GenAI4ELab/papercli-papers huggingface dataset:
Provable Guarantees for Nonlinear Feature Learning in Three-Layer Neural Networks
Authors: Eshaan Nichani; Alex Damian; Jason D. Lee
Venue: NeurIPS 2023 (NeurIPS 2023 spotlight)

Abstract: One of the central questions in the theory of deep learning is to understand how neural networks learn hierarchical features. The ability of deep networks to extract salient features is crucial to both their outstanding generalization ability and the modern deep learning paradigm of pretraining and finetuneing. However, this feature learning process remains poorly understood from a theoretical perspective, with existing analyses largely restricted to two-layer networks. In this work we show that three-layer neural networks have provably richer feature learning capabilities than two-layer networks. We analyze the features learned by a three-layer network trained with layer-wise gradient descent, and present a general purpose theorem which upper bounds the sample complexity and width needed to achieve low test error when the target has specific hierarchical structure. We instantiate our framework in specific statistical learning settings -- single-index models and functions of quadratic features -- and show that in the latter setting three-layer networks obtain a sample complexity improvement over all existing guarantees for two-layer networks. Crucially, this sample complexity improvement relies on the ability of three-layer networks to efficiently learn *nonlinear* features. We then establish a concrete optimization-based depth separation by constructing a function which is efficiently learnable via gradient descent on a three-layer network, yet cannot be learned efficiently by a two-layer network. Our work makes progress towards understanding the provable benefit of three-layer neural networks over two-layer networks in the feature learning regime.
Clustering the Sketch: Dynamic Compression for Embedding Tables
Authors: Henry Tsang; Thomas Dybdahl Ahle
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: Embedding tables are used by machine learning systems  to work with categorical features.
In modern Recommendation Systems, these tables can be very large, necessitating the development of new methods for fitting them in memory, even during training.
We suggest Clustered Compositional Embeddings (CCE) which combines clustering-based compression like quantization to codebooks with dynamic methods like The Hashing Trick and Compositional Embeddings [Shi et al., 2020].
Experimentally CCE achieves the best of both worlds: The high compression rate of codebook-based quantization, but \emph{dynamically} like hashing-based methods, so it can be used during training.
Theoretically, we prove that CCE is guaranteed to converge to the optimal codebook and give a tight bound for the number of iterations required.
Inconsistency, Instability, and Generalization Gap of Deep Neural Network Training
Authors: Rie Johnson; Tong Zhang
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: As deep neural networks are highly expressive, it is important to find solutions with small generalization gap (the difference between the performance on the training data and unseen data).  Focusing on the stochastic nature of training, we first present a theoretical analysis in which the bound of generalization gap depends on what we call inconsistency and instability of model outputs, which can be estimated on unlabeled data.  Our empirical study based on this analysis shows that instability and inconsistency are strongly predictive of generalization gap in various settings.  In particular, our finding indicates that inconsistency is a more reliable indicator of generalization gap than the sharpness of the loss landscape.  Furthermore, we show that algorithmic reduction of inconsistency leads to superior performance.  The results also provide a theoretical basis for existing methods such as co-distillation and ensemble.
Finite-Time Logarithmic Bayes Regret Upper Bounds
Authors: Alexia Atsidakou; Branislav Kveton; Sumeet Katariya; Constantine Caramanis; sujay sanghavi
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: We derive the first finite-time logarithmic Bayes regret upper bounds for Bayesian bandits. In a multi-armed bandit, we obtain $O(c_\Delta \log n)$ and $O(c_h \log^2 n)$ upper bounds for an upper confidence bound algorithm, where $c_h$ and $c_\Delta$ are constants depending on the prior distribution and the gaps of bandit instances sampled from it, respectively. The latter bound asymptotically matches the lower bound of Lai (1987). Our proofs are a major technical departure from prior works, while being simple and general. To show the generality of our techniques, we apply them to linear bandits. Our results provide insights on the value of prior in the Bayesian setting, both in the objective and as a side information given to the learner. They significantly improve upon existing $\tilde{O}(\sqrt{n})$ bounds, which have become standard in the literature despite the logarithmic lower bound of Lai (1987).
Adversarial Resilience in Sequential Prediction via Abstention
Authors: Surbhi Goel; Steve Hanneke; Shay Moran; Abhishek Shetty
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: We study the problem of sequential prediction in the stochastic setting with an adversary that is allowed to inject clean-label adversarial (or out-of-distribution) examples. Algorithms designed to handle purely stochastic data tend to fail in the presence of such adversarial examples, often leading to erroneous predictions. This is undesirable in many high-stakes applications such as medical recommendations, where abstaining from predictions on adversarial examples is preferable to misclassification. On the other hand, assuming fully adversarial data leads to very pessimistic bounds that are often vacuous in practice. 
  
  To move away from these pessimistic guarantees, we propose a new model of sequential prediction that sits between the purely stochastic and fully adversarial settings by allowing the learner to abstain from making a prediction at no cost on adversarial examples, thereby asking the learner to make predictions with certainty. Assuming access to the marginal distribution on the non-adversarial examples, we design a learner whose error scales with the VC dimension (mirroring the stochastic setting) of the hypothesis class, as opposed to the Littlestone dimension which characterizes the fully adversarial setting. Furthermore, we design learners for VC dimension~1 classes and the class of axis-aligned rectangles, which work even in the absence of access to the marginal distribution. Our key technical contribution is a novel measure for quantifying uncertainty for learning VC classes, which may be of independent interest.
Hardness of Low Rank Approximation of Entrywise Transformed Matrix Products
Authors: Tamas Sarlos; Xingyou Song; David Woodruff; Qiuyi Zhang
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: Inspired by fast algorithms in natural language processing, we study low rank approximation in the entrywise transformed setting where we want to find a good rank $k$ approximation to $f(U \cdot V)$, where $U, V^\top \in \mathbb{R}^{n \times r}$ are given, $r = O(\log(n))$, and $f(x)$ is a general scalar function. Previous work in sublinear low rank approximation has shown that if both (1) $U = V^\top$ and (2) $f(x)$ is a PSD kernel function, then there is an $O(nk^{\omega-1})$ time constant relative error approximation algorithm, where $\omega \approx 2.376$ is the exponent of matrix multiplication. We give the first conditional time hardness results for this problem, demonstrating that both conditions (1) and (2) are in fact necessary for getting better than $n^{2-o(1)}$ time for a relative error low rank approximation for a wide class of functions. We give novel reductions from the Strong Exponential Time Hypothesis (SETH) that rely on lower bounding the leverage scores of flat sparse vectors and hold even when the rank of the transformed matrix $f(UV)$ and the target rank are $n^{o(1)}$, and when $U = V^\top$. Furthermore, even when $f(x) = x^p$ is a simple polynomial, we give runtime lower bounds in the case when $U \neq V^\top$ of the form $\Omega(\min(n^{2-o(1)}, \Omega(2^p)))$. Lastly, we demonstrate that our lower bounds are tight by giving an $O(n \cdot \text{poly}(k, 2^p, 1/\epsilon))$ time relative error approximation algorithm and a fast $O(n \cdot \text{poly}(k, p, 1/\epsilon))$ additive error approximation using fast tensor-based sketching. Additionally, since our low rank algorithms rely on matrix-vector product subroutines, our lower bounds extend to show that computing $f(UV)W$, for even a small matrix $W$, requires $\Omega(n^{2-o(1)})$ time.
Front-door Adjustment Beyond Markov Equivalence with Limited Graph Knowledge
Authors: Abhin Shah; Karthikeyan Shanmugam; Murat Kocaoglu
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: Causal effect estimation from data typically requires assumptions about the cause-effect relations either explicitly in the form of a causal graph structure within the Pearlian framework, or implicitly in terms of (conditional) independence statements between counterfactual variables within the potential outcomes framework. When the treatment variable and the outcome variable are confounded, front-door adjustment is an important special case where, given the graph, causal effect of the treatment on the target can be estimated using post-treatment variables. However, the exact formula for front-door adjustment depends on the structure of the graph, which is difficult to learn in practice. In this work, we provide testable conditional independence statements to compute the causal effect using front-door-like adjustment without knowing the graph under limited structural side information. We show that our method is applicable in scenarios where knowing the Markov equivalence class is not sufficient for causal effect estimation. We demonstrate the effectiveness of our method on a class of random graphs as well as real causal fairness benchmarks.
Balancing memorization and generalization in RNNs for high performance brain-machine Interfaces
Authors: Joseph T Costello; Hisham Temmar; Luis H Cubillos; Matthew J Mender; Dylan M Wallace; Matthew S Willsey; Parag G Patil; Cynthia Chestek
Venue: NeurIPS 2023 (NeurIPS 2023 spotlight)

Abstract: Brain-machine interfaces (BMIs) can restore motor function to people with paralysis but are currently limited by the accuracy of real-time decoding algorithms. Recurrent neural networks (RNNs) using modern training techniques have shown promise in accurately predicting movements from neural signals but have yet to be rigorously evaluated against other decoding algorithms in a closed-loop setting. Here we compared RNNs to other neural network architectures in real-time, continuous decoding of finger movements using intracortical signals from nonhuman primates. Across one and two finger online tasks, LSTMs (a type of RNN) outperformed convolutional and transformer-based neural networks, averaging 18% higher throughput than the convolution network. On simplified tasks with a reduced movement set, RNN decoders were allowed to memorize movement patterns and matched able-bodied control. Performance gradually dropped as the number of distinct movements increased but did not go below fully continuous decoder performance. Finally, in a two-finger task where one degree-of-freedom had poor input signals, we recovered functional control using RNNs trained to act both like a movement classifier and continuous decoder. Our results suggest that RNNs can enable functional real-time BMI control by learning and generating accurate movement patterns.
Understanding and Mitigating Copying in Diffusion Models
Authors: Gowthami Somepalli; Vasu Singla; Micah Goldblum; Jonas Geiping; Tom Goldstein
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: Images generated by diffusion models like Stable Diffusion are increasingly widespread. Recent works and even lawsuits have shown that these models are prone to replicating their training data, unbeknownst to the user. In this paper, we first analyze this memorization problem in text-to-image diffusion models.  While it is widely believed that duplicated images in the training set are responsible for content replication at inference time, we observe that the text conditioning of the model plays a similarly important role. In fact, we see in our experiments that data replication often does not happen for unconditional models, while it is common in the text-conditional case. Motivated by our findings, we then propose several techniques for reducing data replication at both training and inference time by randomizing and augmenting image captions in the training set. Code is available at https://github.com/somepago/DCR.
Bootstrapping Vision-Language Learning with Decoupled Language Pre-training
Authors: Yiren Jian; Chongyang Gao; Soroush Vosoughi
Venue: NeurIPS 2023 (NeurIPS 2023 spotlight)

Abstract: We present a novel methodology aimed at optimizing the application of frozen large language models (LLMs) for resource-intensive vision-language (VL) pre-training. The current paradigm uses visual features as prompts to guide language models, with a focus on determining the most relevant visual features for corresponding text. Our approach diverges by concentrating on the language component, specifically identifying the optimal prompts to align with visual features. We introduce the Prompt-Transformer (P-Former), a model that predicts these ideal prompts, which is trained exclusively on linguistic data, bypassing the need for image-text pairings. This strategy subtly bifurcates the end-to-end VL training process into an additional, separate stage. Our experiments reveal that our framework significantly enhances the performance of a robust image-to-text baseline (BLIP-2), and effectively narrows the performance gap between models trained with either 4M or 129M image-text pairs. Importantly, our framework is modality-agnostic and flexible in terms of architectural design, as validated by its successful application in a video learning task using varied base modules. The code will be made available at https://github.com/yiren-jian/BLIText.
On Generalization Bounds for Projective Clustering
Authors: Maria Sofia Bucarelli; Matilde Fjeldsø Larsen; Chris Schwiegelshohn; Mads Toftrup
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: Given a set of points, clustering consists of finding a partition of a point set into $k$ clusters such that the center to which a point is assigned is as close as possible. Most commonly, centers are points themselves, which leads to the famous $k$-median and $k$-means objectives. One may also choose centers to be $j$ dimensional subspaces, which gives rise to subspace clustering. In this paper, we consider learning bounds for these problems. That is, given a set of $n$ samples $P$ drawn independently from some unknown, but fixed distribution $\mathcal{D}$, how quickly does a solution computed on $P$ converge to the optimal clustering of $\mathcal{D}$?
We give several near optimal results. In particular,
 1. For center-based objectives, we show a convergence rate of $\tilde{O}\left(\sqrt{{k}/{n}}\right)$. This matches the known optimal bounds of [Fefferman, Mitter, and Narayanan, Journal of the Mathematical Society 2016] and [Bartlett, Linder, and Lugosi, IEEE Trans. Inf. Theory 1998] for $k$-means and extends it to other important objectives such as $k$-median.
 2. For subspace clustering with $j$-dimensional subspaces, we show a convergence rate of $\tilde{O}\left(\sqrt{{(kj^2)}/{n}}\right)$. These are the first provable bounds for most of these problems. For the specific case of projective clustering, which generalizes $k$-means, we show a converge rate of $\Omega\left(\sqrt{{(kj)}/{n}}\right)$ is necessary, thereby proving that the bounds from [Fefferman, Mitter, and Narayanan, Journal of the Mathematical Society 2016] are essentially optimal.
A Combinatorial Algorithm for Approximating the Optimal Transport in the Parallel and MPC Settings
Authors: Nathaniel Lahn; Sharath Raghvendra; Kaiyi Zhang
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: Optimal Transport is a popular distance metric for measuring similarity between distributions. Exact and approximate combinatorial algorithms for computing the optimal transport distance are hard to parallelize. This has motivated the development of numerical solvers (e.g. Sinkhorn method) that can exploit GPU parallelism and produce approximate solutions. 

We introduce the first parallel combinatorial algorithm to find an additive $\varepsilon$-approximation of the OT distance. The parallel complexity of our algorithm is $O(\log(n)/ \varepsilon^2)$ where $n$ is the total support size for the input distributions. In Massive Parallel Computation (MPC) frameworks such as Hadoop and MapReduce, our algorithm computes an $\varepsilon$-approximate transport plan in $O(\log (\log (n/\varepsilon))/\varepsilon^2)$ rounds with $O(n/\varepsilon)$ space per machine; all prior algorithms in the MPC framework take $\Omega(\log n)$ rounds. 
We also provide a GPU-friendly matrix-based interpretation of our algorithm where each step of the algorithm is row or column manipulation of the matrix. Experiments suggest that our combinatorial algorithm is faster than the state-of-the-art approximate solvers in the GPU, especially for higher values of $n$.
Rethinking the Role of Token Retrieval in Multi-Vector Retrieval
Authors: Jinhyuk Lee; Zhuyun Dai; Sai Meher Karthik Duddu; Tao Lei; Iftekhar Naim; Ming-Wei Chang; Vincent Y Zhao
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: Multi-vector retrieval models such as ColBERT [Khattab et al., 2020] allow token-level interactions between queries and documents, and hence achieve state of the art on many information retrieval benchmarks. However, their non-linear scoring function cannot be scaled to millions of documents, necessitating a three-stage process for inference: retrieving initial candidates via token retrieval, accessing all token vectors, and scoring the initial candidate documents. The non-linear scoring function is applied over all token vectors of each candidate document, making the inference process complicated and slow. In this paper, we aim to simplify the multi-vector retrieval by rethinking the role of token retrieval. We present XTR, ConteXtualized Token Retriever, which introduces a simple, yet novel, objective function that encourages the model to retrieve the most important document tokens first. The improvement to token retrieval allows XTR to rank candidates only using the retrieved tokens rather than all tokens in the document, and enables a newly designed scoring stage that is two-to-three orders of magnitude cheaper than that of ColBERT. On the popular BEIR benchmark, XTR advances the state-of-the-art by 2.8 nDCG@10 without any distillation. Detailed analysis confirms our decision to revisit the token retrieval stage, as XTR demonstrates much better recall of the token retrieval stage compared to ColBERT.
QuIP: 2-Bit Quantization of Large Language Models With Guarantees
Authors: Jerry Chee; Yaohui Cai; Volodymyr Kuleshov; Christopher De Sa
Venue: NeurIPS 2023 (NeurIPS 2023 spotlight)

Abstract: This work studies post-training parameter quantization in large language models (LLMs). We introduce quantization with incoherence processing (QuIP), a new method based on the insight that quantization benefits from incoherent weight and Hessian matrices, i.e., from the weights being even in magnitude and the directions in which it is important to round them accurately being unaligned with the coordinate axes. QuIP consists of two steps: (1) an adaptive rounding procedure minimizing a quadratic proxy objective; (2) efficient pre- and post-processing that ensures weight and Hessian incoherence via multiplication by random orthogonal matrices. We complement QuIP with the first theoretical analysis for an LLM-scale quantization algorithm, and show that our theory also applies to an existing method, OPTQ. Empirically, we find that our incoherence preprocessing improves several existing quantization algorithms and yields the first LLM quantization methods that produce viable results using only two bits per weight. Our code can be found at https://github.com/Cornell-RelaxML/QuIP.
Deep Equilibrium Based Neural Operators for Steady-State PDEs
Authors: Tanya Marwah; Ashwini Pokle; J Zico Kolter; Zachary Chase Lipton; Jianfeng Lu; Andrej Risteski
Venue: NeurIPS 2023 (NeurIPS 2023 poster)

Abstract: Data-driven machine learning approaches are being increasingly used to solve partial differential equations (PDEs). They have shown particularly striking successes when training an operator, which takes as input a PDE in some family, and outputs its solution. However, the architectural design space, especially given structural knowledge of the PDE family of interest, is still poorly understood. We seek to remedy this gap by studying the benefits of weight-tied neural network architectures for steady-state PDEs. To achieve this, we first demonstrate that the solution of most steady-state PDEs can be expressed as a fixed point of a non-linear operator. Motivated by this observation, we propose FNO-DEQ, a deep equilibrium variant of the FNO architecture that directly solves for the solution of a steady-state PDE as the infinite-depth fixed point of an implicit operator layer using a black-box root solver and differentiates analytically through this fixed point resulting in $\mathcal{O}(1)$ training memory. Our experiments indicate that FNO-DEQ-based architectures outperform FNO-based baselines with $4\times$ the number of parameters in predicting the solution to steady-state PDEs such as Darcy Flow and steady-state incompressible Navier-Stokes. Finally, we show FNO-DEQ is more robust when trained with datasets with more noisy observations than the FNO-based baselines, demonstrating the benefits of using appropriate inductive biases in architectural design for different neural network based PDE solvers. Further, we show a universal approximation result that demonstrates that FNO-DEQ can approximate the solution to any steady-state PDE that can be written as a fixed point equation.
Parallel Sampling of Diffusion Models
Authors: Andy Shih; Suneel Belkhale; Stefano Ermon; Dorsa Sadigh; Nima Anari
Venue: NeurIPS 2023 (NeurIPS 2023 spotlight)

Abstract: Diffusion models are powerful generative models but suffer from slow sampling, often taking 1000 sequential denoising steps for one sample. As a result, considerable efforts have been directed toward reducing the number of denoising steps, but these methods hurt sample quality. Instead of reducing the number of denoising steps (trading quality for speed), in this paper we explore an orthogonal approach: can we run the denoising steps in parallel (trading compute for speed)? In spite of the sequential nature of the denoising steps, we show that surprisingly it is possible to parallelize sampling via Picard iterations, by guessing the solution of future denoising steps and iteratively refining until convergence. With this insight, we present ParaDiGMS, a novel method to accelerate the sampling of pretrained diffusion models by denoising multiple steps in parallel. ParaDiGMS is the first diffusion sampling method that enables trading compute for speed and is even compatible with existing fast sampling techniques such as DDIM and DPMSolver. Using ParaDiGMS, we improve sampling speed by 2-4x across a range of robotics and image generation models, giving state-of-the-art sampling speeds of 0.2s on 100-step DiffusionPolicy and 14.6s on 1000-step StableDiffusion-v2 with no measurable degradation of task reward, FID score, or CLIP score.