NeurIPS 2024 Papers

In this paper, we explores the expressivity and trainability of the Fourier Neural Operator (FNO). We establish a mean-field theory for the FNO, analyzing the behavior of the random FNO from an \emph{edge of chaos} perspective. Our investigation into the expressivity of a random FNO involves examining the ordered-chaos phase transition of the network based on the weight distribution. This phase transition demonstrates characteristics unique to the FNO, induced by mode truncation, while also showcasing similarities to those of densely connected networks. Furthermore, we identify a connection between expressivity and trainability: the ordered and chaotic phases correspond to regions of vanishing and exploding gradients, respectively. This finding provides a practical prerequisite for the stable training of the FNO. Our experimental results corroborate our theoretical findings.

Chain-of-Thought (CoT) reasoning is known to improve Large Language Models both empirically and in terms of theoretical approximation power. However, our understanding of the inner workings and conditions of apparition of CoT capabilities remains limited. This paper helps fill this gap by demonstrating how CoT reasoning emerges in transformers in a controlled and interpretable setting. In particular, we observe the appearance of a specialized attention mechanism dedicated to iterative reasoning, which we coined "iteration heads". We track both the emergence and the precise working of these iteration heads down to the attention level, and measure the transferability of the CoT skills to which they give rise between tasks.

This paper reveals the phenomenon of parameter heterogeneity in large language models (LLMs). We find that a small subset of ``cherry'' parameters exhibit a disproportionately large influence on model performance, while the vast majority of parameters have minimal impact. This heterogeneity is found to be prevalent across different model families, scales, and types. Motivated by this observation, we propose CherryQ, a novel quantization method that unifies the optimization of mixed-precision parameters. CherryQ identifies and preserves the critical cherry parameters in high precision while aggressively quantizing the remaining parameters to low precision. Extensive experiments demonstrate the effectiveness of CherryQ. CherryQ outperforms existing quantization approaches in terms of perplexity and downstream task performance. Notably, our 3-bit quantized Vicuna-1.5 exhibits competitive performance compared to their 16-bit counterparts. These findings highlight the potential of CherryQ for enabling efficient deployment of LLMs by taking advantage of parameter heterogeneity.

Machine unlearning is the problem of removing the effect of a subset of training data (the ``forget set'') from a trained model without damaging the model's utility e.g. to comply with users' requests to delete their data, or remove mislabeled, poisoned or otherwise problematic data. With unlearning research still being at its infancy, many fundamental open questions exist: Are there interpretable characteristics of forget sets that substantially affect the difficulty of the problem? How do these characteristics affect different state-of-the-art algorithms? With this paper, we present the first investigation aiming to answer these questions. We identify two key factors affecting unlearning difficulty and the performance of unlearning algorithms. Evaluation on forget sets that isolate these identified factors reveals previously-unknown behaviours of state-of-the-art algorithms that don't materialize on random forget sets. Based on our insights, we develop a framework coined Refined-Unlearning Meta-algorithm (RUM) that encompasses: (i) refining the forget set into homogenized subsets, according to different characteristics; and (ii) a meta-algorithm that employs existing algorithms to unlearn each subset and finally delivers a model that has unlearned the overall forget set. We find that RUM substantially improves top-performing unlearning algorithms. Overall, we view our work as an important step in (i) deepening our scientific understanding of unlearning and (ii) revealing new pathways to improving the state-of-the-art.

The goal of this paper is to investigate the complexity of gradient algorithms when learning sparse functions (juntas). We introduce a type of Statistical Queries ($\mathsf{SQ}$), which we call Differentiable Learning Queries ($\mathsf{DLQ}$), to model gradient queries on a specified loss with respect to an arbitrary model. We provide a tight characterization of the query complexity of $\mathsf{DLQ}$ for learning the support of a sparse function over generic product distributions. This complexity crucially depends on the loss function. For the squared loss, $\mathsf{DLQ}$ matches the complexity of Correlation Statistical Queries $(\mathsf{CSQ})$—potentially much worse than $\mathsf{SQ}$. But for other simple loss functions, including the $\ell_1$ loss, $\mathsf{DLQ}$ always achieves the same complexity as $\mathsf{SQ}$. We also provide evidence that $\mathsf{DLQ}$ can indeed capture learning with (stochastic) gradient descent by showing it correctly describes the complexity of learning with a two-layer neural network in the mean field regime and linear scaling.

Even though neural networks have been long deployed in applications involving tabular data, still existing neural architectures are not explainable by design. In this paper, we propose a new class of interpretable neural networks for tabular data that are both deep and linear at the same time (i.e. mesomorphic). We optimize deep hypernetworks to generate explainable linear models on a per-instance basis. As a result, our models retain the accuracy of black-box deep networks while offering free-lunch explainability for tabular data by design. Through extensive experiments, we demonstrate that our explainable deep networks have comparable performance to state-of-the-art classifiers on tabular data and outperform current existing methods that are explainable by design.

We consider Thompson Sampling (TS) for linear combinatorial semi-bandits and subgaussian rewards. We propose the first known TS whose finite-time regret does not scale exponentially with the dimension of the problem. We further show the mismatched sampling paradox: A learner who knows the rewards distributions and samples from the correct posterior distribution can perform exponentially worse than a learner who does not know the rewards and simply samples from a well-chosen Gaussian posterior. The code used to generate the experiments is available at https://github.com/RaymZhang/CTS-Mismatched-Paradox

This paper questions the effectiveness of a modern predictive uncertainty quantification approach, called *evidential deep learning* (EDL), in which a single neural network model is trained to learn a meta distribution over the predictive distribution by minimizing a specific objective function. Despite their perceived strong empirical performance on downstream tasks, a line of recent studies by Bengs et al. identify limitations of the existing methods to conclude their learned epistemic uncertainties are unreliable, e.g., in that they are non-vanishing even with infinite data. Building on and sharpening such analysis, we 1) provide a sharper understanding of the asymptotic behavior of a wide class of EDL methods by unifying various objective functions; 2) reveal that the EDL methods can be better interpreted as an out-of-distribution detection algorithm based on energy-based-models; and 3) conduct extensive ablation studies to better assess their empirical effectiveness with real-world datasets. Through all these analyses, we conclude that even when EDL methods are empirically effective on downstream tasks, this occurs despite their poor uncertainty quantification capabilities. Our investigation suggests that incorporating model uncertainty can help EDL methods faithfully quantify uncertainties and further improve performance on representative downstream tasks, albeit at the cost of additional computational complexity.

Surveys have recently gained popularity as a tool to study large language models. By comparing models’ survey responses to those of different human reference populations, researchers aim to infer the demographics, political opinions, or values best represented by current language models. In this work, we critically examine language models' survey responses on the basis of the well-established American Community Survey by the U.S. Census Bureau. Evaluating 43 different language models using de-facto standard prompting methodologies, we establish two dominant patterns. First, models' responses are governed by ordering and labeling biases, for example, towards survey responses labeled with the letter “A”. Second, when adjusting for these systematic biases through randomized answer ordering, models across the board trend towards uniformly random survey responses, irrespective of model size or training data. As a result, models consistently appear to better represent subgroups whose aggregate statistics are closest to uniform for the survey under consideration, leading to potentially misguided conclusions about model alignment.

Text-Attributed Graphs (TAGs) augment graph structures with natural language descriptions, facilitating detailed depictions of data and their interconnections across various real-world settings. However, existing TAG datasets predominantly feature textual information only at the nodes, with edges typically represented by mere binary or categorical attributes. This lack of rich textual edge annotations significantly limits the exploration of contextual relationships between entities, hindering deeper insights into graph-structured data. To address this gap, we introduce Textual-Edge Graphs Datasets and Benchmark (TEG-DB), a comprehensive and diverse collection of benchmark textual-edge datasets featuring rich textual descriptions on nodes and edges. The TEG-DB datasets are large-scale and encompass a wide range of domains, from citation networks to social networks. In addition, we conduct extensive benchmark experiments on TEG-DB to assess the extent to which current techniques, including pre-trained language models, graph neural networks, and their combinations, can utilize textual node and edge information. Our goal is to elicit advancements in textual-edge graph research, specifically in developing methodologies that exploit rich textual node and edge descriptions to enhance graph analysis and provide deeper insights into complex real-world networks. The entire TEG-DB project is publicly accessible as an open-source repository on Github, accessible at https://github.com/Zhuofeng-Li/TEG-Benchmark.

We present a comprehensive study of surrogate loss functions for learning to defer. We introduce a broad family of surrogate losses, parameterized by a non-increasing function $\Psi$, and establish their realizable $H$-consistency under mild conditions. For cost functions based on classification error, we further show that these losses admit $H$-consistency bounds when the hypothesis set is symmetric and complete, a property satisfied by common neural network and linear function hypothesis sets. Our results also resolve an open question raised in previous work [Mozannar et al., 2023] by proving the realizable $H$-consistency and Bayes-consistency of a specific surrogate loss. Furthermore, we identify choices of $\Psi$ that lead to $H$-consistent surrogate losses for *any general cost function*, thus achieving Bayes-consistency, realizable $H$-consistency, and $H$-consistency bounds *simultaneously*. We also investigate the relationship between $H$-consistency bounds and realizable $H$-consistency in learning to defer, highlighting key differences from standard classification. Finally, we empirically evaluate our proposed surrogate losses and compare them with existing baselines.

In recent years, transformer-based models have revolutionized deep learning, particularly in sequence modeling. To better understand this phenomenon, there is a growing interest in using Markov input processes to study transformers. However, our current understanding in this regard remains limited with many fundamental questions about how transformers learn Markov chains still unanswered. In this paper, we address this by focusing on first-order Markov chains and single-layer transformers, providing a comprehensive characterization of the learning dynamics in this context. Specifically, we prove that transformer parameters trained on next-token prediction loss can either converge to global or local minima, contingent on the initialization and the Markovian data properties, and we characterize the precise conditions under which this occurs. To the best of our knowledge, this is the first result of its kind highlighting the role of initialization. We further demonstrate that our theoretical findings are corroborated by empirical evidence. Based on these insights, we provide guidelines for the initialization of single-layer transformers and demonstrate their effectiveness. Finally, we outline several open problems in this arena. Code is available at: \url{https://github.com/Bond1995/Markov}.

We consider metrical task systems on general metric spaces with $n$ points, and show that any fully randomized algorithm can be turned into a randomized algorithm that uses only $2\log n$ random bits, and achieves the same competitive ratio up to a factor $2$. This provides the first order-optimal barely random algorithms for metrical task systems, i.e. which use a number of random bits that does not depend on the number of requests addressed to the system. We discuss implications on various aspects of online decision making such as: distributed systems, advice complexity and transaction costs, suggesting broad applicability. We put forward an equivalent view that we call collective metrical task systems where $k$ agents in a metrical task system team up, and suffer the average cost paid by each agent. Our results imply that such team can be $O(\log^2 n)$-competitive as soon as $k\geq n^2$. In comparison, a single agent is always $\Omega(n)$-competitive.

Recent analysis on the training dynamics of Transformers has unveiled an interesting characteristic: the training loss plateaus for a significant number of training steps, and then suddenly (and sharply) drops to near--optimal values. To understand this phenomenon in depth, we formulate the low-rank matrix completion problem as a masked language modeling (MLM) task, and show that it is possible to train a BERT model to solve this task to low error. Furthermore, the loss curve shows a plateau early in training followed by a sudden drop to near-optimal values, despite no changes in the training procedure or hyper-parameters. To gain interpretability insights into this sudden drop, we examine the model's predictions, attention heads, and hidden states before and after this transition. Concretely, we observe that (a) the model transitions from simply copying the masked input to accurately predicting the masked entries; (b) the attention heads transition to interpretable patterns relevant to the task; and (c) the embeddings and hidden states encode information relevant to the problem. We also analyze the training dynamics of individual model components to understand the sudden drop in loss.

The inherent challenge of image fusion lies in capturing the correlation of multi-source images and comprehensively integrating effective information from different sources. Most existing techniques fail to perform dynamic image fusion while notably lacking theoretical guarantees, leading to potential deployment risks in this field. Is it possible to conduct dynamic image fusion with a clear theoretical justification? In this paper, we give our solution from a generalization perspective. We proceed to reveal the generalized form of image fusion and derive a new test-time dynamic image fusion paradigm. It provably reduces the upper bound of generalization error. Specifically, we decompose the fused image into multiple components corresponding to its source data. The decomposed components represent the effective information from the source data, thus the gap between them reflects the \textit{Relative Dominability} (RD) of the uni-source data in constructing the fusion image. Theoretically, we prove that the key to reducing generalization error hinges on the negative correlation between the RD-based fusion weight and the uni-source reconstruction loss. Intuitively, RD dynamically highlights the dominant regions of each source and can be naturally converted to the corresponding fusion weight, achieving robust results. Extensive experiments and discussions with in-depth analysis on multiple benchmarks confirm our findings and superiority. Our code is available at https://github.com/Yinan-Xia/TTD.

Recent studies suggest that deep learning models' inductive bias towards favoring simpler features may be an origin of shortcut learning. Yet, there has been limited focus on understanding the complexities of the myriad features that models learn. In this work, we introduce a new metric for quantifying feature complexity, based on V-information and capturing whether a feature requires complex computational transformations to be extracted. Using this V-information metric, we analyze the complexities of 10,000 features—represented as directions in the penultimate layer—that were extracted from a standard ImageNet-trained vision model. Our study addresses four key questions: First, we ask what features look like as a function of complexity, and find a spectrum of simple-to-complex features present within the model. Second, we ask when features are learned during training. We find that simpler features dominate early in training, and more complex features emerge gradually. Third, we investigate where within the network simple and complex features "flow," and find that simpler features tend to bypass the visual hierarchy via residual connections. Fourth, we explore the connection between features' complexity and their importance for driving the network's decision. We find that complex features tend to be less important. Surprisingly, important features become accessible at earlier layers during training, like a "sedimentation process," allowing the model to build upon these foundational elements.

Lossless compression of large-scale scientific floating-point data is critical yet challenging due to the presence of high-order information and noise that arises from model truncation and discretization errors. Existing entropy coding techniques fail to effectively leverage the mechanisms underlying the data generation process. This paper introduces MeLLoC(Mechanism Learning for Lossless Compression), a novel approach that combines high-order mechanism learning with classical encoding to enhance lossless compression for scientific data. The key idea is to treat the data as discrete samples from an underlying physical field described by differential equations and solve an inverse problem to identify the governing equation coefficients exhibiting more compressible numeric representations. Periodic extension techniques are employed to accelerate the decompression. Through extensive experiments on various scientific datasets, MeLLoC consistently outperforms state-of-the-art lossless compressors while offering compelling trade-offs between compression ratios and computational costs. This work opens up new avenues for exploiting domain knowledge and high-order information to improve data compression in scientific computing.

Image classification is one of the most fundamental capabilities of machine vision intelligence. In this work, we revisit the image classification task using visually-grounded language models (VLMs) such as GPT-4V and LLaVA. We find that existing proprietary and public VLMs, despite often using CLIP as a vision encoder and having many more parameters, significantly underperform CLIP on standard image classification benchmarks like ImageNet. To understand the reason, we explore several hypotheses concerning the inference algorithms, training objectives, and data processing in VLMs. Our analysis reveals that the primary cause is data-related: critical information for image classification is encoded in the VLM's latent space but can only be effectively decoded with enough training data. Specifically, there is a strong correlation between the frequency of class exposure during VLM training and instruction-tuning and the VLM's performance in those classes; when trained with sufficient data, VLMs can match the accuracy of state-of-the-art classification models. Based on these findings, we enhance a VLM by integrating classification-focused datasets into its training, and demonstrate that the enhanced classification performance of the VLM transfers to its general capabilities, resulting in an improvement of 11.8% on the newly collected ImageWikiQA dataset.

Large multimodal models (LMMs) combine unimodal encoders and large language models (LLMs) to perform multimodal tasks. Despite recent advancements towards the interpretability of these models, understanding internal representations of LMMs remains largely a mystery. In this paper, we present a novel framework for the interpretation of LMMs. We propose a dictionary learning based approach, applied to the representation of tokens. The elements of the learned dictionary correspond to our proposed concepts. We show that these concepts are well semantically grounded in both vision and text. Thus we refer to these as ``multi-modal concepts''. We qualitatively and quantitatively evaluate the results of the learnt concepts. We show that the extracted multimodal concepts are useful to interpret representations of test samples. Finally, we evaluate the disentanglement between different concepts and the quality of grounding concepts visually and textually. Our implementation is publicly available: https://github.com/mshukor/xl-vlms.