by 1D) multiplication tasks. Our method significantly reduces the Count of Sequential Intermediate Digits (CSID) to O(1), a new metric we introduce to assess equation complexity. Through comprehensive testing, RevOrder not only achieves perfect accuracy in basic arithmetic operations but also substantially boosts LLM performance in division tasks, particularly with large numbers where traditional models struggle. Implementation of RevOrder is cost-effective for both training and inference phases. Moreover, applying RevOrder to fine-tune the LLaMA2-7B model on the GSM8K math task results in a considerable improvement, reducing equation calculation errors by 46% and increasing overall scores from 41.6 to 44.4.

Autoregressive decoding limits the efficiency of transformers for Machine Translation (MT). The community proposed specific network architectures and learning-based methods to solve this issue, which are expensive and require changes to the MT model, trading inference speed at the cost of the translation quality. In this paper, we propose to address the problem from the point of view of decoding algorithms, as a less explored but rather compelling direction. We propose to reframe the standard greedy autoregressive decoding of MT with a parallel formulation leveraging Jacobi and Gauss-Seidel fixed-point iteration methods for fast inference. This formulation allows to speed up existing models without training or modifications while retaining translation quality. We present three parallel decoding algorithms and test them on different languages and models showing how the parallelization introduces a speedup up to 38% w.r.t. the standard autoregressive decoding and nearly 2x when scaling the method on parallel resources. Finally, we introduce a decoding dependency graph visualizer (DDGviz) that let us see how the model has learned the conditional dependence between tokens and inspect the decoding procedure.

Speculative decoding has emerged as a powerful method to improve latency and throughput in hosting large language models. However, most existing implementations focus on generating a single sequence. Real-world generative AI applications often require multiple responses and how to perform speculative decoding in a batched setting while preserving its latency benefits poses non-trivial challenges. This paper describes a system of batched speculative decoding that sets a new state of the art in multi-sequence generation latency and that demonstrates superior GPU utilization as well as quality of generations within a time budget. For example, for a 7.8B-size model on a single A100 GPU and with a batch size of 8, each sequence is generated at an average speed of 5.8ms per token, the overall throughput being 1.1K tokens per second. These results represent state-of-the-art latency and a 2.15X speed-up over optimized regular decoding. Within a time budget that regular decoding does not finish, our system is able to generate sequences with HumanEval Pass@First of 43% and Pass@All of 61%, far exceeding what's feasible with single-sequence speculative decoding. Our peak GPU utilization during decoding reaches as high as 15.8%, more than 3X the highest of that of regular decoding and around 10X of single-sequence speculative decoding.

In the context of multi-step reasoning, language models (LMs) probabilities are often miscalibrated -- solutions with high probabilities are not always correct. Therefore, greedy decoding, which is the standard decoding method for reasoning tasks, often yields incorrect solutions. In addition, methods such as self-consistency and verifiers rely on sampling from the LM distribution and do not tackle the underlying issue. To address this, we introduce Guiding Multi-step ReAsoning with a CorrectnEss Discriminator (GRACE), a stepwise decoding approach that nudges the model towards producing correct reasoning steps. GRACE employs a discriminator model, which is trained to differentiate correct steps from invalid ones, to adjust decoding preferences based on the correctness of each reasoning step. Importantly, GRACE does not require fine-tuning or re-training the LMs. When compared with conventional decoding strategies over four popular math reasoning benchmarks, GRACE exhibits significant improvements in both final answer accuracy and step correctness, outperforming both greedy decoding and self-consistency.Our code can be found at \url{https://github.com/mukhal/grace.}

Long-form numerical reasoning in financial analysis aims to generate a reasoning program to calculate the correct answer for a given question. Previous work followed a retriever-generator framework, where the retriever selects key facts from a long-form document, and the generator generates a reasoning program based on retrieved facts. However, they treated all facts equally without considering the different contributions of facts with and without numbers. Meanwhile, the program consistency were ignored under supervised training, resulting in lower training accuracy and diversity. To solve these problems, we proposed APOLLO to improve the long-form numerical reasoning framework. For the retriever, we adopt a number-aware negative sampling strategy to enable the retriever to be more discriminative on key numerical facts. For the generator, we design consistency-based reinforcement learning and target program augmentation strategy based on the consistency of program execution results. Experimental results on the FinQA and ConvFinQA leaderboard verify the effectiveness of our proposed method, achieving the new state-of-the-art.

Despite the progress in machine translation quality estimation and evaluation in the last years, decoding in neural machine translation (NMT) is mostly oblivious to this and centers around finding the most probable translation according to the model (MAP decoding), approximated with beam search. In this paper, we bring together these two lines of research and propose quality-aware decoding for NMT, by leveraging recent breakthroughs in reference-free and reference-based MT evaluation through various inference methods like N-best reranking and minimum Bayes risk decoding. We perform an extensive comparison of various possible candidate generation and ranking methods across four datasets and two model classes and find that quality-aware decoding consistently outperforms MAP-based decoding according both to state-of-the-art automatic metrics (COMET and BLEURT) and to human assessments. Our code is available at https://github.com/deep-spin/qaware-decode.

Inference-time scaling has emerged as a powerful alternative to parameter scaling for improving language model performance on complex reasoning tasks. While existing methods have shown strong performance gains under fixed compute budgets, there has been little focus on optimally utilizing that budget during inference. In this work, we introduce A*-decoding, a search-based inference-time strategy that builds on the A* search algorithm to optimally utilize a fixed compute budget by prioritizing high-quality reasoning paths during generation. We frame language model decoding as a structured search in a state space of partial solutions, applying the A* transition model to identify promising continuations guided by an external process supervision signal. In our experiments, A*-decoding reaches the performance levels of strong inference scaling baselines like best-of-N and particle filtering while using up to 3x fewer tokens and 30% fewer PRM passes under equivalent compute budgets. On the MATH500 and AIME 2024 benchmarks, A*-decoding enables Llama-3.2-1B-Instruct to match the performance of the 70x larger Llama-3.1-70B-Instruct, and allows Qwen3-1.7B to reach o1-like reasoning accuracy. These results highlight the power of structured search in decoding, offering an alternative to brute-force sampling or scale-driven gains. Our work demonstrates how thoughtful inference-time strategies can enhance reasoning in SLMs, pointing toward future advances in more efficient and scalable language model deployment.

When quantizing neural networks for efficient inference, low-bit integers are the go-to format for efficiency. However, low-bit floating point numbers have an extra degree of freedom, assigning some bits to work on an exponential scale instead. This paper in-depth investigates this benefit of the floating point format for neural network inference. We detail the choices that can be made for the FP8 format, including the important choice of the number of bits for the mantissa and exponent, and show analytically in which settings these choices give better performance. Then we show how these findings translate to real networks, provide an efficient implementation for FP8 simulation, and a new algorithm that enables the learning of both the scale parameters and the number of exponent bits in the FP8 format. Our chief conclusion is that when doing post-training quantization for a wide range of networks, the FP8 format is better than INT8 in terms of accuracy, and the choice of the number of exponent bits is driven by the severity of outliers in the network. We also conduct experiments with quantization-aware training where the difference in formats disappears as the network is trained to reduce the effect of outliers.

Text generation with beam search has proven successful in a wide range of applications. The commonly-used implementation of beam decoding follows a first come, first served heuristic: it keeps a set of already completed sequences over time steps and stops when the size of this set reaches the beam size. We introduce a patience factor, a simple modification to this decoding algorithm, that generalizes the stopping criterion and provides flexibility to the depth of search. Extensive empirical results demonstrate that the patience factor improves decoding performance of strong pretrained models on news text summarization and machine translation over diverse language pairs, with a negligible inference slowdown. Our approach only modifies one line of code and can be thus readily incorporated in any implementation.

Contemporary machine learning models, such as language models, are powerful, but come with immense resource requirements both at training and inference time. It has been shown that decoder-only language models can be trained to a competitive state with ternary weights (1.58 bits per weight), facilitating efficient inference. Here, we start our exploration with non-transformer model architectures, investigating 1.58-bit training for multi-layer perceptrons and graph neural networks. Then, we explore 1.58-bit training in other transformer-based language models, namely encoder-only and encoder-decoder models. Our results show that in all of these settings, 1.58-bit training is on par with or sometimes even better than the standard 32/16-bit models.

Speculative decoding is an inference-acceleration method for large language models (LLMs) where a small language model generates a draft-token sequence which is further verified by the target LLM in parallel. Recent works have advanced this method by establishing a draft-token tree, achieving superior performance over a single-sequence speculative decoding. However, those works independently generate tokens at each level of the tree, not leveraging the tree's entire diversifiability. Besides, their empirical superiority has been shown for fixed length of sequences, implicitly granting more computational resource to LLM for the tree-based methods. None of the existing works has conducted empirical studies with fixed target computational budgets despite its importance to resource-bounded devices. We present Recursive Speculative Decoding (RSD), a novel tree-based method that samples draft tokens without replacement and maximizes the diversity of the tree. During RSD's drafting, the tree is built by either Gumbel-Top-k trick that draws tokens without replacement in parallel or Stochastic Beam Search that samples sequences without replacement while early-truncating unlikely draft sequences and reducing the computational cost of LLM. We empirically evaluate RSD with Llama 2 and OPT models, showing that RSD outperforms the baseline methods, consistently for fixed draft sequence length and in most cases for fixed computational budgets at LLM.

We introduce an algorithm where the individual bits representing the weights of a neural network are learned. This method allows training weights with integer values on arbitrary bit-depths and naturally uncovers sparse networks, without additional constraints or regularization techniques. We show better results than the standard training technique with fully connected networks and similar performance as compared to standard training for convolutional and residual networks. By training bits in a selective manner we found that the biggest contribution to achieving high accuracy is given by the first three most significant bits, while the rest provide an intrinsic regularization. As a consequence more than 90\% of a network can be used to store arbitrary codes without affecting its accuracy. These codes may be random noise, binary files or even the weights of previously trained networks.

Deployment of autoregressive large language models (LLMs) is costly, and as these models increase in size, the associated costs will become even more considerable. Consequently, different methods have been proposed to accelerate the token generation process and reduce costs. Speculative decoding (SD) is among the most promising approaches to speed up the LLM decoding process by verifying multiple tokens in parallel and using an auxiliary smaller draft model to generate the possible tokens. In SD, usually, one draft model is used to serve a specific target model; however, in practice, LLMs are diverse, and we might need to deal with many target models or more than one target model simultaneously. In this scenario, it is not clear which draft model should be used for which target model, and searching among different draft models or training customized draft models can further increase deployment costs. In this paper, we first introduce a novel multi-target scenario for the deployment of draft models for faster inference. Then, we present a novel, more efficient sorted speculative decoding mechanism that outperforms regular baselines in multi-target settings. We evaluated our method on Spec-Bench in different settings, including base models such as Vicuna 7B, 13B, and LLama Chat 70B. Our results suggest that our draft models perform better than baselines for multiple target models at the same time.

Existing neural generation approaches create multi-sentence text as a single sequence. In this paper we propose a structured convolutional decoder that is guided by the content structure of target summaries. We compare our model with existing sequential decoders on three data sets representing different domains. Automatic and human evaluation demonstrate that our summaries have better content coverage.

The auto-regressive decoding of Large Language Models (LLMs) results in significant overheads in their hardware performance. While recent research has investigated various speculative decoding techniques for multi-token generation, these efforts have primarily focused on improving processing speed such as throughput. Crucially, they often neglect other metrics essential for real-life deployments, such as memory consumption and training cost. To overcome these limitations, we propose a novel parallel prompt decoding that requires only 0.0002% trainable parameters, enabling efficient training on a single A100-40GB GPU in just 16 hours. Inspired by the human natural language generation process, PPD approximates outputs generated at future timesteps in parallel by using multiple prompt tokens. This approach partially recovers the missing conditional dependency information necessary for multi-token generation, resulting in up to a 28% higher acceptance rate for long-range predictions. Furthermore, we present a hardware-aware dynamic sparse tree technique that adaptively optimizes this decoding scheme to fully leverage the computational capacities on different GPUs. Through extensive experiments across LLMs ranging from MobileLlama to Vicuna-13B on a wide range of benchmarks, our approach demonstrates up to 2.49times speedup and maintains a minimal runtime memory overhead of just 0.0004%. More importantly, our parallel prompt decoding can serve as an orthogonal optimization for synergistic integration with existing speculative decoding, showing up to 1.22times further speed improvement. Our code is available at https://github.com/hmarkc/parallel-prompt-decoding.

We explore different ways to utilize position-based cross-attention in seq2seq networks to enable length generalization in algorithmic tasks. We show that a simple approach of interpolating the original and reversed encoded representations combined with relative attention allows near-perfect length generalization for both forward and reverse lookup tasks or copy tasks that had been generally hard to tackle. We also devise harder diagnostic tasks where the relative distance of the ideal attention position varies with timestep. In such settings, the simple interpolation trick with relative attention is not sufficient. We introduce novel variants of location attention building on top of Dubois et al. (2020) to address the new diagnostic tasks. We also show the benefits of our approaches for length generalization in SCAN (Lake & Baroni, 2018) and CFQ (Keysers et al., 2020). Our code is available on GitHub.

Large Language Models (LLMs) have revolutionized natural language processing by unifying tasks into text generation, yet their large parameter sizes and autoregressive nature limit inference speed. SAM-Decoding addresses this by introducing a novel retrieval-based speculative decoding method that uses a suffix automaton for efficient and accurate draft generation. Unlike n-gram matching used by the existing method, SAM-Decoding finds the longest suffix match in generating text and text corpuss, achieving an average time complexity of O(1) per generation step. SAM-Decoding constructs static and dynamic suffix automatons for the text corpus and input prompts, respectively, enabling fast and precise draft generation. Meanwhile, it is designed as an approach that can be combined with existing methods, allowing SAM-Decoding to adaptively select a draft generation strategy based on the matching length, thus increasing the inference speed of the LLM. When combined with Token Recycling, evaluations show SAM-Decoding outperforms existing model-free methods, achieving a speedup of 2.27times over autoregressive decoding on Spec-Bench. When combined with EAGLE2, it reaches a speedup of 2.49times, surpassing all current approaches. Our code is available at https://github.com/hyx1999/SAM-Decoding.

Many applications today provide users with multiple auto-complete drafts as they type, including GitHub's code completion, Gmail's smart compose, and Apple's messaging auto-suggestions. Under the hood, language models support this by running an autoregressive inference pass to provide a draft. Consequently, providing k drafts to the user requires running an expensive language model k times. To alleviate the computation cost of running k inference passes, we propose Superposed Decoding, a new decoding algorithm that generates k drafts at the computation cost of one autoregressive inference pass. We achieve this by feeding a superposition of the most recent token embeddings from the k drafts as input to the next decoding step of the language model. At every inference step we combine the k drafts with the top-k tokens to get k^2 new drafts and cache the k most likely options, using an n-gram interpolation with minimal compute overhead to filter out incoherent generations. Our experiments show that k drafts from Superposed Decoding are at least as coherent and factual as Nucleus Sampling and Greedy Decoding respectively, while being at least 2.44times faster for kge3. In a compute-normalized setting, user evaluations demonstrably favor text generated by Superposed Decoding over Nucleus Sampling. Code and more examples open-sourced at https://github.com/RAIVNLab/SuperposedDecoding.

Decoding methods for large language models often trade-off between diversity of outputs and parallelism of computation. Methods such as beam search and Gumbel top-k sampling can guarantee a different output for each element of the beam, but are not easy to parallelize. Alternatively, methods such as temperature sampling and its modifications (top-k sampling, nucleus sampling, typical decoding, and others), are embarrassingly parallel, but have no guarantees about duplicate samples. We present a framework for sampling according to an arithmetic code book implicitly defined by a large language model, compatible with common sampling variations, with provable beam diversity under certain conditions, as well as being embarrassingly parallel and providing unbiased and consistent expectations from the original model. We demonstrate the effectiveness of our approach on WMT machine translation, more than halving the standard deviation when estimating expected BLEU score reward, and closing the BLEU score gap between independent sampling and beam search by up to 63%.

We propose Speculative Decoding (SpecDec), for the first time ever, to formally study exploiting the idea of speculative execution to accelerate autoregressive (AR) decoding. Speculative Decoding has two innovations: Spec-Drafter -- an independent model specially optimized for efficient and accurate drafting -- and Spec-Verification -- a reliable method for verifying the drafted tokens efficiently in the decoding paradigm. Experimental results on various seq2seq tasks including machine translation and abstractive summarization show our approach can achieve around 5times speedup for the popular Transformer architectures with comparable generation quality to beam search decoding, refreshing the impression that the draft-then-verify paradigm introduces only 1.4timessim2times speedup. In addition to the remarkable speedup, we also demonstrate 3 additional advantages of SpecDec, revealing its practical value for accelerating generative models in real-world applications. Our models and codes are available at https://github.com/hemingkx/SpecDec.

Quite surprisingly, exact maximum a posteriori (MAP) decoding of neural language generators frequently leads to low-quality results. Rather, most state-of-the-art results on language generation tasks are attained using beam search despite its overwhelmingly high search error rate. This implies that the MAP objective alone does not express the properties we desire in text, which merits the question: if beam search is the answer, what was the question? We frame beam search as the exact solution to a different decoding objective in order to gain insights into why high probability under a model alone may not indicate adequacy. We find that beam search enforces uniform information density in text, a property motivated by cognitive science. We suggest a set of decoding objectives that explicitly enforce this property and find that exact decoding with these objectives alleviates the problems encountered when decoding poorly calibrated language generation models. Additionally, we analyze the text produced using various decoding strategies and see that, in our neural machine translation experiments, the extent to which this property is adhered to strongly correlates with BLEU.

Ever since neural models were adopted in data-to-text language generation, they have invariably been reliant on extrinsic components to improve their semantic accuracy, because the models normally do not exhibit the ability to generate text that reliably mentions all of the information provided in the input. In this paper, we propose a novel decoding method that extracts interpretable information from encoder-decoder models' cross-attention, and uses it to infer which attributes are mentioned in the generated text, which is subsequently used to rescore beam hypotheses. Using this decoding method with T5 and BART, we show on three datasets its ability to dramatically reduce semantic errors in the generated outputs, while maintaining their state-of-the-art quality.

The dominance of large decoder-only language models has overshadowed encoder-decoder architectures, despite their fundamental efficiency advantages in sequence processing. For small language models (SLMs) - those with 1 billion parameters or fewer - our systematic analysis across GPU, CPU, and NPU platforms reveals that encoder-decoder architectures achieve 47% lower first-token latency and 4.7x higher throughput compared to decoder-only models on edge devices. These gains may be attributed to encoder-decoder's one-time input processing and efficient separation of understanding and generation phases. We introduce a novel knowledge distillation framework that enables encoder-decoder models to leverage capabilities from large scalable decoder-only teachers while preserving their architectural advantages, achieving up to 6 average performance points improvement across diverse tasks, with significant gains in asymmetric sequence tasks where input and output distributions can benefit from different processing approaches. When combined with modern advances like Rotary Positional Embeddings (RoPE) and Vision encoders, our systematic investigation demonstrates that encoder-decoder architectures provide a more practical path toward deploying capable language models in resource-constrained environments. Our findings challenge the prevailing trend toward decoder-only scaling, showing that architectural choices become increasingly crucial as parameter budgets decrease, particularly for on-device and edge deployments where computational efficiency is paramount.

The rapid growth in the parameters of large language models (LLMs) has made inference latency a fundamental bottleneck, limiting broader application of LLMs. Speculative decoding represents a lossless approach to accelerate inference through a guess-and-verify paradigm, leveraging the parallel capabilities of modern hardware. Some speculative decoding methods rely on additional structures to guess draft tokens, such as small models or parameter-efficient architectures, which need extra training before use. Alternatively, retrieval-based train-free techniques build libraries from pre-existing corpora or by n-gram generation. However, they face challenges like large storage requirements, time-consuming retrieval, and limited adaptability. Observing that candidate tokens generated during the decoding process are likely to reoccur in future sequences, we propose Token Recycling. This approach stores candidate tokens in an adjacency matrix and employs a breadth-first search (BFS)-like algorithm on the matrix to construct a draft tree. The tree is then validated through tree attention. New candidate tokens from the decoding process are then used to update the matrix. Token Recycling requires \textless2MB of additional storage and achieves approximately 2x speedup across all sizes of LLMs. It significantly outperforms existing train-free methods by 30\% and even a training method by 25\%. It can be directly applied to any existing LLMs and tasks without the need for adaptation.

Visual autoregressive models typically adhere to a raster-order ``next-token prediction" paradigm, which overlooks the spatial and temporal locality inherent in visual content. Specifically, visual tokens exhibit significantly stronger correlations with their spatially or temporally adjacent tokens compared to those that are distant. In this paper, we propose Neighboring Autoregressive Modeling (NAR), a novel paradigm that formulates autoregressive visual generation as a progressive outpainting procedure, following a near-to-far ``next-neighbor prediction" mechanism. Starting from an initial token, the remaining tokens are decoded in ascending order of their Manhattan distance from the initial token in the spatial-temporal space, progressively expanding the boundary of the decoded region. To enable parallel prediction of multiple adjacent tokens in the spatial-temporal space, we introduce a set of dimension-oriented decoding heads, each predicting the next token along a mutually orthogonal dimension. During inference, all tokens adjacent to the decoded tokens are processed in parallel, substantially reducing the model forward steps for generation. Experiments on ImageNet256times 256 and UCF101 demonstrate that NAR achieves 2.4times and 8.6times higher throughput respectively, while obtaining superior FID/FVD scores for both image and video generation tasks compared to the PAR-4X approach. When evaluating on text-to-image generation benchmark GenEval, NAR with 0.8B parameters outperforms Chameleon-7B while using merely 0.4 of the training data. Code is available at https://github.com/ThisisBillhe/NAR.

Despite the ubiquity of mobile and wearable text messaging applications, the problem of keyboard text decoding is not tackled sufficiently in the light of the enormous success of the deep learning Recurrent Neural Network (RNN) and Convolutional Neural Networks (CNN) for natural language understanding. In particular, considering that the keyboard decoders should operate on devices with memory and processor resource constraints, makes it challenging to deploy industrial scale deep neural network (DNN) models. This paper proposes a sequence-to-sequence neural attention network system for automatic text correction and completion. Given an erroneous sequence, our model encodes character level hidden representations and then decodes the revised sequence thus enabling auto-correction and completion. We achieve this by a combination of character level CNN and gated recurrent unit (GRU) encoder along with and a word level gated recurrent unit (GRU) attention decoder. Unlike traditional language models that learn from billions of words, our corpus size is only 12 million words; an order of magnitude smaller. The memory footprint of our learnt model for inference and prediction is also an order of magnitude smaller than the conventional language model based text decoders. We report baseline performance for neural keyboard decoders in such limited domain. Our models achieve a word level accuracy of 90% and a character error rate CER of 2.4% over the Twitter typo dataset. We present a novel dataset of noisy to corrected mappings by inducing the noise distribution from the Twitter data over the OpenSubtitles 2009 dataset; on which our model predicts with a word level accuracy of 98% and sequence accuracy of 68.9%. In our user study, our model achieved an average CER of 2.6% with the state-of-the-art non-neural touch-screen keyboard decoder at CER of 1.6%.

Drafting-then-verifying decoding methods such as speculative decoding are widely adopted training-free methods to accelerate the inference of large language models (LLMs). Instead of employing an autoregressive process to decode tokens sequentially, speculative decoding initially creates drafts with an efficient small model. Then LLMs are required to conduct verification and correction in a non-autoregressive fashion to minimize time overhead. Generating longer drafts can lead to even more significant speedups once verified, but also incurs substantial trial and error costs if it fails. Suffering from the high verification failure probability, existing decoding methods cannot draft too much content for verification at one time, achieving sub-optimal inference acceleration. In this paper, we introduce Ouroboros, which constructs a phrase candidate pool from the verification process of LLMs to provide candidates for draft generation of the small model. Thereby, Ouroboros can further improve the efficiency and effectiveness of the initial drafts. The experimental results on typical text generation tasks show that Ouroboros achieves speedups of up to 1.9x and 2.8x compared to lookahead decoding and speculative decoding, respectively. The source code of Ouroboros is available at https://github.com/thunlp/Ouroboros.

Transformer-based large language models have achieved remarkable performance across various natural language processing tasks. However, they often struggle with seemingly easy tasks like arithmetic despite their vast capabilities. This stark disparity raise human's concerns about their safe and ethical use, hinder their widespread adoption.In this paper, we focus on a typical arithmetic task, integer multiplication, to explore and explain the imperfection of transformers in this domain. We provide comprehensive analysis of a vanilla transformer trained to perform n-digit integer multiplication. Our observations indicate that the model decomposes multiplication task into multiple parallel subtasks, sequentially optimizing each subtask for each digit to complete the final multiplication. Based on observation and analysis, we infer the reasons of transformers deficiencies in multiplication tasks lies in their difficulty in calculating successive carryovers and caching intermediate results, and confirmed this inference through experiments. Guided by these findings, we propose improvements to enhance transformers performance on multiplication tasks. These enhancements are validated through rigorous testing and mathematical modeling, not only enhance transformer's interpretability, but also improve its performance, e.g., we achieve over 99.9% accuracy on 5-digit integer multiplication with a tiny transformer, outperform LLMs GPT-4. Our method contributes to the broader fields of model understanding and interpretability, paving the way for analyzing more complex tasks and Transformer models. This work underscores the importance of explainable AI, helping to build trust in large language models and promoting their adoption in critical applications.

Large pre-trained language models (LMs) are known to encode substantial amounts of linguistic information. However, high-level reasoning skills, such as numerical reasoning, are difficult to learn from a language-modeling objective only. Consequently, existing models for numerical reasoning have used specialized architectures with limited flexibility. In this work, we show that numerical reasoning is amenable to automatic data generation, and thus one can inject this skill into pre-trained LMs, by generating large amounts of data, and training in a multi-task setup. We show that pre-training our model, GenBERT, on this data, dramatically improves performance on DROP (49.3 rightarrow 72.3 F1), reaching performance that matches state-of-the-art models of comparable size, while using a simple and general-purpose encoder-decoder architecture. Moreover, GenBERT generalizes well to math word problem datasets, while maintaining high performance on standard RC tasks. Our approach provides a general recipe for injecting skills into large pre-trained LMs, whenever the skill is amenable to automatic data augmentation.

Autoregressive language models demonstrate excellent performance in various scenarios. However, the inference efficiency is limited by its one-step-one-word generation mode, which has become a pressing problem recently as the models become increasingly larger. Speculative decoding employs a "draft and then verify" mechanism to allow multiple tokens to be generated in one step, realizing lossless acceleration. Existing methods mainly adopt fixed heuristic draft structures, which fail to adapt to different situations to maximize the acceptance length during verification. To alleviate this dilemma, we proposed OPT-Tree, an algorithm to construct adaptive and scalable draft trees. It searches the optimal tree structure that maximizes the mathematical expectation of the acceptance length in each decoding step. Experimental results reveal that OPT-Tree outperforms the existing draft structures and achieves a speed-up ratio of up to 3.2 compared with autoregressive decoding. If the draft model is powerful enough and the node budget is sufficient, it can generate more than ten tokens in a single step. Our code is available at https://github.com/Jikai0Wang/OPT-Tree.

Neural machine translation is a relatively new approach to statistical machine translation based purely on neural networks. The neural machine translation models often consist of an encoder and a decoder. The encoder extracts a fixed-length representation from a variable-length input sentence, and the decoder generates a correct translation from this representation. In this paper, we focus on analyzing the properties of the neural machine translation using two models; RNN Encoder--Decoder and a newly proposed gated recursive convolutional neural network. We show that the neural machine translation performs relatively well on short sentences without unknown words, but its performance degrades rapidly as the length of the sentence and the number of unknown words increase. Furthermore, we find that the proposed gated recursive convolutional network learns a grammatical structure of a sentence automatically.

Decoder-only Transformers often struggle with complex reasoning tasks, particularly arithmetic reasoning requiring multiple sequential operations. In this work, we identify representation collapse in the model's intermediate layers as a key factor limiting their reasoning capabilities. To address this, we propose Sequential Variance-Covariance Regularization (Seq-VCR), which enhances the entropy of intermediate representations and prevents collapse. Combined with dummy pause tokens as substitutes for chain-of-thought (CoT) tokens, our method significantly improves performance in arithmetic reasoning problems. In the challenging 5 times 5 integer multiplication task, our approach achieves 99.5% exact match accuracy, outperforming models of the same size (which yield 0% accuracy) and GPT-4 with five-shot CoT prompting (44%). We also demonstrate superior results on arithmetic expression and longest increasing subsequence (LIS) datasets. Our findings highlight the importance of preventing intermediate layer representation collapse to enhance the reasoning capabilities of Transformers and show that Seq-VCR offers an effective solution without requiring explicit CoT supervision.

Speculative decoding is a relatively new decoding framework that leverages small and efficient draft models to reduce the latency of LLMs. In this study, we introduce GliDe and CaPE, two low-hassle modifications to vanilla speculative decoding to further improve the decoding speed of a frozen LLM. Specifically, GliDe is a modified draft model architecture that reuses the cached keys and values from the target LLM, while CaPE is a proposal expansion method that uses the draft model's confidence scores to help select additional candidate tokens for verification. Extensive experiments on different benchmarks demonstrate that our proposed GliDe draft model significantly reduces the expected decoding latency. Additional evaluation using walltime reveals that GliDe can accelerate Vicuna models up to 2.17x and further extend the improvement to 2.61x with CaPE. We will release our code, data, and the trained draft models.

Speculative decoding (SD), where an extra draft model is employed to provide multiple draft tokens first and then the original target model verifies these tokens in parallel, has shown great power for LLM inference acceleration. However, existing SD methods suffer from the mutual waiting problem, i.e., the target model gets stuck when the draft model is guessing tokens, and vice versa. This problem is directly incurred by the asynchronous execution of the draft model and the target model, and is exacerbated due to the fixed draft length in speculative decoding. To address these challenges, we propose a conceptually simple, flexible, and general framework to boost speculative decoding, namely Parallel spEculative decoding with Adaptive dRaft Length (PEARL). Specifically, PEARL proposes pre-verify to verify the first draft token in advance during the drafting phase, and post-verify to generate more draft tokens during the verification phase. PEARL parallels the drafting phase and the verification phase via applying the two strategies, and achieves adaptive draft length for different scenarios, which effectively alleviates the mutual waiting problem. Moreover, we theoretically demonstrate that the mean accepted tokens of PEARL is more than existing draft-then-verify works. Experiments on various text generation benchmarks demonstrate the effectiveness of our \name, leading to a superior speedup performance up to 3.79times and 1.52times, compared to auto-regressive decoding and vanilla speculative decoding, respectively.

Existing speculative decoding methods typically require additional model structure and training processes to assist the model for draft token generation. This makes the migration of acceleration methods to the new model more costly and more demanding on device memory. To address this problem, we propose the Make Some Noise (MSN) training framework as a replacement for the supervised fine-tuning stage of the large language model. The training method simply introduces some noise at the input for the model to learn the denoising task. It significantly enhances the parallel decoding capability of the model without affecting the original task capability. In addition, we propose a tree-based retrieval-augmented Jacobi (TR-Jacobi) decoding strategy to further improve the inference speed of MSN models. Experiments in both the general and code domains have shown that MSN can improve inference speed by 2.3-2.7x times without compromising model performance. The MSN model also achieves comparable acceleration ratios to the SOTA model with additional model structure on Spec-Bench.

Autoregressive decoding is the only part of sequence-to-sequence models that prevents them from massive parallelization at inference time. Non-autoregressive models enable the decoder to generate all output symbols independently in parallel. We present a novel non-autoregressive architecture based on connectionist temporal classification and evaluate it on the task of neural machine translation. Unlike other non-autoregressive methods which operate in several steps, our model can be trained end-to-end. We conduct experiments on the WMT English-Romanian and English-German datasets. Our models achieve a significant speedup over the autoregressive models, keeping the translation quality comparable to other non-autoregressive models.

Large language models (LLMs) have demonstrated remarkable capabilities across various tasks. However, their widespread application is hindered by the resource-intensive decoding process. To address this challenge, current approaches have incorporated additional decoding heads to enable parallel prediction of multiple subsequent tokens, thereby achieving inference acceleration. Nevertheless, the accuracy of these decoding heads falls short of the auto-regressive decoding approach. In light of these limitations, we propose Chimera, a novel framework specifically designed for speculative sampling. Within this framework, we introduce a lightweight draft model that effectively utilizes previously generated tokens to predict subsequent words. To ensure both accuracy and efficiency, we present two strategies within the lightweight draft model. Firstly, we focus on capturing short-range dependencies at the bottom layer. Secondly, we leverage the readily available representations from the original LLM.Through empirical evaluation on the Vicuna and LlaMA-2 series, Chimera demonstrates impressive results, achieving an average latency speedup ratio of 2.7x compared to the vanilla auto-regressive decoding approach. This highlights the potential of our proposed framework in significantly improving the efficiency of large language models during the decoding process.

In this paper, we propose ZipAR, a training-free, plug-and-play parallel decoding framework for accelerating auto-regressive (AR) visual generation. The motivation stems from the observation that images exhibit local structures, and spatially distant regions tend to have minimal interdependence. Given a partially decoded set of visual tokens, in addition to the original next-token prediction scheme in the row dimension, the tokens corresponding to spatially adjacent regions in the column dimension can be decoded in parallel, enabling the ``next-set prediction'' paradigm. By decoding multiple tokens simultaneously in a single forward pass, the number of forward passes required to generate an image is significantly reduced, resulting in a substantial improvement in generation efficiency. Experiments demonstrate that ZipAR can reduce the number of model forward passes by up to 91% on the Emu3-Gen model without requiring any additional retraining.

Speculative Decoding (SD) has emerged as a widely used paradigm to accelerate the inference of large language models (LLMs) without compromising generation quality. It works by efficiently drafting multiple tokens using a compact model and then verifying them in parallel using the target LLM. Notably, Self-Speculative Decoding proposes skipping certain layers to construct the draft model, which eliminates the need for additional parameters or training. Despite its strengths, we observe in this work that drafting with layer skipping exhibits significant sensitivity to domain shifts, leading to a substantial drop in acceleration performance. To enhance the domain generalizability of this paradigm, we introduce KNN-SSD, an algorithm that leverages K-Nearest Neighbor (KNN) search to match different skipped layers with various domain inputs. We evaluated our algorithm in various models and multiple tasks, observing that its application leads to 1.3x-1.6x speedup in LLM inference.

We present a decoder-only Transformer architecture that robustly generalizes to sequence lengths substantially longer than those seen during training. Our model, SWAN-GPT, interleaves layers without positional encodings (NoPE) and sliding-window attention layers equipped with rotary positional encodings (SWA-RoPE). Experiments demonstrate strong performance on sequence lengths significantly longer than the training length without the need for additional long-context training. This robust length extrapolation is achieved through our novel architecture, enhanced by a straightforward dynamic scaling of attention scores during inference. In addition, SWAN-GPT is more computationally efficient than standard GPT architectures, resulting in cheaper training and higher throughput. Further, we demonstrate that existing pre-trained decoder-only models can be efficiently converted to the SWAN architecture with minimal continued training, enabling longer contexts. Overall, our work presents an effective approach for scaling language models to longer contexts in a robust and efficient manner.

Pre-trained language models have been successful in natural language generation (NLG) tasks. While various decoding methods have been employed, they often produce suboptimal results. We first present an empirical analysis of three NLG tasks: summarization, machine translation, and constrained text generation. We found that selecting the best output from the results of multiple decoding methods can significantly improve performance. To further improve reranking for NLG tasks, we proposed a novel method, PairReranker, which uses a single encoder and a pairwise loss function to jointly encode a source input and a pair of candidates and compare them. Experiments on three NLG tasks demonstrated the effectiveness and flexibility of PairReranker, showing strong results, compared with previous baselines. In addition, our PairReranker can generalize to significantly improve GPT-3 (text-davinci-003) results (e.g., 24.55\% on CommonGen and 11.35\% on WMT18 zh-en), even though our rerankers are not trained with any GPT-3 candidates.

Existing large language model-based code generation pipelines typically use beam search or sampling algorithms during the decoding process. Although the programs they generate achieve high token-matching-based scores, they often fail to compile or generate incorrect outputs. The main reason is that conventional Transformer decoding algorithms may not be the best choice for code generation. In this work, we propose a novel Transformer decoding algorithm, Planning-Guided Transformer Decoding (PG-TD), that uses a planning algorithm to do lookahead search and guide the Transformer to generate better programs. Specifically, instead of simply optimizing the likelihood of the generated sequences, the Transformer makes use of a planner to generate candidate programs and test them on public test cases. The Transformer can therefore make more informed decisions and generate tokens that will eventually lead to higher-quality programs. We also design a mechanism that shares information between the Transformer and the planner to make our algorithm computationally efficient. We empirically evaluate our framework with several large language models as backbones on public coding challenge benchmarks, showing that 1) it can generate programs that consistently achieve higher performance compared with competing baseline methods; 2) it enables controllable code generation, such as concise codes and highly-commented codes by optimizing modified objective.

Large language models (LLMs) continue to face challenges in reliably solving reasoning tasks, particularly those that require precise rule following, as often found in mathematical reasoning. This paper introduces a novel neurosymbolic method that improves LLM reasoning by encoding hidden states into neurosymbolic vectors, enabling problem-solving within a neurosymbolic vector space. The results are decoded and merged with the original hidden state, significantly boosting the model's performance on numerical reasoning tasks. By offloading computation through neurosymbolic representations, this method enhances efficiency, reliability, and interpretability. Experimental results demonstrate an average of 88.6% lower cross-entropy loss and 15.4 times more problems correctly solved on a suite of mathematical reasoning tasks compared to chain-of-thought prompting and supervised fine-tuning (LoRA), without degrading performance on other tasks. We make our code available at: https://github.com/vdhanraj/Neurosymbolic-LLM.

Large language models like GPT-4 exhibit emergent capabilities across general-purpose tasks, such as basic arithmetic, when trained on extensive text data, even though these tasks are not explicitly encoded by the unsupervised, next-token prediction objective. This study investigates how small transformers, trained from random initialization, can efficiently learn arithmetic operations such as addition, multiplication, and elementary functions like square root, using the next-token prediction objective. We first demonstrate that conventional training data is not the most effective for arithmetic learning, and simple formatting changes can significantly improve accuracy. This leads to sharp phase transitions as a function of training data scale, which, in some cases, can be explained through connections to low-rank matrix completion. Building on prior work, we then train on chain-of-thought style data that includes intermediate step results. Even in the complete absence of pretraining, this approach significantly and simultaneously improves accuracy, sample complexity, and convergence speed. We also study the interplay between arithmetic and text data during training and examine the effects of few-shot prompting, pretraining, and model scale. Additionally, we discuss length generalization challenges. Our work highlights the importance of high-quality, instructive data that considers the particular characteristics of the next-word prediction objective for rapidly eliciting arithmetic capabilities.

Next token prediction paradigm has been prevailing for autoregressive models in the era of LLMs. The current default sampling choice for popular LLMs is temperature scaling together with nucleus sampling to balance diversity and coherence. Nevertheless, such approach leads to inferior performance in various NLP tasks when the model is not certain about testing questions. To this end, we propose a brand new training-free decoding strategy, dubbed as Cautious Next Token Prediction (CNTP). In the decoding process, if the model has comparatively high prediction entropy at a certain step, we sample multiple trials starting from the step independently and stop when encountering any punctuation. Then we select the trial with the lowest perplexity score viewed as the most probable and reliable trial path given the model's capacity. The trial number is negatively correlated with the prediction confidence, i.e., the less confident the model is, the more trials it should sample. This is consistent with human beings' behaviour: when feeling uncertain or unconfident, one tends to think more creatively, exploring multiple thinking paths, to cautiously select the path one feels most confident about. Extensive experiments on both LLMs and MLLMs show that our proposed CNTP approach outperforms existing standard decoding strategies consistently by a clear margin. Moreover, the integration of CNTP with self consistency can further improve over vanilla self consistency. We believe our proposed CNTP has the potential to become one of the default choices for LLM decoding. Code is available at https://github.com/wyzjack/CNTP.

Large Language Models (LLMs) are proficient in natural language processing tasks, but their deployment is often restricted by extensive parameter sizes and computational demands. This paper focuses on post-training quantization (PTQ) in LLMs, specifically 4-bit weight and 8-bit activation (W4A8) quantization, to enhance computational efficiency -- a topic less explored compared to weight-only quantization. We present two innovative techniques: activation-quantization-aware scaling (AQAS) and sequence-length-aware calibration (SLAC) to enhance PTQ by considering the combined effects on weights and activations and aligning calibration sequence lengths to target tasks. Moreover, we introduce dINT, a hybrid data format combining integer and denormal representations, to address the underflow issue in W4A8 quantization, where small values are rounded to zero. Through rigorous evaluations of LLMs, including OPT and LLaMA, we demonstrate that our techniques significantly boost task accuracies to levels comparable with full-precision models. By developing arithmetic units compatible with dINT, we further confirm that our methods yield a 2times hardware efficiency improvement compared to 8-bit integer MAC unit.

When applied to question answering and other text generation tasks, language models (LMs) may be queried generatively (by sampling answers from their output distribution) or discriminatively (by using them to score or rank a set of candidate outputs). These procedures sometimes yield very different predictions. How do we reconcile mutually incompatible scoring procedures to obtain coherent LM predictions? We introduce a new, a training-free, game-theoretic procedure for language model decoding. Our approach casts language model decoding as a regularized imperfect-information sequential signaling game - which we term the CONSENSUS GAME - in which a GENERATOR seeks to communicate an abstract correctness parameter using natural language sentences to a DISCRIMINATOR. We develop computational procedures for finding approximate equilibria of this game, resulting in a decoding algorithm we call EQUILIBRIUM-RANKING. Applied to a large number of tasks (including reading comprehension, commonsense reasoning, mathematical problem-solving, and dialog), EQUILIBRIUM-RANKING consistently, and sometimes substantially, improves performance over existing LM decoding procedures - on multiple benchmarks, we observe that applying EQUILIBRIUM-RANKING to LLaMA-7B outperforms the much larger LLaMA-65B and PaLM-540B models. These results highlight the promise of game-theoretic tools for addressing fundamental challenges of truthfulness and consistency in LMs.

A non-invasive brain-computer interface (BCI) enables direct interaction between the user and external devices, typically via electroencephalogram (EEG) signals. However, decoding EEG signals across different headsets remains a significant challenge due to differences in the number and locations of the electrodes. To address this challenge, we propose a spatial distillation based distribution alignment (SDDA) approach for heterogeneous cross-headset transfer in non-invasive BCIs. SDDA uses first spatial distillation to make use of the full set of electrodes, and then input/feature/output space distribution alignments to cope with the significant differences between the source and target domains. To our knowledge, this is the first work to use knowledge distillation in cross-headset transfers. Extensive experiments on six EEG datasets from two BCI paradigms demonstrated that SDDA achieved superior performance in both offline unsupervised domain adaptation and online supervised domain adaptation scenarios, consistently outperforming 10 classical and state-of-the-art transfer learning algorithms.

Recently, dynamic computation methods have shown notable acceleration for Large Language Models (LLMs) by skipping several layers of computations through elaborate heuristics or additional predictors. However, in the decoding process of existing approaches, different samples are assigned different computational budgets, which cannot guarantee a stable and precise acceleration effect. Furthermore, existing approaches generally skip multiple contiguous layers at the bottom or top of the layers, leading to a drastic change in the model's layer-wise representations, and thus a consequent performance degeneration. Therefore, we propose a Unified Layer Skipping strategy, which selects the number of layers to skip computation based solely on the target speedup ratio, and then skips the corresponding number of intermediate layer computations in a balanced manner. Since the Unified Layer Skipping strategy is independent of input samples, it naturally supports popular acceleration techniques such as batch decoding and KV caching, thus demonstrating more practicality for real-world applications. Experimental results on two common tasks, i.e., machine translation and text summarization, indicate that given a target speedup ratio, the Unified Layer Skipping strategy significantly enhances both the inference performance and the actual model throughput over existing dynamic approaches.

Fine-tuned language models use greedy decoding to answer reading comprehension questions with relative success. However, this approach does not ensure that the answer is a span in the given passage, nor does it guarantee that it is the most probable one. Does greedy decoding actually perform worse than an algorithm that does adhere to these properties? To study the performance and optimality of greedy decoding, we present exact-extract, a decoding algorithm that efficiently finds the most probable answer span in the context. We compare the performance of T5 with both decoding algorithms on zero-shot and few-shot extractive question answering. When no training examples are available, exact-extract significantly outperforms greedy decoding. However, greedy decoding quickly converges towards the performance of exact-extract with the introduction of a few training examples, becoming more extractive and increasingly likelier to generate the most probable span as the training set grows. We also show that self-supervised training can bias the model towards extractive behavior, increasing performance in the zero-shot setting without resorting to annotated examples. Overall, our results suggest that pretrained language models are so good at adapting to extractive question answering, that it is often enough to fine-tune on a small training set for the greedy algorithm to emulate the optimal decoding strategy.

Despite the remarkable advances in language modeling, current mainstream decoding methods still struggle to generate texts that align with human texts across different aspects. In particular, sampling-based methods produce less-repetitive texts which are often disjunctive in discourse, while search-based methods maintain topic coherence at the cost of increased repetition. Overall, these methods fall short in achieving holistic alignment across a broad range of aspects. In this work, we frame decoding from a language model as an optimization problem with the goal of strictly matching the expected performance with human texts measured by multiple metrics of desired aspects simultaneously. The resulting decoding distribution enjoys an analytical solution that scales the input language model distribution via a sequence-level energy function defined by these metrics. And most importantly, we prove that this induced distribution is guaranteed to improve the perplexity on human texts, which suggests a better approximation to the underlying distribution of human texts. To facilitate tractable sampling from this globally normalized distribution, we adopt the Sampling-Importance-Resampling technique. Experiments on various domains and model scales demonstrate the superiority of our method in metrics alignment with human texts and human evaluation over strong baselines.

Scaling the size of language models to tens of billions of parameters has led to impressive performance on a wide range of tasks. At generation, these models are used auto-regressively, requiring a forward pass for each generated token, and thus reading the full set of parameters from memory. This memory access forms the primary bottleneck for generation and it worsens as the model size increases. Moreover, executing a forward pass for multiple tokens in parallel often takes nearly the same time as it does for just one token. These two observations lead to the development of speculative sampling, where a second smaller model is used to draft a few tokens, that are then validated or rejected using a single forward pass of the large model. Unfortunately, this method requires two models that share the same tokenizer and thus limits its adoption. As an alternative, we propose to use parallel decoding as a way to draft multiple tokens from a single model with no computational cost, nor the need for a second model. Our approach only requires an additional input token that marks the words that will be generated simultaneously. We show promising performance (up to 30% speed-up) while requiring only as few as O(d_{emb}) additional parameters.

Open-ended text generation with autoregressive language models (LMs) is one of the core tasks in natural language processing. However, maximization-based decoding methods (e.g., greedy/beam search) often lead to the degeneration problem, i.e., the generated text is unnatural and contains undesirable repetitions. Existing solutions to this problem either introduce randomness prone to incoherence or require a look-ahead mechanism that demands extra computational overhead. In this study, we formulate open-ended text generation from a new perspective, i.e., we view it as an exploration process within a directed graph. Thereby, we understand the phenomenon of degeneration as circular loops within the directed graph. Based on our formulation, we propose a novel decoding method -- momentum decoding -- which encourages the LM to greedily explore new nodes outside the current graph. Meanwhile, it also allows the LM to return to the existing nodes with a momentum downgraded by a pre-defined resistance function. We extensively test our approach on three benchmarks from different domains through automatic and human evaluations. The results show that momentum decoding performs comparably with the current state of the art while enjoying notably improved inference speed and computation FLOPs. Furthermore, we conduct a detailed analysis to reveal the merits and inner workings of our approach. Our codes and other related resources are publicly available at https://github.com/gmftbyGMFTBY/MomentumDecoding.

Masked generative models (MGMs) have emerged as a powerful framework for image synthesis, combining parallel decoding with strong bidirectional context modeling. However, generating high-quality samples typically requires many iterative decoding steps, resulting in high inference costs. A straightforward way to speed up generation is by decoding more tokens in each step, thereby reducing the total number of steps. However, when many tokens are decoded simultaneously, the model can only estimate the univariate marginal distributions independently, failing to capture the dependency among them. As a result, reducing the number of steps significantly compromises generation fidelity. In this work, we introduce ReCAP (Reused Context-Aware Prediction), a plug-and-play module that accelerates inference in MGMs by constructing low-cost steps via reusing feature embeddings from previously decoded context tokens. ReCAP interleaves standard full evaluations with lightweight steps that cache and reuse context features, substantially reducing computation while preserving the benefits of fine-grained, iterative generation. We demonstrate its effectiveness on top of three representative MGMs (MaskGIT, MAGE, and MAR), including both discrete and continuous token spaces and covering diverse architectural designs. In particular, on ImageNet256 class-conditional generation, ReCAP achieves up to 2.4x faster inference than the base model with minimal performance drop, and consistently delivers better efficiency-fidelity trade-offs under various generation settings.

We introduce ARPG, a novel visual autoregressive model that enables randomized parallel generation, addressing the inherent limitations of conventional raster-order approaches, which hinder inference efficiency and zero-shot generalization due to their sequential, predefined token generation order. Our key insight is that effective random-order modeling necessitates explicit guidance for determining the position of the next predicted token. To this end, we propose a novel guided decoding framework that decouples positional guidance from content representation, encoding them separately as queries and key-value pairs. By directly incorporating this guidance into the causal attention mechanism, our approach enables fully random-order training and generation, eliminating the need for bidirectional attention. Consequently, ARPG readily generalizes to zero-shot tasks such as image inpainting, outpainting, and resolution expansion. Furthermore, it supports parallel inference by concurrently processing multiple queries using a shared KV cache. On the ImageNet-1K 256 benchmark, our approach attains an FID of 1.94 with only 64 sampling steps, achieving over a 20-fold increase in throughput while reducing memory consumption by over 75% compared to representative recent autoregressive models at a similar scale.

We study lossless acceleration for seq2seq generation with a novel decoding algorithm -- Aggressive Decoding. Unlike the previous efforts (e.g., non-autoregressive decoding) speeding up seq2seq generation at the cost of quality loss, our approach aims to yield the identical (or better) generation compared with autoregressive decoding but in a significant speedup, achieved by innovative cooperation of aggressive decoding and verification that are both efficient due to parallel computing. We propose two Aggressive Decoding paradigms for 2 kinds of seq2seq tasks: 1) For the seq2seq tasks whose inputs and outputs are highly similar (e.g., Grammatical Error Correction), we propose Input-guided Aggressive Decoding (IAD) that aggressively copies from the input sentence as drafted decoded tokens to verify in parallel; 2) For other general seq2seq tasks (e.g., Machine Translation), we propose Generalized Aggressive Decoding (GAD) that first employs an additional non-autoregressive decoding model for aggressive decoding and then verifies in parallel in the autoregressive manner. We test Aggressive Decoding on the most popular 6-layer Transformer model on GPU in multiple seq2seq tasks: 1) For IAD, we show that it can introduce a 7x-9x speedup for the Transformer in Grammatical Error Correction and Text Simplification tasks with the identical results as greedy decoding; 2) For GAD, we observe a 3x-5x speedup with the identical or even better quality in two important seq2seq tasks: Machine Translation and Abstractive Summarization. Moreover, Aggressive Decoding can benefit even more from stronger computing devices that are better at parallel computing. Given the lossless quality as well as significant and promising speedup, we believe Aggressive Decoding may potentially evolve into a de facto standard for efficient and lossless seq2seq generation in the near future.

The rapid advancement of large language models (LLMs) has revolutionized code generation tasks across various programming languages. However, the unique characteristics of programming languages, particularly those like Verilog with specific syntax and lower representation in training datasets, pose significant challenges for conventional tokenization and decoding approaches. In this paper, we introduce a novel application of speculative decoding for Verilog code generation, showing that it can improve both inference speed and output quality, effectively achieving speed and quality all in one. Unlike standard LLM tokenization schemes, which often fragment meaningful code structures, our approach aligns decoding stops with syntactically significant tokens, making it easier for models to learn the token distribution. This refinement addresses inherent tokenization issues and enhances the model's ability to capture Verilog's logical constructs more effectively. Our experimental results show that our method achieves up to a 5.05x speedup in Verilog code generation and increases pass@10 functional accuracy on RTLLM by up to 17.19% compared to conventional training strategies. These findings highlight speculative decoding as a promising approach to bridge the quality gap in code generation for specialized programming languages.

We introduce Reward-Guided Speculative Decoding (RSD), a novel framework aimed at improving the efficiency of inference in large language models (LLMs). RSD synergistically combines a lightweight draft model with a more powerful target model, incorporating a controlled bias to prioritize high-reward outputs, in contrast to existing speculative decoding methods that enforce strict unbiasedness. RSD employs a process reward model to evaluate intermediate decoding steps and dynamically decide whether to invoke the target model, optimizing the trade-off between computational cost and output quality. We theoretically demonstrate that a threshold-based mixture strategy achieves an optimal balance between resource utilization and performance. Extensive evaluations on challenging reasoning benchmarks, including Olympiad-level tasks, show that RSD delivers significant efficiency gains against decoding with the target model only (up to 4.4x fewer FLOPs), while achieving significant better accuracy than parallel decoding method on average (up to +3.5). These results highlight RSD as a robust and cost-effective approach for deploying LLMs in resource-intensive scenarios.

Financial forecasting has been an important and active area of machine learning research because of the challenges it presents and the potential rewards that even minor improvements in prediction accuracy or forecasting may entail. Traditionally, financial forecasting has heavily relied on quantitative indicators and metrics derived from structured financial statements. Earnings conference call data, including text and audio, is an important source of unstructured data that has been used for various prediction tasks using deep earning and related approaches. However, current deep learning-based methods are limited in the way that they deal with numeric data; numbers are typically treated as plain-text tokens without taking advantage of their underlying numeric structure. This paper describes a numeric-oriented hierarchical transformer model to predict stock returns, and financial risk using multi-modal aligned earnings calls data by taking advantage of the different categories of numbers (monetary, temporal, percentages etc.) and their magnitude. We present the results of a comprehensive evaluation of NumHTML against several state-of-the-art baselines using a real-world publicly available dataset. The results indicate that NumHTML significantly outperforms the current state-of-the-art across a variety of evaluation metrics and that it has the potential to offer significant financial gains in a practical trading context.

Length generalization, defined as the ability to extrapolate from shorter training sequences to longer test ones, is a significant challenge for language models. This issue persists even with large-scale Transformers handling relatively straightforward tasks. In this paper, we test the Transformer's ability of length generalization using the task of addition of two integers. We show that the success of length generalization is intricately linked to the data format and the type of position encoding. Using the right combination of data format and position encodings, we show for the first time that standard Transformers can extrapolate to a sequence length that is 2.5x the input length. Nevertheless, unlike in-distribution generalization, length generalization remains fragile, significantly influenced by factors like random weight initialization and training data order, leading to large variances across different random seeds.

Multiplications are responsible for most of the computational cost involved in neural network training and inference. Recent research has thus looked for ways to reduce the cost associated with them. Inspired by Mogami (2020), we replace multiplication with a cheap piecewise affine approximation that is achieved by adding the bit representation of the floating point numbers together as integers. We show that transformers can be trained with the resulting modified matrix multiplications on both vision and language tasks with little to no performance impact, and without changes to the training hyperparameters. We further replace all non-linearities in the networks making them fully and jointly piecewise affine in both inputs and weights. Finally, we show that we can eliminate all multiplications in the entire training process, including operations in the forward pass, backward pass and optimizer update, demonstrating the first successful training of modern neural network architectures in a fully multiplication-free fashion.

In recent years, many interpretability methods have been proposed to help interpret the internal states of Transformer-models, at different levels of precision and complexity. Here, to analyze encoder-decoder Transformers, we propose a simple, new method: DecoderLens. Inspired by the LogitLens (for decoder-only Transformers), this method involves allowing the decoder to cross-attend representations of intermediate encoder layers instead of using the final encoder output, as is normally done in encoder-decoder models. The method thus maps previously uninterpretable vector representations to human-interpretable sequences of words or symbols. We report results from the DecoderLens applied to models trained on question answering, logical reasoning, speech recognition and machine translation. The DecoderLens reveals several specific subtasks that are solved at low or intermediate layers, shedding new light on the information flow inside the encoder component of this important class of models.

Speculative decoding (SPD) aims to accelerate the auto-regressive token generation process of a target Large Language Model (LLM). Some approaches employ a draft model with multiple heads to predict a sequence of future tokens, where each head handles a token in the sequence. The target LLM verifies the predicted sequence and accepts aligned tokens, enabling efficient multi-token generation. However, existing methods assume that all tokens within a sequence are equally important, employing identical head structures and relying on a single-generation paradigm, either serial or parallel. To this end, we theoretically demonstrate that initial tokens in the draft sequence are more important than later ones. Building on this insight, we propose Gumiho, a hybrid model combining serial and parallel heads. Specifically, given the critical importance of early tokens, we employ a sophisticated Transformer architecture for the early draft heads in a serial configuration to improve accuracy. For later tokens, we utilize multiple lightweight MLP heads operating in parallel to enhance efficiency. By allocating more advanced model structures and longer running times to the early heads, Gumiho achieves improved overall performance. The experimental results demonstrate that our method outperforms existing approaches, fully validating its effectiveness.

This paper introduces an approach for training o1-like RAG models that retrieve and reason over relevant information step by step before generating the final answer. Conventional RAG methods usually perform a single retrieval step before the generation process, which limits their effectiveness in addressing complex queries due to imperfect retrieval results. In contrast, our proposed method, CoRAG (Chain-of-Retrieval Augmented Generation), allows the model to dynamically reformulate the query based on the evolving state. To train CoRAG effectively, we utilize rejection sampling to automatically generate intermediate retrieval chains, thereby augmenting existing RAG datasets that only provide the correct final answer. At test time, we propose various decoding strategies to scale the model's test-time compute by controlling the length and number of sampled retrieval chains. Experimental results across multiple benchmarks validate the efficacy of CoRAG, particularly in multi-hop question answering tasks, where we observe more than 10 points improvement in EM score compared to strong baselines. On the KILT benchmark, CoRAG establishes a new state-of-the-art performance across a diverse range of knowledge-intensive tasks. Furthermore, we offer comprehensive analyses to understand the scaling behavior of CoRAG, laying the groundwork for future research aimed at developing factual and grounded foundation models.

Many LLM tasks are performed in large batches or even offline, and the performance indictor for which is throughput. These tasks usually show the characteristic of prefix sharing, where different prompt input can partially show the common prefix. However, the existing LLM inference engines tend to optimize the streaming requests and show limitations of supporting the large batched tasks with the prefix sharing characteristic. The existing solutions use the LRU-based cache to reuse the KV context of common prefix. The KV context that is about to be reused may prematurely be evicted with the implicit cache management. Even if not evicted, the lifetime of the shared KV context is extended since requests sharing the same context are not scheduled together, resulting in larger memory usage. These streaming oriented systems schedule the requests in the first-come-first-serve or similar order. As a result, the requests with larger ratio of decoding steps may be scheduled too late to be able to mix with the prefill chunks to increase the hardware utilization. Besides, the token and request number based batching can limit the size of token-batch, which keeps the GPU from saturating for the iterations dominated by decoding tokens. We propose BatchLLM to address the above problems. BatchLLM explicitly identifies the common prefixes globally. The requests sharing the same prefix will be scheduled together to reuse the KV context the best, which also shrinks the lifetime of common KV memory. BatchLLM reorders the requests and schedules the requests with larger ratio of decoding first to better mix the decoding tokens with the latter prefill chunks and applies memory-centric token batching to enlarge the token-batch sizes, which helps to increase the GPU utilization. Extensive evaluation shows that BatchLLM outperforms vLLM by 1.1x to 2x on a set of microbenchmarks and two typical industry workloads.

Although transformers are remarkably effective for many tasks, there are some surprisingly easy-looking regular languages that they struggle with. Hahn shows that for languages where acceptance depends on a single input symbol, a transformer's classification decisions become less and less confident (that is, with cross-entropy approaching 1 bit per string) as input strings get longer and longer. We examine this limitation using two languages: PARITY, the language of bit strings with an odd number of 1s, and FIRST, the language of bit strings starting with a 1. We demonstrate three ways of overcoming the limitation suggested by Hahn's lemma. First, we settle an open question by constructing a transformer that recognizes PARITY with perfect accuracy, and similarly for FIRST. Second, we use layer normalization to bring the cross-entropy of both models arbitrarily close to zero. Third, when transformers need to focus on a single position, as for FIRST, we find that they can fail to generalize to longer strings; we offer a simple remedy to this problem that also improves length generalization in machine translation.

Recent large-scale neural autoregressive sequence models have shown impressive performances on a variety of natural language generation tasks. However, their generated sequences often exhibit degenerate properties such as non-termination, undesirable repetition, and premature termination, when generated with decoding algorithms such as greedy search, beam search, top-k sampling, and nucleus sampling. In this paper, we focus on the problem of non-terminating sequences resulting from an incomplete decoding algorithm. We first define an incomplete probable decoding algorithm which includes greedy search, top-k sampling, and nucleus sampling, beyond the incomplete decoding algorithm originally put forward by Welleck et al. (2020). We then propose a non-monotonic self-terminating language model, which significantly relaxes the constraint of monotonically increasing termination probability in the originally proposed self-terminating language model by Welleck et al. (2020), to address the issue of non-terminating sequences when using incomplete probable decoding algorithms. We prove that our proposed model prevents non-terminating sequences when using not only incomplete probable decoding algorithms but also beam search. We empirically validate our model on sequence completion tasks with various architectures.

Large Vision-Language Models (LVLMs) have demonstrated remarkable capabilities across a range of multimodal tasks. However, their inference efficiency is constrained by the large number of visual tokens processed during decoding. To address this challenge, we propose Per-Layer Per-Head Vision Token Pruning (PLPHP), a two-level fine-grained pruning method including Layer-Level Retention Rate Allocation and Head-Level Vision Token Pruning. Motivated by the Vision Token Re-attention phenomenon across decoder layers, we dynamically adjust token retention rates layer by layer. Layers that exhibit stronger attention to visual information preserve more vision tokens, while layers with lower vision attention are aggressively pruned. Furthermore, PLPHP applies pruning at the attention head level, enabling different heads within the same layer to independently retain critical context. Experiments on multiple benchmarks demonstrate that PLPHP delivers an 18% faster decoding speed and reduces the Key-Value Cache (KV Cache) size by over 50%, all at the cost of 0.46% average performance drop, while also achieving notable performance improvements in multi-image tasks. These results highlight the effectiveness of fine-grained token pruning and contribute to advancing the efficiency and scalability of LVLMs. Our source code will be made publicly available.

Non-autoregressive (nAR) models for machine translation (MT) manifest superior decoding speed when compared to autoregressive (AR) models, at the expense of impaired fluency of their outputs. We improve the fluency of a nAR model with connectionist temporal classification (CTC) by employing additional features in the scoring model used during beam search decoding. Since the beam search decoding in our model only requires to run the network in a single forward pass, the decoding speed is still notably higher than in standard AR models. We train models for three language pairs: German, Czech, and Romanian from and into English. The results show that our proposed models can be more efficient in terms of decoding speed and still achieve a competitive BLEU score relative to AR models.

Despite the extensive success of pretrained language models as encoders for building NLP systems, they haven't seen prominence as decoders for sequence generation tasks. We explore the question of whether these models can be adapted to be used as universal decoders. To be considered "universal," a decoder must have an implicit representation for any target sentence s, such that it can recover that sentence exactly when conditioned on its representation. For large transformer-based language models trained on vast amounts of English text, we investigate whether such representations can be easily discovered using standard optimization methods. We present and compare three representation injection techniques for transformer-based models and three accompanying methods which map sentences to and from this representation space. Experiments show that not only do representations exist for sentences from a variety of genres. More importantly, without needing complex optimization algorithms, our methods recover these sentences almost perfectly without fine-tuning the underlying language model at all.

We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that are discrete tokens corresponding to positions in an input sequence. Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence and Neural Turing Machines, because the number of target classes in each step of the output depends on the length of the input, which is variable. Problems such as sorting variable sized sequences, and various combinatorial optimization problems belong to this class. Our model solves the problem of variable size output dictionaries using a recently proposed mechanism of neural attention. It differs from the previous attention attempts in that, instead of using attention to blend hidden units of an encoder to a context vector at each decoder step, it uses attention as a pointer to select a member of the input sequence as the output. We call this architecture a Pointer Net (Ptr-Net). We show Ptr-Nets can be used to learn approximate solutions to three challenging geometric problems -- finding planar convex hulls, computing Delaunay triangulations, and the planar Travelling Salesman Problem -- using training examples alone. Ptr-Nets not only improve over sequence-to-sequence with input attention, but also allow us to generalize to variable size output dictionaries. We show that the learnt models generalize beyond the maximum lengths they were trained on. We hope our results on these tasks will encourage a broader exploration of neural learning for discrete problems.

While instruction-tuned language models have demonstrated impressive zero-shot generalization, these models often struggle to generate accurate responses when faced with instructions that fall outside their training set. This paper presents Instructive Decoding (ID), a simple yet effective approach that augments the efficacy of instruction-tuned models. Specifically, ID adjusts the logits for next-token prediction in a contrastive manner, utilizing predictions generated from a manipulated version of the original instruction, referred to as a noisy instruction. This noisy instruction aims to elicit responses that could diverge from the intended instruction yet remain plausible. We conduct experiments across a spectrum of such noisy instructions, ranging from those that insert semantic noise via random words to others like 'opposite' that elicit the deviated responses. Our approach achieves considerable performance gains across various instruction-tuned models and tasks without necessitating any additional parameter updates. Notably, utilizing 'opposite' as the noisy instruction in ID, which exhibits the maximum divergence from the original instruction, consistently produces the most significant performance gains across multiple models and tasks.

Test-time scaling (TTS), which involves dynamic allocation of compute during inference, offers a promising way to improve reasoning in large language models. While existing TTS methods work well, they often rely on long decoding paths or require a large number of samples to be generated, increasing the token usage and inference latency. We observe the surprising fact that for reasoning tasks, shorter traces are much more likely to be correct than longer ones. Motivated by this, we introduce First Finish Search (FFS), a training-free parallel decoding strategy that launches n independent samples and returns as soon as any one completes. We evaluate FFS alongside simple decoding, beam search, majority voting, and budget forcing on four reasoning models (DeepSeek-R1, R1-Distill-Qwen-32B, QwQ-32B and Phi-4-Reasoning-Plus) and across four datasets (AIME24, AIME25-I, AIME25-II and GPQA Diamond). With DeepSeek-R1, FFS achieves 82.23% accuracy on the AIME datasets, a 15% improvement over DeepSeek-R1's standalone accuracy, nearly matching OpenAI's o4-mini performance. Our theoretical analysis explains why stopping at the shortest trace is likely to yield a correct answer and identifies the conditions under which early stopping may be suboptimal. The elegance and simplicity of FFS demonstrate that straightforward TTS strategies can perform remarkably well, revealing the untapped potential of simple approaches at inference time.

With the help of simple fine-tuning, one can artificially embed hidden text into large language models (LLMs). This text is revealed only when triggered by a specific query to the LLM. Two primary applications are LLM fingerprinting and steganography. In the context of LLM fingerprinting, a unique text identifier (fingerprint) is embedded within the model to verify licensing compliance. In the context of steganography, the LLM serves as a carrier for hidden messages that can be disclosed through a designated trigger. Our work demonstrates that embedding hidden text in the LLM via fine-tuning, though seemingly secure due to the vast number of potential triggers (any sequence of characters or tokens could serve as a trigger), is susceptible to extraction through analysis of the LLM's output decoding process. We propose a novel approach to extraction called Unconditional Token Forcing. It is premised on the hypothesis that iteratively feeding each token from the LLM's vocabulary into the model should reveal sequences with abnormally high token probabilities, indicating potential embedded text candidates. Additionally, our experiments show that when the first token of a hidden fingerprint is used as an input, the LLM not only produces an output sequence with high token probabilities, but also repetitively generates the fingerprint itself. We also present a method to hide text in such a way that it is resistant to Unconditional Token Forcing, which we named Unconditional Token Forcing Confusion.

Recent research suggests that tree search algorithms (e.g. Monte Carlo Tree Search) can dramatically boost LLM performance on complex mathematical reasoning tasks. However, they often require more than 10 times the computational resources of greedy decoding due to wasteful search strategies, making them difficult to be deployed in practical applications. This study introduces a novel guided tree search algorithm with dynamic node selection and node-level exploration budget (maximum number of children) calculation to tackle this issue. By considering the search progress towards the final answer (history) and the guidance from a value network (future) trained without any step-wise annotations, our algorithm iteratively selects the most promising tree node before expanding it within the boundaries of the allocated computational budget. Experiments conducted on the GSM8K and TabMWP datasets demonstrate that our approach not only offers competitive performance but also enjoys significantly lower computational costs compared to baseline methods.

The recently released GPT-4 Code Interpreter has demonstrated remarkable proficiency in solving challenging math problems, primarily attributed to its ability to seamlessly reason with natural language, generate code, execute code, and continue reasoning based on the execution output. In this paper, we present a method to fine-tune open-source language models, enabling them to use code for modeling and deriving math equations and, consequently, enhancing their mathematical reasoning abilities. We propose a method of generating novel and high-quality datasets with math problems and their code-based solutions, referred to as MathCodeInstruct. Each solution interleaves natural language, code, and execution results. We also introduce a customized supervised fine-tuning and inference approach. This approach yields the MathCoder models, a family of models capable of generating code-based solutions for solving challenging math problems. Impressively, the MathCoder models achieve state-of-the-art scores among open-source LLMs on the MATH (45.2%) and GSM8K (83.9%) datasets, substantially outperforming other open-source alternatives. Notably, the MathCoder model not only surpasses ChatGPT-3.5 and PaLM-2 on GSM8K and MATH but also outperforms GPT-4 on the competition-level MATH dataset. The dataset and models will be released at https://github.com/mathllm/MathCoder.

In this paper, we leverage low-level compiler intermediate representations (IR) to improve code translation. Traditional transpilers rely on syntactic information and handcrafted rules, which limits their applicability and produces unnatural-looking code. Applying neural machine translation (NMT) approaches to code has successfully broadened the set of programs on which one can get a natural-looking translation. However, they treat the code as sequences of text tokens, and still do not differentiate well enough between similar pieces of code which have different semantics in different languages. The consequence is low quality translation, reducing the practicality of NMT, and stressing the need for an approach significantly increasing its accuracy. Here we propose to augment code translation with IRs, specifically LLVM IR, with results on the C++, Java, Rust, and Go languages. Our method improves upon the state of the art for unsupervised code translation, increasing the number of correct translations by 11% on average, and up to 79% for the Java -> Rust pair with greedy decoding. We extend previous test sets for code translation, by adding hundreds of Go and Rust functions. Additionally, we train models with high performance on the problem of IR decompilation, generating programming source code from IR, and study using IRs as intermediary pivot for translation.

Large language models (LLMs) have demonstrated remarkable abilities in representation learning for program synthesis and understanding tasks. The quality of the learned representations appears to be dictated by the neural scaling laws as a function of the number of model parameters and observations, while imposing upper bounds on the model performance by the amount of available data and compute, which is costly. In this study, we attempt to render the training of LLMs for program synthesis more efficient by unifying four key components: (1) model architectures, (2) learning methods, (3) infill sampling, and, (4) data distributions. Specifically, for the model architecture, we attempt to unify encoder and decoder-based models into a single prefix-LM. For learning methods, (i) causal language modeling, (ii) span corruption, (iii) infilling are unified into a simple learning algorithm. For infill sampling, we explore the claim of a "free lunch" hypothesis. For data distributions, the effect of a mixture distribution of programming and natural languages on model performance is explored. We conduct a comprehensive series of empirical experiments on 1B LLMs, for which failures and successes of this exploration are distilled into four lessons. We will provide a final recipe for training and release CodeGen2 models in size 1B, 3.7B, 7B, and, 16B parameters, along with the training framework as open-source: https://github.com/salesforce/CodeGen2.

Minimum Bayes risk (MBR) decoding is a decision rule of text generation tasks that outperforms conventional maximum a posterior (MAP) decoding using beam search by selecting high-quality outputs based on a utility function rather than those with high-probability. Typically, it finds the most suitable hypothesis from the set of hypotheses under the sampled pseudo-references. mbrs is a library of MBR decoding, which can flexibly combine various metrics, alternative expectation estimations, and algorithmic variants. It is designed with a focus on speed measurement and calling count of code blocks, transparency, reproducibility, and extensibility, which are essential for researchers and developers. We published our mbrs as an MIT-licensed open-source project, and the code is available on GitHub. GitHub: https://github.com/naist-nlp/mbrs

Traditional approaches to semantic parsing (SP) work by training individual models for each available parallel dataset of text-meaning pairs. In this paper, we explore the idea of polyglot semantic translation, or learning semantic parsing models that are trained on multiple datasets and natural languages. In particular, we focus on translating text to code signature representations using the software component datasets of Richardson and Kuhn (2017a,b). The advantage of such models is that they can be used for parsing a wide variety of input natural languages and output programming languages, or mixed input languages, using a single unified model. To facilitate modeling of this type, we develop a novel graph-based decoding framework that achieves state-of-the-art performance on the above datasets, and apply this method to two other benchmark SP tasks.

Neural sequence models are widely used to model time-series data. Equally ubiquitous is the usage of beam search (BS) as an approximate inference algorithm to decode output sequences from these models. BS explores the search space in a greedy left-right fashion retaining only the top-B candidates - resulting in sequences that differ only slightly from each other. Producing lists of nearly identical sequences is not only computationally wasteful but also typically fails to capture the inherent ambiguity of complex AI tasks. To overcome this problem, we propose Diverse Beam Search (DBS), an alternative to BS that decodes a list of diverse outputs by optimizing for a diversity-augmented objective. We observe that our method finds better top-1 solutions by controlling for the exploration and exploitation of the search space - implying that DBS is a better search algorithm. Moreover, these gains are achieved with minimal computational or memory over- head as compared to beam search. To demonstrate the broad applicability of our method, we present results on image captioning, machine translation and visual question generation using both standard quantitative metrics and qualitative human studies. Further, we study the role of diversity for image-grounded language generation tasks as the complexity of the image changes. We observe that our method consistently outperforms BS and previously proposed techniques for diverse decoding from neural sequence models.

This technical report describes the design and training of novel speculative decoding draft models, for accelerating the inference speeds of large language models in a production environment. By conditioning draft predictions on both context vectors and sampled tokens, we can train our speculators to efficiently predict high-quality n-grams, which the base model then accepts or rejects. This allows us to effectively predict multiple tokens per inference forward pass, accelerating wall-clock inference speeds of highly optimized base model implementations by a factor of 2-3x. We explore these initial results and describe next steps for further improvements.

We present CoDa (Constrained Generation based Data Augmentation), a controllable, effective, and training-free data augmentation technique for low-resource (data-scarce) NLP. Our approach is based on prompting off-the-shelf instruction-following Large Language Models (LLMs) for generating text that satisfies a set of constraints. Precisely, we extract a set of simple constraints from every instance in the low-resource dataset and verbalize them to prompt an LLM to generate novel and diverse training instances. Our findings reveal that synthetic data that follows simple constraints in the downstream dataset act as highly effective augmentations, and CoDa can achieve this without intricate decoding-time constrained generation techniques or fine-tuning with complex algorithms that eventually make the model biased toward the small number of training instances. Additionally, CoDa is the first framework that provides users explicit control over the augmentation generation process, thereby also allowing easy adaptation to several domains. We demonstrate the effectiveness of CoDa across 11 datasets spanning 3 tasks and 3 low-resource settings. CoDa outperforms all our baselines, qualitatively and quantitatively, with improvements of 0.12%-7.19%. Code is available here: https://github.com/Sreyan88/CoDa

Large language models (LLMs) suffer from low efficiency as the mismatch between the requirement of auto-regressive decoding and the design of most contemporary GPUs. Specifically, billions to trillions of parameters must be loaded to the GPU cache through its limited memory bandwidth for computation, but only a small batch of tokens is actually computed. Consequently, the GPU spends most of its time on memory transfer instead of computation. Recently, parallel decoding, a type of speculative decoding algorithms, is becoming more popular and has demonstrated impressive efficiency improvement in generation. It introduces extra decoding heads to large models, enabling them to predict multiple subsequent tokens simultaneously and verify these candidate continuations in a single decoding step. However, this approach deviates from the training objective of next token prediction used during pre-training, resulting in a low hit rate for candidate tokens. In this paper, we propose a new speculative decoding algorithm, Clover, which integrates sequential knowledge into the parallel decoding process. This enhancement improves the hit rate of speculators and thus boosts the overall efficiency. Clover transmits the sequential knowledge from pre-speculated tokens via the Regressive Connection, then employs an Attention Decoder to integrate these speculated tokens. Additionally, Clover incorporates an Augmenting Block that modifies the hidden states to better align with the purpose of speculative generation rather than next token prediction. The experiment results demonstrate that Clover outperforms the baseline by up to 91% on Baichuan-Small and 146% on Baichuan-Large, respectively, and exceeds the performance of the previously top-performing method, Medusa, by up to 37% on Baichuan-Small and 57% on Baichuan-Large, respectively.

Inference from large autoregressive models like Transformers is slow - decoding K tokens takes K serial runs of the model. In this work we introduce speculative decoding - an algorithm to sample from autoregressive models faster without any changes to the outputs, by computing several tokens in parallel. At the heart of our approach lie the observations that (1) hard language-modeling tasks often include easier subtasks that can be approximated well by more efficient models, and (2) using speculative execution and a novel sampling method, we can make exact decoding from the large models faster, by running them in parallel on the outputs of the approximation models, potentially generating several tokens concurrently, and without changing the distribution. Our method can accelerate existing off-the-shelf models without retraining or architecture changes. We demonstrate it on T5-XXL and show a 2X-3X acceleration compared to the standard T5X implementation, with identical outputs.

Learning latent representations from long text sequences is an important first step in many natural language processing applications. Recurrent Neural Networks (RNNs) have become a cornerstone for this challenging task. However, the quality of sentences during RNN-based decoding (reconstruction) decreases with the length of the text. We propose a sequence-to-sequence, purely convolutional and deconvolutional autoencoding framework that is free of the above issue, while also being computationally efficient. The proposed method is simple, easy to implement and can be leveraged as a building block for many applications. We show empirically that compared to RNNs, our framework is better at reconstructing and correcting long paragraphs. Quantitative evaluation on semi-supervised text classification and summarization tasks demonstrate the potential for better utilization of long unlabeled text data.

Large Language Models (LLMs) have demonstrated remarkable performance in many applications, including challenging reasoning problems via chain-of-thoughts (CoTs) techniques that generate ``thinking tokens'' before answering the questions. While existing theoretical works demonstrate that CoTs with discrete tokens boost the capability of LLMs, recent work on continuous CoTs lacks a theoretical understanding of why it outperforms discrete counterparts in various reasoning tasks such as directed graph reachability, a fundamental graph reasoning problem that includes many practical domain applications as special cases. In this paper, we prove that a two-layer transformer with D steps of continuous CoTs can solve the directed graph reachability problem, where D is the diameter of the graph, while the best known result of constant-depth transformers with discrete CoTs requires O(n^2) decoding steps where n is the number of vertices (D<n). In our construction, each continuous thought vector is a superposition state that encodes multiple search frontiers simultaneously (i.e., parallel breadth-first search (BFS)), while discrete CoTs must choose a single path sampled from the superposition state, which leads to sequential search that requires many more steps and may be trapped into local solutions. We also performed extensive experiments to verify that our theoretical construction aligns well with the empirical solution obtained via training dynamics. Notably, encoding of multiple search frontiers as a superposition state automatically emerges in training continuous CoTs, without explicit supervision to guide the model to explore multiple paths simultaneously.

In this paper, we present Paramanu-Ganita, a 208 million parameter novel Auto Regressive (AR) decoder based language model on mathematics. The model is pretrained from scratch at context size of 4096 on our curated mixed mathematical corpus. We evaluate our model on both perplexity metric and GSM8k mathematical benchmark. Paramanu-Ganita despite being 35 times smaller than 7B LLMs, outperformed generalist LLMs such as LLaMa-1 7B by 28.4% points, LLaMa-2 7B by 27.6% points, Falcon 7B by 32.6% points, PaLM 8B by 35.3% points, and math specialised LLMs such as Minerva 8B by 23.2% points, and LLEMMA-7B by 3.0% points in GSM8k test accuracy metric respectively. Paramanu-Ganita also outperformed giant LLMs like PaLM 62B by 6.4% points, Falcon 40B by 19.8% points, LLaMa-1 33B by 3.8% points and Vicuna 13B by 11.8% points respectively. The large significant margin improvement in performance of our math model over the existing LLMs signifies that reasoning capabilities of language model are just not restricted to LLMs with humongous number of parameters. Paramanu-Ganita took 146 hours of A100 training whereas math specialised LLM, LLEMMA 7B, was trained for 23,000 A100 hours of training equivalent. Thus, our approach of pretraining powerful domain specialised language models from scratch for domain adaptation is much more cost-effective than performing continual training of LLMs for domain adaptation. Hence, we conclude that for strong mathematical reasoning abilities of language model, we do not need giant LLMs and immense computing power to our end. In the end, we want to point out that we have only trained Paramanu-Ganita only on a part of our entire mathematical corpus and yet to explore the full potential of our model.

We propose Step-by-Step Coding (SBSC): a multi-turn math reasoning framework that enables Large Language Models (LLMs) to generate sequence of programs for solving Olympiad level math problems. At each step/turn, by leveraging the code execution outputs and programs of previous steps, the model generates the next sub-task and the corresponding program to solve it. This way, SBSC, sequentially navigates to reach the final answer. SBSC allows more granular, flexible and precise approach to problem-solving compared to existing methods. Extensive experiments highlight the effectiveness of SBSC in tackling competition and Olympiad-level math problems. For Claude-3.5-Sonnet, we observe SBSC (greedy decoding) surpasses existing state-of-the-art (SOTA) program generation based reasoning strategies by absolute 10.7% on AMC12, 8% on AIME and 12.6% on MathOdyssey. Given SBSC is multi-turn in nature, we also benchmark SBSC's greedy decoding against self-consistency decoding results of existing SOTA math reasoning strategies and observe performance gain by absolute 6.2% on AMC, 6.7% on AIME and 7.4% on MathOdyssey.

Speculative decoding (SD) accelerates large language model inference by using a smaller draft model to predict multiple tokens, which are then verified in parallel by the larger target model. However, the limited capacity of the draft model often necessitates tree-based sampling to improve prediction accuracy, where multiple candidates are generated at each step. We identify a key limitation in this approach: the candidates at the same step are derived from the same representation, limiting diversity and reducing overall effectiveness. To address this, we propose Jakiro, leveraging Mixture of Experts (MoE), where independent experts generate diverse predictions, effectively decoupling correlations among candidates. Furthermore, we introduce a hybrid inference strategy, combining autoregressive decoding for initial tokens with parallel decoding for subsequent stages, and enhance the latter with contrastive mechanism in features to improve accuracy. Our method significantly boosts prediction accuracy and achieves higher inference speedups. Extensive experiments across diverse models validate the effectiveness and robustness of our approach, establishing a new SOTA in speculative decoding. Our codes are available at https://github.com/haiduo/Jakiro.

Accelerating the inference of large language models (LLMs) is a critical challenge in generative AI. Speculative decoding (SD) methods offer substantial efficiency gains by generating multiple tokens using a single target forward pass. However, existing SD approaches require the drafter and target models to share the same vocabulary, thus limiting the pool of possible drafters, often necessitating the training of a drafter from scratch. We present three new SD methods that remove this shared-vocabulary constraint. All three methods preserve the target distribution (i.e., they are lossless) and work with off-the-shelf models without requiring additional training or modifications. Empirically, on summarization, programming, and long-context tasks, our algorithms achieve significant speedups over standard autoregressive decoding. By enabling any off-the-shelf model to serve as drafter and requiring no retraining, this work substantially broadens the applicability of the SD framework in practice.

Language models have demonstrated remarkable capabilities in reasoning tasks through test-time scaling techniques like best-of-N sampling and tree search. However, these approaches often demand substantial computational resources, creating a critical trade-off between performance and efficiency. We introduce STAND (STochastic Adaptive N-gram Drafting), a novel model-free speculative decoding approach that leverages the inherent redundancy in reasoning trajectories to achieve significant acceleration without compromising accuracy. Our analysis reveals that reasoning paths frequently reuse similar reasoning patterns, enabling efficient model-free token prediction without requiring separate draft models. By introducing stochastic drafting and preserving probabilistic information through a memory-efficient logit-based N-gram module, combined with optimized Gumbel-Top-K sampling and data-driven tree construction, STAND significantly improves token acceptance rates. Extensive evaluations across multiple models and reasoning tasks (AIME-2024, GPQA-Diamond, and LiveCodeBench) demonstrate that STAND reduces inference latency by 60-65% compared to standard autoregressive decoding while maintaining accuracy. Furthermore, STAND outperforms state-of-the-art speculative decoding methods by 14-28% in throughput and shows strong performance even in single-trajectory scenarios, reducing inference latency by 48-58%. As a model-free approach, STAND can be applied to any existing language model without additional training, being a powerful plug-and-play solution for accelerating language model reasoning.

The recent rise of large language models (LLMs) has resulted in increased efforts towards running LLMs at reduced precision. Running LLMs at lower precision supports resource constraints and furthers their democratization, enabling users to run billion-parameter LLMs on their personal devices. To supplement this ongoing effort, we propose INT-FP-QSim: an open-source simulator that enables flexible evaluation of LLMs and vision transformers at various numerical precisions and formats. INT-FP-QSim leverages existing open-source repositories such as TensorRT, QPytorch and AIMET for a combined simulator that supports various floating point and integer formats. With the help of our simulator, we survey the impact of different numerical formats on the performance of LLMs and vision transformers at 4-bit weights and 4-bit or 8-bit activations. We also compare recently proposed methods like Adaptive Block Floating Point, SmoothQuant, GPTQ and RPTQ on the model performances. We hope INT-FP-QSim will enable researchers to flexibly simulate models at various precisions to support further research in quantization of LLMs and vision transformers.

Transformer-based long context generative models power emerging AI applications like hour-long video understanding and project-level coding agent. Deploying long context transformers (e.g., 100K to 10M tokens) is prohibitively expensive compared to short context (e.g., 4K tokens) model variants. Reducing the cost of long-context transformers is becoming a pressing research and engineering challenge starting from the year of 2024. This work describes a concurrent programming framework for quantitatively analyzing the efficiency challenges in serving multiple long-context requests under limited size of GPU high-bandwidth memory (HBM) regime. We give a detailed analysis of how all additional computational costs, compared to 4K context, trace back to one single source: the large size of the KV cache. We use a 34B GPT-3.5 level model of 50K context on A100 NVLink as a running example, and describe how its large KV cache causes four types of deployment challenges: (1) prefilling long inputs takes much longer compute time and GPU memory than short inputs; (2) after prefilling, the large KV cache residing on the GPU HBM substantially restricts the number of concurrent users being served; (3) during decoding, repeatedly reading the KV cache from HBM to SM largely increases latency; (4) when KV cache memory overflows, swapping it from HBM to DDR causes significant context switching latency. We use this framework to analyze existing works and identify possibilities of combining them to build end-to-end systems. Overall, this work offers a foundational framework for analyzing long context transformer deployment and identifies directions towards reducing the inference cost of 1M context to be as cheap as 4K.

Code generation using large language models (LLMs) is highly sensitive to the choice of tokens during decoding, especially at points of uncertainty that critically affect the generated program's logic. Conventional decoding methods such as greedy search and beam search apply uniform treatment to all tokens, neglecting the unique uncertainty characteristics inherent in code generation, which can result in suboptimal outputs. In this work, we conduct an empirical analysis demonstrating that a significant portion of generation errors arises from incorrect token ranking at high-uncertainty steps, where the ground truth token exists in the candidate set but fails to be ranked first. Inspired by this insight, we introduce AdaDec, an adaptive decoding framework guided by token-level uncertainty quantified via Shannon entropy. AdaDec dynamically learns uncertainty thresholds tailored to each model and employs a pause-then-rerank mechanism with lookahead when the uncertainty surpasses these thresholds. Evaluation on the HumanEval and MBPP benchmarks reveals that AdaDec achieves up to a 15.5% improvement in Pass@1 accuracy compared to greedy decoding, matches or outperforms traditional beam search, and reduces both computational overhead and latency through targeted, selective pausing. Our findings suggest that uncertainty-aware adaptive decoding holds considerable potential for enhancing both the reliability and efficiency of code generation with LLMs.

Large Language Models (LLMs) frequently suffer from inefficiencies, largely attributable to the discord between the requirements of auto-regressive decoding and the architecture of contemporary GPUs. Recently, regressive lightweight speculative decoding has garnered attention for its notable efficiency improvements in text generation tasks. This approach utilizes a lightweight regressive draft model, like a Recurrent Neural Network (RNN) or a single transformer decoder layer, leveraging sequential information to iteratively predict potential tokens. Specifically, RNN draft models are computationally economical but tend to deliver lower accuracy, while attention decoder layer models exhibit the opposite traits. This paper presents Clover-2, an advanced iteration of Clover, an RNN-based draft model designed to achieve comparable accuracy to that of attention decoder layer models while maintaining minimal computational overhead. Clover-2 enhances the model architecture and incorporates knowledge distillation to increase Clover's accuracy and improve overall efficiency. We conducted experiments using the open-source Vicuna 7B and LLaMA3-Instruct 8B models. The results demonstrate that Clover-2 surpasses existing methods across various model architectures, showcasing its efficacy and robustness.

Recent advances in reasoning models have demonstrated significant improvements in accuracy, particularly for complex tasks such as mathematical reasoning, by employing detailed and comprehensive reasoning processes. However, generating these lengthy reasoning sequences is computationally expensive and time-consuming. To address this inefficiency, we leverage the inherent parallelizability of certain tasks to accelerate the reasoning process. Specifically, when multiple parallel reasoning branches exist, we decode multiple tokens per step using a specialized attention mask, processing them within a single sequence, avoiding additional memory usage. Experimental results show that our method achieves over 100% speedup in decoding time while maintaining the answer quality.

It has been observed in recent years that transformers have problems with length generalization for certain types of reasoning and arithmetic tasks. In particular, the performance of a transformer model trained on tasks (say addition) up to a certain length (e.g., 5 digit numbers) drops sharply when applied to longer instances of the same problem. This work proposes an approach based on task hinting towards addressing length generalization. Our key idea is that while training the model on task-specific data, it is helpful to simultaneously train the model to solve a simpler but related auxiliary task as well. We study the classical sorting problem as a canonical example to evaluate our approach. We design a multitask training framework and show that task hinting significantly improve length generalization. For sorting we show that it is possible to train models on data consisting of sequences having length at most 20, and improve the test accuracy on sequences of length 100 from less than 1% (for standard training) to more than 92% (via task hinting). Our study uncovers several interesting aspects of length generalization. We observe that while several auxiliary tasks may seem natural a priori, their effectiveness in improving length generalization differs dramatically. We further use probing and visualization-based techniques to understand the internal mechanisms via which the model performs the task, and propose a theoretical construction consistent with the observed learning behaviors of the model. Based on our construction, we show that introducing a small number of length dependent parameters into the training procedure can further boost the performance on unseen lengths. Finally, we also show the efficacy of our task hinting based approach beyond sorting, giving hope that these techniques will be applicable in broader contexts.

Pre-trained large language models (LLMs) exhibit impressive mathematical reasoning capabilities, yet how they compute basic arithmetic, such as addition, remains unclear. This paper shows that pre-trained LLMs add numbers using Fourier features -- dimensions in the hidden state that represent numbers via a set of features sparse in the frequency domain. Within the model, MLP and attention layers use Fourier features in complementary ways: MLP layers primarily approximate the magnitude of the answer using low-frequency features, while attention layers primarily perform modular addition (e.g., computing whether the answer is even or odd) using high-frequency features. Pre-training is crucial for this mechanism: models trained from scratch to add numbers only exploit low-frequency features, leading to lower accuracy. Introducing pre-trained token embeddings to a randomly initialized model rescues its performance. Overall, our analysis demonstrates that appropriate pre-trained representations (e.g., Fourier features) can unlock the ability of Transformers to learn precise mechanisms for algorithmic tasks.

We propose LLM-FP4 for quantizing both weights and activations in large language models (LLMs) down to 4-bit floating-point values, in a post-training manner. Existing post-training quantization (PTQ) solutions are primarily integer-based and struggle with bit widths below 8 bits. Compared to integer quantization, floating-point (FP) quantization is more flexible and can better handle long-tail or bell-shaped distributions, and it has emerged as a default choice in many hardware platforms. One characteristic of FP quantization is that its performance largely depends on the choice of exponent bits and clipping range. In this regard, we construct a strong FP-PTQ baseline by searching for the optimal quantization parameters. Furthermore, we observe a high inter-channel variance and low intra-channel variance pattern in activation distributions, which adds activation quantization difficulty. We recognize this pattern to be consistent across a spectrum of transformer models designed for diverse tasks, such as LLMs, BERT, and Vision Transformer models. To tackle this, we propose per-channel activation quantization and show that these additional scaling factors can be reparameterized as exponential biases of weights, incurring a negligible cost. Our method, for the first time, can quantize both weights and activations in the LLaMA-13B to only 4-bit and achieves an average score of 63.1 on the common sense zero-shot reasoning tasks, which is only 5.8 lower than the full-precision model, significantly outperforming the previous state-of-the-art by 12.7 points. Code is available at: https://github.com/nbasyl/LLM-FP4.

Generalizing to longer sentences is important for recent Transformer-based language models. Besides algorithms manipulating explicit position features, the success of Transformers without position encodings (NoPE) provides a new way to overcome the challenge. In this paper, we study the length generalization property of NoPE. We find that although NoPE can extend to longer sequences than the commonly used explicit position encodings, it still has a limited context length. We identify a connection between the failure of NoPE's generalization and the distraction of attention distributions. We propose a parameter-efficient tuning for searching attention heads' best temperature hyper-parameters, which substantially expands NoPE's context size. Experiments on long sequence language modeling, the synthetic passkey retrieval task and real-world long context tasks show that NoPE can achieve competitive performances with state-of-the-art length generalization algorithms. The source code is publicly accessible

Large language models (LLMs) have seen significant adoption for natural language tasks, owing their success to massive numbers of model parameters (e.g., 70B+); however, LLM inference incurs significant computation and memory costs. Recent approaches propose parallel decoding strategies, such as Skeleton-of-Thought (SoT), to improve performance by breaking prompts down into sub-problems that can be decoded in parallel; however, they often suffer from reduced response quality. Our key insight is that we can request additional information, specifically dependencies and difficulty, when generating the sub-problems to improve both response quality and performance. In this paper, we propose Skeleton Graph Decoding (SGD), which uses dependencies exposed between sub-problems to support information forwarding between dependent sub-problems for improved quality while exposing parallelization opportunities for decoding independent sub-problems. Additionally, we leverage difficulty estimates for each sub-problem to select an appropriately-sized model, improving performance without significantly reducing quality. Compared to standard autoregressive generation and SoT, SGD achieves a 1.69x speedup while improving quality by up to 51%.

This research aims to accelerate the inference speed of large language models (LLMs) with billions of parameters. We propose Smart Parallel Auto-Correct dEcoding (SPACE), an innovative approach designed for achieving lossless acceleration of LLMs. By integrating semi-autoregressive inference and speculative decoding capabilities, SPACE uniquely enables autoregressive LLMs to parallelize token generation and verification. This is realized through a specialized semi-autoregressive supervised fine-tuning process that equips existing LLMs with the ability to simultaneously predict multiple tokens. Additionally, an auto-correct decoding algorithm facilitates the simultaneous generation and verification of token sequences within a single model invocation. Through extensive experiments on a range of LLMs, SPACE has demonstrated inference speedup ranging from 2.7x-4.0x on HumanEval-X while maintaining output quality.

Parallel decoding methods such as Jacobi decoding show promise for more efficient LLM inference as it breaks the sequential nature of the LLM decoding process and transforms it into parallelizable computation. However, in practice, it achieves little speedup compared to traditional autoregressive (AR) decoding, primarily because Jacobi decoding seldom accurately predicts more than one token in a single fixed-point iteration step. To address this, we develop a new approach aimed at realizing fast convergence from any state to the fixed point on a Jacobi trajectory. This is accomplished by refining the target LLM to consistently predict the fixed point given any state as input. Extensive experiments demonstrate the effectiveness of our method, showing 2.4times to 3.4times improvements in generation speed while preserving generation quality across both domain-specific and open-domain benchmarks.

Pre-trained models for programming languages have recently demonstrated great success on code intelligence. To support both code-related understanding and generation tasks, recent works attempt to pre-train unified encoder-decoder models. However, such encoder-decoder framework is sub-optimal for auto-regressive tasks, especially code completion that requires a decoder-only manner for efficient inference. In this paper, we present UniXcoder, a unified cross-modal pre-trained model for programming language. The model utilizes mask attention matrices with prefix adapters to control the behavior of the model and leverages cross-modal contents like AST and code comment to enhance code representation. To encode AST that is represented as a tree in parallel, we propose a one-to-one mapping method to transform AST in a sequence structure that retains all structural information from the tree. Furthermore, we propose to utilize multi-modal contents to learn representation of code fragment with contrastive learning, and then align representations among programming languages using a cross-modal generation task. We evaluate UniXcoder on five code-related tasks over nine datasets. To further evaluate the performance of code fragment representation, we also construct a dataset for a new task, called zero-shot code-to-code search. Results show that our model achieves state-of-the-art performance on most tasks and analysis reveals that comment and AST can both enhance UniXcoder.

This paper studies a novel pre-training technique with unpaired speech data, Speech2C, for encoder-decoder based automatic speech recognition (ASR). Within a multi-task learning framework, we introduce two pre-training tasks for the encoder-decoder network using acoustic units, i.e., pseudo codes, derived from an offline clustering model. One is to predict the pseudo codes via masked language modeling in encoder output, like HuBERT model, while the other lets the decoder learn to reconstruct pseudo codes autoregressively instead of generating textual scripts. In this way, the decoder learns to reconstruct original speech information with codes before learning to generate correct text. Comprehensive experiments on the LibriSpeech corpus show that the proposed Speech2C can relatively reduce the word error rate (WER) by 19.2% over the method without decoder pre-training, and also outperforms significantly the state-of-the-art wav2vec 2.0 and HuBERT on fine-tuning subsets of 10h and 100h. We release our code and model at https://github.com/microsoft/SpeechT5/tree/main/Speech2C.

Deep neural networks perform well on classification tasks where data streams are i.i.d. and labeled data is abundant. Challenges emerge with non-stationary training data streams such as continual learning. One powerful approach that has addressed this challenge involves pre-training of large encoders on volumes of readily available data, followed by task-specific tuning. Given a new task, however, updating the weights of these encoders is challenging as a large number of weights needs to be fine-tuned, and as a result, they forget information about the previous tasks. In the present work, we propose a model architecture to address this issue, building upon a discrete bottleneck containing pairs of separate and learnable key-value codes. Our paradigm will be to encode; process the representation via a discrete bottleneck; and decode. Here, the input is fed to the pre-trained encoder, the output of the encoder is used to select the nearest keys, and the corresponding values are fed to the decoder to solve the current task. The model can only fetch and re-use a sparse number of these key-value pairs during inference, enabling localized and context-dependent model updates. We theoretically investigate the ability of the discrete key-value bottleneck to minimize the effect of learning under distribution shifts and show that it reduces the complexity of the hypothesis class. We empirically verify the proposed method under challenging class-incremental learning scenarios and show that the proposed model - without any task boundaries - reduces catastrophic forgetting across a wide variety of pre-trained models, outperforming relevant baselines on this task.

This paper introduces Multimodal Speculative Decoding (MSD) to accelerate Multimodal Large Language Models (MLLMs) inference. Speculative decoding has been shown to accelerate Large Language Models (LLMs) without sacrificing accuracy. However, current speculative decoding methods for MLLMs fail to achieve the same speedup as they do for LLMs. To address this, we reimagine speculative decoding specifically for MLLMs. Our analysis of MLLM characteristics reveals two key design principles for MSD: (1) Text and visual tokens have fundamentally different characteristics and need to be processed separately during drafting. (2) Both language modeling ability and visual perception capability are crucial for the draft model. For the first principle, MSD decouples text and visual tokens in the draft model, allowing each to be handled based on its own characteristics. For the second principle, MSD uses a two-stage training strategy: In stage one, the draft model is trained on text-only instruction-tuning datasets to improve its language modeling ability. In stage two, MSD gradually introduces multimodal data to enhance the visual perception capability of the draft model. Experiments show that MSD boosts inference speed by up to 2.29times for LLaVA-1.5-7B and up to 2.46times for LLaVA-1.5-13B on multimodal benchmarks, demonstrating its effectiveness. Our code is available at https://github.com/Lyn-Lucy/MSD.

The output structure of database-like tables, consisting of values structured in horizontal rows and vertical columns identifiable by name, can cover a wide range of NLP tasks. Following this constatation, we propose a framework for text-to-table neural models applicable to problems such as extraction of line items, joint entity and relation extraction, or knowledge base population. The permutation-based decoder of our proposal is a generalized sequential method that comprehends information from all cells in the table. The training maximizes the expected log-likelihood for a table's content across all random permutations of the factorization order. During the content inference, we exploit the model's ability to generate cells in any order by searching over possible orderings to maximize the model's confidence and avoid substantial error accumulation, which other sequential models are prone to. Experiments demonstrate a high practical value of the framework, which establishes state-of-the-art results on several challenging datasets, outperforming previous solutions by up to 15%.

The current large auto-regressive models can generate high-quality, high-resolution images, but these models require hundreds or even thousands of steps of next-token prediction during inference, resulting in substantial time consumption. In existing studies, Jacobi decoding, an iterative parallel decoding algorithm, has been used to accelerate the auto-regressive generation and can be executed without training. However, the Jacobi decoding relies on a deterministic criterion to determine the convergence of iterations. Thus, it works for greedy decoding but is incompatible with sampling-based decoding which is crucial for visual quality and diversity in the current auto-regressive text-to-image generation. In this paper, we propose a training-free probabilistic parallel decoding algorithm, Speculative Jacobi Decoding (SJD), to accelerate auto-regressive text-to-image generation. By introducing a probabilistic convergence criterion, our SJD accelerates the inference of auto-regressive text-to-image generation while maintaining the randomness in sampling-based token decoding and allowing the model to generate diverse images. Specifically, SJD facilitates the model to predict multiple tokens at each step and accepts tokens based on the probabilistic criterion, enabling the model to generate images with fewer steps than the conventional next-token-prediction paradigm. We also investigate the token initialization strategies that leverage the spatial locality of visual data to further improve the acceleration ratio under specific scenarios. We conduct experiments for our proposed SJD on multiple auto-regressive text-to-image generation models, showing the effectiveness of model acceleration without sacrificing the visual quality.

As recently demonstrated, Deep Neural Networks (DNN), usually trained using single precision IEEE 754 floating point numbers (binary32), can also work using lower precision. Therefore, 16-bit and 8-bit compressed format have attracted considerable attention. In this paper, we focused on two families of formats that have already achieved interesting results in compressing binary32 numbers in machine learning applications, without sensible degradation of the accuracy: bfloat and posit. Even if 16-bit and 8-bit bfloat/posit are routinely used for reducing the storage of the weights/biases of trained DNNs, the inference still often happens on the 32-bit FPU of the CPU (especially if GPUs are not available). In this paper we propose a way to decompress a tensor of bfloat/posits just before computations, i.e., after the compressed operands have been loaded within the vector registers of a vector capable CPU, in order to save bandwidth usage and increase cache efficiency. Finally, we show the architectural parameters and considerations under which this solution is advantageous with respect to the uncompressed one.

Recent studies have showcased remarkable capabilities of decoder-only models in many NLP tasks, including translation. Yet, the machine translation field has been largely dominated by encoder-decoder models based on the Transformer architecture. As a consequence, scaling laws of encoder-decoder models for neural machine translation have already been well studied, but decoder-only models have received less attention. This work explores the scaling laws of decoder-only models on the multilingual and multidomain translation task. We trained a collection of six decoder-only models, ranging from 70M to 7B parameters, on a sentence-level, multilingual and multidomain dataset. We conducted a series of experiments showing that the loss of decoder-only models can be estimated using a scaling law similar to the one discovered for large language models, but we also show that this scaling law has difficulties to generalize to too large models or to a different data distribution. We also study different scaling methods and show that scaling the depth and the width of a model lead to similar test loss improvements, but with different impact on the model's efficiency.

In this paper, we prove representation bottlenecks of a cascaded convolutional decoder network, considering the capacity of representing different frequency components of an input sample. We conduct the discrete Fourier transform on each channel of the feature map in an intermediate layer of the decoder network. Then, we introduce the rule of the forward propagation of such intermediate-layer spectrum maps, which is equivalent to the forward propagation of feature maps through a convolutional layer. Based on this, we find that each frequency component in the spectrum map is forward propagated independently with other frequency components. Furthermore, we prove two bottlenecks in representing feature spectrums. First, we prove that the convolution operation, the zero-padding operation, and a set of other settings all make a convolutional decoder network more likely to weaken high-frequency components. Second, we prove that the upsampling operation generates a feature spectrum, in which strong signals repetitively appears at certain frequencies.

Transformers have impressive generalization capabilities on tasks with a fixed context length. However, they fail to generalize to sequences of arbitrary length, even for seemingly simple tasks such as duplicating a string. Moreover, simply training on longer sequences is inefficient due to the quadratic computation complexity of the global attention mechanism. In this work, we demonstrate that this failure mode is linked to positional encodings being out-of-distribution for longer sequences (even for relative encodings) and introduce a novel family of positional encodings that can overcome this problem. Concretely, our randomized positional encoding scheme simulates the positions of longer sequences and randomly selects an ordered subset to fit the sequence's length. Our large-scale empirical evaluation of 6000 models across 15 algorithmic reasoning tasks shows that our method allows Transformers to generalize to sequences of unseen length (increasing test accuracy by 12.0% on average).

What is the computational model behind a Transformer? Where recurrent neural networks have direct parallels in finite state machines, allowing clear discussion and thought around architecture variants or trained models, Transformers have no such familiar parallel. In this paper we aim to change that, proposing a computational model for the transformer-encoder in the form of a programming language. We map the basic components of a transformer-encoder -- attention and feed-forward computation -- into simple primitives, around which we form a programming language: the Restricted Access Sequence Processing Language (RASP). We show how RASP can be used to program solutions to tasks that could conceivably be learned by a Transformer, and how a Transformer can be trained to mimic a RASP solution. In particular, we provide RASP programs for histograms, sorting, and Dyck-languages. We further use our model to relate their difficulty in terms of the number of required layers and attention heads: analyzing a RASP program implies a maximum number of heads and layers necessary to encode a task in a transformer. Finally, we see how insights gained from our abstraction might be used to explain phenomena seen in recent works.

The decoding algorithm is critical for open-ended text generation, transforming latent representations into coherent and meaningful outputs. This paper investigates the self-reinforcement effect in text generation and the effectiveness of a repetition penalty to mitigate it. However, determining the optimal repetition penalty value is challenging. To tackle this, we propose a forgetting mechanism that disregards distant tokens, reducing the burden of penalty selection. In addition, we introduce a length penalty to address overly short sentences caused by excessive penalties. Our penalty decoding approach incorporating three strategies helps resolve issues with sampling methods deviating from factual information. Experimental results demonstrate the efficacy of our approach in generating high-quality sentences resembling human output.

Large Language Models (LLMs) typically have billions of parameters and are thus often difficult to interpret in their operation. Such black-box models can pose a significant risk to safety when trusted to make important decisions. The lack of interpretability of LLMs is more related to their sheer size, rather than the complexity of their individual components. The TARS method for knowledge removal (Davies et al 2024) provides strong evidence for the hypothesis that that linear layer weights which act directly on the residual stream may have high correlation with different concepts encoded in the residual stream. Building upon this, we attempt to decode neuron weights directly into token probabilities through the final projection layer of the model (the LM-head). Firstly, we show that with Llama 3.1 8B we can utilise the LM-head to decode specialised feature neurons that respond strongly to certain concepts, with examples such as "dog" and "California". This is then confirmed by demonstrating that these neurons can be clamped to affect the probability of the concept in the output. This extends to the fine-tuned assistant Llama 3.1 8B instruct model, where we find that over 75% of neurons in the up-projection layers have the same top associated token compared to the pretrained model. Finally, we demonstrate that clamping the "dog" neuron leads the instruct model to always discuss dogs when asked about its favourite animal. Through our method, it is possible to map the entirety of Llama 3.1 8B's up-projection neurons in less than 15 minutes with no parallelization.