GenAI4ELab/papercli-papers huggingface dataset:
Discretization-invariance? On the Discretization Mismatch Errors in Neural Operators
Authors: Wenhan Gao; Ruichen Xu; Yuefan Deng; Yi Liu
Venue: ICLR 2025 (ICLR 2025 Poster)

Abstract: In recent years, neural operators have emerged as a prominent approach for learning mappings between function spaces, such as the solution operators of parametric PDEs. A notable example is the Fourier Neural Operator (FNO), which models the integral kernel as a convolution operator and uses the Convolution Theorem to learn the kernel directly in the frequency domain. The parameters are decoupled from the resolution of the data, allowing the FNO to take inputs of different resolutions.
However, training at a lower resolution and inferring at a finer resolution does not guarantee consistent performance, nor can fine details, present only in fine-scale data, be learned solely from coarse data. In this work, we address this misconception by defining and examining the discretization mismatch error: the discrepancy between the outputs of the neural operator when using different discretizations of the input data. We demonstrate that neural operators may suffer from discretization mismatch errors that hinder their effectiveness when inferred on data with resolutions different from that of the training data or when trained on data with varying resolutions. As neural operators underpin many critical cross-resolution scientific tasks, such as climate modeling and fluid dynamics, understanding discretization mismatch errors is essential. Based on our findings, we propose a Cross-Resolution Operator-learning Pipeline that is free of aliasing and discretization mismatch errors, enabling efficient cross-resolution and multi-spatial-scale learning, and resulting in superior performance.
(Mis)Fitting Scaling Laws: A Survey of Scaling Law Fitting Techniques in Deep Learning
Authors: Margaret Li; Sneha Kudugunta; Luke Zettlemoyer
Venue: ICLR 2025 (ICLR 2025 Poster)

Abstract: Modern foundation models rely heavily on using scaling laws to guide crucial training decisions. Researchers often extrapolate the optimal architecture and hyper parameters settings from smaller training runs by describing the relationship between, loss, or task performance, and scale. All components of this process vary, from the specific equation being fit, to the training setup, to the optimization method. Each of these factors may affect the fitted law, and therefore, the conclusions of a given study. We discuss discrepancies in the conclusions that several prior works reach, on questions such as the optimal token to parameter ratio. We augment this discussion with our own analysis of the critical impact that changes in specific details may effect in a scaling study, and the resulting altered conclusions. Additionally, we survey over 50 papers that study scaling trends: while 45 of these papers quantify these trends using a power law, most under-report crucial details needed to reproduce their findings. To mitigate this, we we propose a checklist for authors to consider while contributing to scaling law research.
Semantic Aware Representation Learning for Lifelong Learning
Authors: Fahad Sarfraz; Elahe Arani; Bahram Zonooz
Venue: ICLR 2025 (ICLR 2025 Poster)

Abstract: The human brain excels at lifelong learning by not only encoding information in sparse activation codes but also leveraging rich semantic structures and relationships between newly encountered and previously learned objects. This ability to utilize semantic similarities is crucial for efficient learning and knowledge consolidation, yet is often underutilized in current continual learning approaches. To bridge this gap, we propose Semantic-Aware Representation Learning (SARL) which employs sparse activations and a principled approach to evaluate similarities between objects encountered across different tasks and subsequently uses them to guide representation learning. Using these relationships, SARL enhances the reusability of features and reduces interference between tasks. This approach empowers the model to adapt to new information while maintaining stability, significantly improving performance in complex incremental learning scenarios. Our analysis demonstrates that SARL achieves a superior balance between plasticity and stability by harnessing the underlying semantic structure.
Singular Subspace Perturbation Bounds via Rectangular Random Matrix Diffusions
Authors: Peiyao Lai; Oren Mangoubi
Venue: ICLR 2025 (ICLR 2025 Poster)

Abstract: Given a matrix $A \in \mathbb{R}^{m\times d}$ with singular values $\sigma_1\geq \cdots \geq \sigma_d$, and a random matrix $G \in \mathbb{R}^{m\times d}$ with iid $N(0,T)$ entries for some $T>0$, we derive  new bounds on the Frobenius distance between subspaces spanned by the top-$k$ (right) singular vectors of $A$ and $A+G$. This problem arises in numerous applications in statistics where a data matrix may be corrupted by Gaussian noise, and in the analysis of the Gaussian mechanism in differential privacy, where Gaussian noise is added to data to preserve private information. We show that, for matrices $A$ where the gaps in the top-$k$ singular values are roughly $\Omega(\sigma_k-\sigma_{k+1})$ the expected Frobenius distance between the subspaces is $\tilde{O}(\frac{\sqrt{d}}{\sigma_k-\sigma_{k+1}} \times \sqrt{T})$, improving on previous bounds by a factor of $\frac{\sqrt{m}}{\sqrt{d}}$. To obtain our bounds we view the perturbation to the singular vectors as a diffusion process-- the Dyson-Bessel process-- and use tools from stochastic calculus to track the evolution of the subspace spanned by the top-$k$ singular vectors, which may be of independent interest.
LeanAgent: Lifelong Learning for Formal Theorem Proving
Authors: Adarsh Kumarappan; Mo Tiwari; Peiyang Song; Robert Joseph George; Chaowei Xiao; Anima Anandkumar
Venue: ICLR 2025 (ICLR 2025 Poster)

Abstract: Large Language Models (LLMs) have been successful in mathematical reasoning tasks such as formal theorem proving when integrated with interactive proof assistants like Lean. Existing approaches involve training or fine-tuning an LLM on a specific dataset to perform well on particular domains, such as undergraduate-level mathematics. These methods struggle with generalizability to advanced mathematics. A fundamental limitation is that these approaches operate on static domains, failing to capture how mathematicians often work across multiple domains and projects simultaneously or cyclically. We present LeanAgent, a novel lifelong learning framework for formal theorem proving that continuously generalizes to and improves on ever-expanding mathematical knowledge without forgetting previously learned knowledge. LeanAgent introduces several key innovations, including a curriculum learning strategy that optimizes the learning trajectory in terms of mathematical difficulty, a dynamic database for efficient management of evolving mathematical knowledge, and progressive training to balance stability and plasticity. LeanAgent successfully generates formal proofs for 155 theorems across 23 diverse Lean repositories where formal proofs were previously missing, many from advanced mathematics. It performs significantly better than the static LLM baseline, proving challenging theorems in domains like abstract algebra and algebraic topology while showcasing a clear progression of learning from basic concepts to advanced topics. In addition, we analyze LeanAgent's superior performance on key lifelong learning metrics. LeanAgent achieves exceptional scores in stability and backward transfer, where learning new tasks improves performance on previously learned tasks. This emphasizes LeanAgent's continuous generalizability and improvement, explaining its superior theorem-proving performance.
Multilevel Generative Samplers for Investigating Critical Phenomena
Authors: Ankur Singha; Elia Cellini; Kim Andrea Nicoli; Karl Jansen; Stefan Kühn; Shinichi Nakajima
Venue: ICLR 2025 (ICLR 2025 Poster)

Abstract: Investigating critical phenomena or phase transitions is of high interest in physics and chemistry, for which Monte Carlo (MC) simulations, a crucial tool for numerically analyzing macroscopic properties of given systems, are often hindered by an emerging divergence of correlation length---known as scale invariance at criticality (SIC) in the renormalization group theory.  SIC causes the system to behave the same at any length scale, from which many existing sampling methods suffer: long-range correlations cause critical slowing down in Markov chain Monte Carlo (MCMC), and require intractably large receptive fields for generative samplers. In this paper, we propose a Renormalization-informed Generative Critical Sampler (RiGCS)---a novel sampler specialized for near-critical systems, where SIC is leveraged as an advantage rather than a nuisance. Specifically, RiGCS builds on MultiLevel Monte Carlo (MLMC) with Heat Bath (HB) algorithms, which perform ancestral sampling from low-resolution to high-resolution lattice configurations with site wise-independent conditional HB sampling.  Although MLMC-HB is highly efficient under exact SIC, it suffers from a low acceptance rate under slight SIC violation. Notably, SIC violation always occurs in finite-size systems, and may induce long-range and higher-order interactions in the renormalized distributions, which are not considered by independent HB samplers.  RiGCS enhances MLMC-HB by replacing a part of the conditional HB sampler with generative models that capture those residual interactions and improve the sampling efficiency. Our experiments show that the effective sample size of RiGCS is a few orders of magnitude higher than state-of-the-art generative model baselines in sampling configurations for $128 \times 128$ two-dimensional Ising systems.  SIC also allows us to adopt a specialized sequential training protocol with model transfer, which significantly accelerates training.
Certifying Counterfactual Bias in LLMs
Authors: Isha Chaudhary; Qian Hu; Manoj Kumar; Morteza Ziyadi; Rahul Gupta; Gagandeep Singh
Venue: ICLR 2025 (ICLR 2025 Poster)

Abstract: Large Language Models (LLMs) can produce biased responses that can cause representational harms. However, conventional studies are insufficient to thoroughly
evaluate biases across LLM responses for different demographic groups (a.k.a.
counterfactual bias), as they do not scale to large number of inputs and do not
provide guarantees. Therefore, we propose the first framework, LLMCert-B that
certifies LLMs for counterfactual bias on distributions of prompts. A certificate
consists of high-confidence bounds on the probability of unbiased LLM responses
for any set of counterfactual prompts - prompts differing by demographic groups,
sampled from a distribution. We illustrate counterfactual bias certification for
distributions of counterfactual prompts created by applying prefixes sampled from
prefix distributions, to a given set of prompts. We consider prefix distributions consisting random token sequences, mixtures of manual jailbreaks, and perturbations
of jailbreaks in LLM’s embedding space. We generate non-trivial certificates for
SOTA LLMs, exposing their vulnerabilities over distributions of prompts generated
from computationally inexpensive prefix distributions.
Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces
Authors: Saket Tiwari; Omer Gottesman; George Konidaris
Venue: ICLR 2025 (ICLR 2025 Oral)

Abstract: Advances in reinforcement learning (RL) have led to its successful application in complex tasks with continuous state and action spaces. Despite these advances in practice, most theoretical work pertains to finite state and action spaces. We propose building a theoretical understanding of continuous state and action spaces by employing a geometric lens to understand the locally attained set of states. The set of all parametrised policies learnt through a semi-gradient based approach induce a set of attainable states in RL. We show that training dynamics of a two layer neural policy induce a low dimensional manifold of attainable states embedded in the high-dimensional nominal state space trained using an actor-critic algorithm. We prove that, under certain conditions, the dimensionality of this manifold is of the order of the dimensionality of the action space. This is the first result of its kind, linking the geometry of the state space to the dimensionality of the action space. We empirically corroborate this upper bound for four MuJoCo environments and also demonstrate the results in a toy environment with varying dimensionality. We also show the applicability of this theoretical result by introducing a local manifold learning layer to the policy and value function networks to improve the performance in control environments with very high degrees of freedom by changing one layer of the neural network to learn sparse representations.
Not All Heads Matter: A Head-Level KV Cache Compression Method with Integrated Retrieval and Reasoning
Authors: Yu Fu; Zefan Cai; Abedelkadir Asi; Wayne Xiong; Yue Dong; Wen Xiao
Venue: ICLR 2025 (ICLR 2025 Poster)

Abstract: Key-Value (KV) caching is a common technique to enhance the computational efficiency of Large Language Models (LLMs), but its memory overhead grows rapidly with input length. Prior work has shown that not all tokens are equally important for text generation, proposing layer-level KV cache compression to selectively retain key information. Recognizing the distinct roles of attention heads in generation, we propose HeadKV, a head-level KV cache compression method, and HeadKV-R2, which leverages a novel contextual reasoning ability estimation for compression. Our approach operates at the level of individual heads, estimating their importance for contextual QA tasks that require both retrieval and reasoning capabilities. Extensive experiments across diverse benchmarks (LongBench, LooGLE), model architectures (e.g., Llama-3-8B-Instruct, Mistral-7B-Instruct), and long-context abilities tests demonstrate that our head-level KV cache compression significantly outperforms strong baselines, particularly in low-resource settings (KV size = 64 & 128). Notably, our method retains just 1.5% of the KV cache while achieving 97% of the performance of the full KV cache on the contextual question answering benchmark.
Preble: Efficient Distributed Prompt Scheduling for LLM Serving
Authors: Vikranth Srivatsa; Zijian He; Reyna Abhyankar; Dongming Li; Yiying Zhang
Venue: ICLR 2025 (ICLR 2025 Poster)

Abstract: Prompts to large language models (LLMs) have evolved beyond simple user questions.
For LLMs to solve complex problems, today’s practices are to include domain-specific
instructions, illustration of tool usages, and/or long context such as textbook chapters in
prompts. As such, many parts of prompts are repetitive across requests. Recent works
propose to cache and reuse KV state of prompts. However, they are all confined to a single-
GPU optimization, while production LLM serving systems are distributed by nature.

This paper proposes Preble, the first distributed LLM serving platform that targets and op-
timizes for prompt sharing. We designed a distributed scheduling system that co-optimizes
KV state reuse and computation load-balancing with a new scheduling algorithm and a
hierarchical scheduling mechanism. Our evaluation of Preble with real workloads and re-
quest arrival patterns on two open-source LLMs shows that Preble outperforms the SOTA
serving systems by 1.5× to 14.5× on average latency and 2× to 10× on p99 latency.
Sufficient Context: A New Lens on Retrieval Augmented Generation Systems
Authors: Hailey Joren; Jianyi Zhang; Chun-Sung Ferng; Da-Cheng Juan; Ankur Taly; Cyrus Rashtchian
Venue: ICLR 2025 (ICLR 2025 Poster)

Abstract: Augmenting LLMs with context leads to improved performance across many applications. Despite much research on Retrieval Augmented Generation (RAG) systems, an open question is whether errors arise because LLMs fail to utilize the context from retrieval or the context itself is insufficient to answer the query. To shed light on this, we develop a new notion of sufficient context, along with a method to classify instances that have enough information to answer the query. We then use sufficient context to analyze several models and datasets. By stratifying errors based on context sufficiency, we find that larger models with higher baseline performance (Gemini 1.5 Pro, GPT 4o, Claude 3.5) excel at answering queries when the context is sufficient, but often output incorrect answers instead of abstaining when the context is not. On the other hand, smaller models with lower baseline performance (Llama 3.1, Mistral 3, Gemma 2) hallucinate or abstain often, even with sufficient context. We further categorize cases when the context is useful, and improves accuracy, even though it does not fully answer the query and the model errs without the context. Building on our findings, we explore ways to reduce hallucinations in RAG systems, including a new selective generation method that leverages sufficient context information for guided abstention. Our method improves the fraction of correct answers among times where the model responds by 2--10% for Gemini, GPT, and Gemma. Code for our selective generation method and the prompts used in our autorater analysis are available on our [github](https://github.com/hljoren/sufficientcontext).
Exploratory Preference Optimization: Harnessing Implicit Q*-Approximation for Sample-Efficient RLHF
Authors: Tengyang Xie; Dylan J Foster; Akshay Krishnamurthy; Corby Rosset; Ahmed Hassan Awadallah; Alexander Rakhlin
Venue: ICLR 2025 (ICLR 2025 Poster)

Abstract: This paper investigates a basic question in reinforcement learning from human feedback (RLHF) from a theoretical perspective: how to efficiently explore in an online manner under preference feedback and general function approximation. We take the initial step towards a theoretical understanding of this problem by proposing a novel algorithm, *Exploratory Preference Optimization* (XPO). This algorithm is elegantly simple---requiring only a one-line modification to (online) Direct Preference Optimization  (DPO; Rafailov et al., 2023)---yet provides the strongest known provable guarantees. XPO augments the DPO objective with a novel and principled *exploration bonus*, enabling the algorithm to strategically explore beyond the support of the initial model and preference feedback data. We prove that XPO is provably sample-efficient and converges to a near-optimal policy under natural exploration conditions, regardless of the initial model's coverage. Our analysis builds on the observation that DPO implicitly performs a form of *Bellman error minimization*. It synthesizes previously disparate techniques from language modeling and theoretical reinforcement learning in a serendipitous fashion through the lens of *KL-regularized Markov decision processes*.
MoLEx: Mixture of Layer Experts for Fine-tuning with Sparse Upcycling
Authors: Rachel Teo; Tan Minh Nguyen
Venue: ICLR 2025 (ICLR 2025 Poster)

Abstract: Large-scale pre-training of deep models, followed by fine-tuning them to adapt to downstream tasks, has become the cornerstone of natural language processing (NLP). The prevalence of vast corpses of data coupled with computational resources has led to large models with a considerable number of parameters. While the massive size of these models has led to remarkable success in many NLP tasks, a detriment is the expense required to retrain all the base model's parameters for the adaptation to each task or domain. Parameter Efficient Fine-Tuning (PEFT) provides a highly effective solution for this challenge by minimizing the number of parameters required to be trained in adjusting to the new task while maintaining the quality of the model. While existing methods have achieved impressive results, they mainly focus on adapting a subset of parameters using adapters, weight reparameterization, and prompt engineering. In this paper, we study layers as extractors of different types of linguistic information that are valuable when used in conjunction with each other. We then propose the Mixture of Layer Experts (MoLEx), a novel Sparse Mixture of Experts (SMoE) whose experts are layers in the pre-trained model. In particular, MoLEx is applied at each layer of the pre-trained model. It performs a conditional computation of a mixture of layers during fine-tuning to provide the model with more structural knowledge about the data. By providing an avenue for information exchange between layers, MoLEx enables the model to make a more well-informed prediction for the downstream task, leading to better fine-tuning results with the same number of effective parameters. As experts can be processed in parallel, MoLEx introduces minimal additional computational overhead. We empirically corroborate the advantages of MoLEx when combined with popular PEFT baseline methods on a variety of downstream fine-tuning tasks, including the popular GLUE benchmark for natural language understanding (NLU) as well as the natural language generation (NLG) End-to-End Challenge (E2E).
Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallel
Authors: Shivam Gupta; Linda Cai; Sitan Chen
Venue: ICLR 2025 (ICLR 2025 Poster)

Abstract: Sampling algorithms play an important role in controlling the quality and runtime of diffusion model inference. In recent years, a number of works (Chen et al., 2023c;b; Benton et al., 2023; Lee et al., 2022) have analyzed algorithms for diffusion sampling with provable guarantees; these works show that for essentially any data distribution, one can approximately sample in polynomial time given a sufficiently accurate estimate of its score functions at different noise levels. 

In this work, we propose a new scheme inspired by Shen and Lee's randomized midpoint method for log-concave sampling  (Shen & Lee, 2019). We prove that this approach achieves the best known dimension dependence for sampling from arbitrary smooth distributions in total variation distance ($\widetilde O(d^{5/12})$ compared to $\widetilde O(\sqrt{d})$ from prior work). We also show that our algorithm can be parallelized to run in only $\widetilde O(\log^2 d)$ parallel rounds, constituting the first provable guarantees for parallel sampling with diffusion models.
    
As a byproduct of our methods, for the well-studied problem of log-concave sampling in total variation distance, we give an algorithm and simple analysis achieving dimension dependence $\widetilde O(d^{5/12})$ compared to $\widetilde O(\sqrt{d})$ from prior work.
X-ALMA: Plug & Play Modules and Adaptive Rejection for Quality Translation at Scale
Authors: Haoran Xu; Kenton Murray; Philipp Koehn; Hieu Hoang; Akiko Eriguchi; Huda Khayrallah
Venue: ICLR 2025 (ICLR 2025 Spotlight)

Abstract: Large language models (LLMs) have achieved remarkable success across various NLP tasks with a focus on English due to English-centric pre-training and limited multilingual data. In this work, we focus on the problem of translation, and 
while some multilingual LLMs claim to support for hundreds of languages, models often fail to provide high-quality responses for mid- and low-resource languages, leading to imbalanced performance heavily skewed in favor of high-resource languages. We introduce **X-ALMA**, a model designed to ensure top-tier performance across 50 diverse languages, regardless of their resource levels. X-ALMA surpasses state-of-the-art open-source multilingual LLMs, such as Aya-101 and Aya-23, in every single translation direction on the FLORES-200 and WMT'23 test datasets according to COMET-22. This is achieved by plug-and-play language-specific module architecture to prevent language conflicts during training and a carefully designed training regimen with novel optimization methods to maximize the translation performance. After the final stage of training regimen, our proposed **A**daptive **R**ejection **P**reference **O**ptimization (**ARPO**) surpasses existing preference optimization methods in translation tasks.