NeurIPS 2024 Papers

In this work, we conduct a systematic study of stochastic saddle point problems (SSP) and stochastic variational inequalities (SVI) under the constraint of $(\epsilon,\delta)$-differential privacy (DP) in both Euclidean and non-Euclidean setups. We first consider Lipschitz convex-concave SSPs in the $\ell_p/\ell_q$ setup, $p,q\in[1,2]$. That is, we consider the case where the primal problem has an $\ell_p$-setup (i.e., the primal parameter is constrained to an $\ell_p$ bounded domain and the loss is $\ell_p$-Lipschitz with respect to the primal parameter) and the dual problem has an $\ell_q$ setup. Here, we obtain a bound of $\tilde{O}\big(\frac{1}{\sqrt{n}} + \frac{\sqrt{d}}{n\epsilon}\big)$ on the strong SP-gap, where $n$ is the number of samples and $d$ is the dimension. This rate is nearly optimal for any $p,q\in[1,2]$. Without additional assumptions, such as smoothness or linearity requirements, prior work under DP has only obtained this rate when $p=q=2$ (i.e., only in the Euclidean setup). Further, existing algorithms have each only been shown to work for specific settings of $p$ and $q$ and under certain assumptions on the loss and the feasible set, whereas we provide a general algorithm for DP SSPs whenever $p,q\in[1,2]$. Our result is obtained via a novel analysis of the recursive regularization algorithm. In particular, we develop new tools for analyzing generalization, which may be of independent interest. Next, we turn our attention towards SVIs with a monotone, bounded and Lipschitz operator and consider $\ell_p$-setups, $p\in[1,2]$. Here, we provide the first analysis which obtains a bound on the strong VI-gap of $\tilde{O}\big(\frac{1}{\sqrt{n}} + \frac{\sqrt{d}}{n\epsilon}\big)$. For $p-1=\Omega(1)$, this rate is near optimal due to existing lower bounds. To obtain this result, we develop a modified version of recursive regularization. Our analysis builds on the techniques we develop for SSPs as well as employing additional novel components which handle difficulties arising from adapting the recursive regularization framework to SVIs.

Adaptation of pretrained vision-language models such as CLIP to various downstream tasks have raised great interest in recent researches. Previous works have proposed a variety of test-time adaptation (TTA) methods to achieve strong generalization without any knowledge of the target domain. However, existing training-required TTA approaches like TPT necessitate entropy minimization that involves large computational overhead, while training-free methods like TDA overlook the potential for information mining from the test samples themselves. In this paper, we break down the design of existing popular training-required and training-free TTA methods and bridge the gap between them within our framework. Specifically, we maintain a light-weight key-value memory for feature retrieval from instance-agnostic historical samples and instance-aware boosting samples. The historical samples are filtered from the testing data stream and serve to extract useful information from the target distribution, while the boosting samples are drawn from regional bootstrapping and capture the knowledge of the test sample itself. We theoretically justify the rationality behind our method and empirically verify its effectiveness on both the out-of-distribution and the cross-domain datasets, showcasing its applicability in real-world situations.

Recent methodologies in LLM self-training mostly rely on LLM generating responses and filtering those with correct output answers as training data. This approach often yields a low-quality fine-tuning training set (e.g., incorrect plans or intermediate reasoning). In this paper, we develop a reinforced self-training approach, called ReST-MCTS*, based on integrating process reward guidance with tree search MCTS* for collecting higher-quality reasoning traces as well as per-step value to train policy and reward models. ReST-MCTS* circumvents the per-step manual annotation typically used to train process rewards by tree-search-based reinforcement learning: Given oracle final correct answers, ReST-MCTS* is able to infer the correct process rewards by estimating the probability this step can help lead to the correct answer. These inferred rewards serve dual purposes: they act as value targets for further refining the process reward model and also facilitate the selection of high-quality traces for policy model self-training. We first show that the tree-search policy in ReST-MCTS* achieves higher accuracy compared with prior LLM reasoning baselines such as Best-of-N and Tree-of-Thought, within the same search budget. We then show that by using traces searched by this tree-search policy as training data, we can continuously enhance the three language models for multiple iterations, and outperform other self-training algorithms such as ReST$^\text{EM}$ and Self-Rewarding LM.

We consider estimation of a linear functional of the treatment effect from adaptively collected data. This problem finds a variety of applications including off-policy evaluation in contextual bandits, and estimation of the average treatment effect in causal inference. While a certain class of augmented inverse propensity weighting (AIPW) estimators enjoys desirable asymptotic properties including the semi-parametric efficiency, much less is known about their non-asymptotic theory with adaptively collected data. To fill in the gap, we first present generic upper bounds on the mean-squared error of the class of AIPW estimators that crucially depends on a sequentially weighted error between the treatment effect and its estimates. Motivated by this, we propose a general reduction scheme that allows one to produce a sequence of estimates for the treatment effect via online learning to minimize the sequentially weighted estimation error. To illustrate this, we provide three concrete instantiations in (1) the tabular case; (2) the case of linear function approximation; and (3) the case of general function approximation for the outcome model. We then provide a local minimax lower bound to show the instance-dependent optimality of the AIPW estimator using no-regret online learning algorithms.

Though vision transformers (ViTs) have achieved state-of-the-art performance in a variety of settings, they exhibit surprising failures when performing tasks involving visual relations. This begs the question: how do ViTs attempt to perform tasks that require computing visual relations between objects? Prior efforts to interpret ViTs tend to focus on characterizing relevant low-level visual features. In contrast, we adopt methods from mechanistic interpretability to study the higher-level visual algorithms that ViTs use to perform abstract visual reasoning. We present a case study of a fundamental, yet surprisingly difficult, relational reasoning task: judging whether two visual entities are the same or different. We find that pretrained ViTs fine-tuned on this task often exhibit two qualitatively different stages of processing despite having no obvious inductive biases to do so: 1) a perceptual stage wherein local object features are extracted and stored in a disentangled representation, and 2) a relational stage wherein object representations are compared. In the second stage, we find evidence that ViTs can learn to represent somewhat abstract visual relations, a capability that has long been considered out of reach for artificial neural networks. Finally, we demonstrate that failures at either stage can prevent a model from learning a generalizable solution to our fairly simple tasks. By understanding ViTs in terms of discrete processing stages, one can more precisely diagnose and rectify shortcomings of existing and future models.

Existing prompt-tuning methods have demonstrated impressive performances in continual learning (CL), by selecting and updating relevant prompts in the vision-transformer models. On the contrary, this paper aims to learn each task by tuning the prompts in the direction orthogonal to the subspace spanned by previous tasks' features, so as to ensure no interference on tasks that have been learned to overcome catastrophic forgetting in CL. However, different from the orthogonal projection in the traditional CNN architecture, the prompt gradient orthogonal projection in the ViT architecture shows completely different and greater challenges, i.e., 1) the high-order and non-linear self-attention operation; 2) the drift of prompt distribution brought by the LayerNorm in the transformer block. Theoretically, we have finally deduced two consistency conditions to achieve the prompt gradient orthogonal projection, which provide a theoretical guarantee of eliminating interference on previously learned knowledge via the self-attention mechanism in visual prompt tuning. In practice, an effective null-space-based approximation solution has been proposed to implement the prompt gradient orthogonal projection. Extensive experimental results demonstrate the effectiveness of anti-forgetting on four class-incremental benchmarks with diverse pre-trained baseline models, and our approach achieves superior performances to state-of-the-art methods. Our code is available at https://github.com/zugexiaodui/VPTinNSforCL

Recent research has made significant progress in optimizing diffusion models for downstream objectives, which is an important pursuit in fields such as graph generation for drug design. However, directly applying these models to graph presents challenges, resulting in suboptimal performance. This paper introduces graph diffusion policy optimization (GDPO), a novel approach to optimize graph diffusion models for arbitrary (e.g., non-differentiable) objectives using reinforcement learning. GDPO is based on an eager policy gradient tailored for graph diffusion models, developed through meticulous analysis and promising improved performance. Experimental results show that GDPO achieves state-of-the-art performance in various graph generation tasks with complex and diverse objectives. Code is available at https://github.com/sail-sg/GDPO.

A computational problem in biological reward-based learning is how credit assignment is performed in the nucleus accumbens (NAc). Much research suggests that NAc dopamine encodes temporal-difference (TD) errors for learning value predictions. However, dopamine is synchronously distributed in regionally homogeneous concentrations, which does not support explicit credit assignment (like used by backpropagation). It is unclear whether distributed errors alone are sufficient for synapses to make coordinated updates to learn complex, nonlinear reward-based learning tasks. We design a new deep Q-learning algorithm, Artificial Dopamine, to computationally demonstrate that synchronously distributed, per-layer TD errors may be sufficient to learn surprisingly complex RL tasks. We empirically evaluate our algorithm on MinAtar, the DeepMind Control Suite, and classic control tasks, and show it often achieves comparable performance to deep RL algorithms that use backpropagation.

The branch-and-cut algorithm is the method of choice to solve large scale integer programming problems in practice. A key ingredient of branch-and-cut is the use of *cutting planes* which are derived constraints that reduce the search space for an optimal solution. Selecting effective cutting planes to produce small branch-and-cut trees is a critical challenge in the branch-and-cut algorithm. Recent advances have employed a data-driven approach to select good cutting planes from a parameterized family, aimed at reducing the branch-and-bound tree size (in expectation) for a given distribution of integer programming instances. We extend this idea to the selection of the best cut generating function (CGF), which is a tool in the integer programming literature for generating a wide variety of cutting planes that generalize the well-known Gomory Mixed-Integer (GMI) cutting planes. We provide rigorous sample complexity bounds for the selection of an effective CGF from certain parameterized families that provably performs well for any specified distribution on the problem instances. Our empirical results show that the selected CGF can outperform the GMI cuts for certain distributions. Additionally, we explore the sample complexity of using neural networks for instance-dependent CGF selection.

We introduce Image2Struct, a benchmark to evaluate vision-language models (VLMs) on extracting structure from images. Our benchmark 1) captures real-world use cases, 2) is fully automatic and does not require human judgment, and 3) is based on a renewable stream of fresh data. In Image2Struct, VLMs are prompted to generate the underlying structure (e.g., LaTeX code or HTML) from an input image (e.g., webpage screenshot). The structure is then rendered to produce an output image (e.g., rendered webpage), which is compared against the input image to produce a similarity score. This round-trip evaluation allows us to quantitatively evaluate VLMs on tasks with multiple valid structures. We create a pipeline that downloads fresh data from active online communities upon execution and evaluates the VLMs without human intervention. We introduce three domains (Webpages, LaTeX, and Musical Scores) and use five image metrics (pixel similarity, cosine similarity between the Inception vectors, learned perceptual image patch similarity, structural similarity index measure, and earth mover similarity) that allow efficient and automatic comparison between pairs of images. We evaluate Image2Struct on 14 prominent VLMs and find that scores vary widely, indicating that Image2Struct can differentiate between the performances of different VLMs. Additionally, the best score varies considerably across domains (e.g., 0.402 on sheet music vs. 0.830 on LaTeX equations), indicating that Image2Struct contains tasks of varying difficulty. For transparency, we release the full results at https://crfm.stanford.edu/helm/image2struct/v1.0.1/.

Humans can communicate and observe media with different modalities, such as texts, sounds, and images. For robots to be more generalizable embodied agents, they should be capable of following instructions and perceiving the world with adaptation to diverse modalities. Current robotic learning methodologies often focus on single-modal task specification and observation, thereby limiting their ability to process rich multi-modal information. Addressing this limitation, we present an end-to-end general-purpose multi-modal system named Any-to-Policy Embodied Agents. This system empowers robots to handle tasks using various modalities, whether in combinations like text-image, audio-image, text-point cloud, or in isolation. Our innovative approach involves training a versatile modality network that adapts to various inputs and connects with policy networks for effective control. Because of the lack of existing multi-modal robotics datasets for evaluation, we assembled a comprehensive real-world dataset encompassing 30 robotic tasks. Each task in this dataset is richly annotated across multiple modalities, providing a robust foundation for assessment. We conducted extensive validation of our proposed unified modality embodied agent using several simulation benchmarks, including Franka Kitchen, Meta-World, and Maniskill2, as well as in our real-world settings. Our experiments showcase the promising capability of building embodied agents that can adapt to diverse multi-modal in a unified framework.

The modern study and use of surfaces is a research topic grounded in centuries of mathematical and empirical inquiry. From a mathematical point of view, curvature is an invariant that characterises the intrinsic geometry and the extrinsic shape of a surface. Yet, in modern applications the focus has shifted away from finding expressive representations of surfaces, and towards the design of efficient neural network architectures to process them. The literature suggests a tendency to either overlook the representation of the processed surface, or use overcomplicated representations whose ability to capture the essential features of a surface is opaque. We propose using curvature as the input of neural network architectures for surface processing, and explore this proposition through experiments making use of the shape operator. Our results show that using curvature as input leads to significant a increase in performance on segmentation and classification tasks, while allowing far less computational overhead than current methods.

Solving Olympiad-level mathematical problems represents a significant advancement in machine intelligence and automated reasoning. Current machine learning methods, however, struggle to solve Olympiad-level problems beyond Euclidean plane geometry due to a lack of large-scale, high-quality datasets. The challenge is even greater in algebraic systems, which involve infinite reasoning spaces within finite conditions. To address these issues, we propose *AIPS*, an *Algebraic Inequality Proving System* capable of autonomously generating complex inequality theorems and effectively solving Olympiad-level inequality problems without requiring human demonstrations. During proof search in a mixed reasoning manner, a value curriculum learning strategy on generated datasets is implemented to improve proving performance, demonstrating strong mathematical intuitions. On a test set of 20 International Mathematical Olympiad-level inequality problems, AIPS successfully solved 10, outperforming state-of-the-art methods. Furthermore, AIPS automatically generated a vast array of non-trivial theorems without human intervention, some of which have been evaluated by professional contestants and deemed to reach the level of the International Mathematical Olympiad. Notably, one theorem was selected as a competition problem in a major city's 2024 Mathematical Olympiad. All the materials are available at [sites.google.com/view/aips2](https://sites.google.com/view/aips2)

The study of modern machine learning models often necessitates storing vast quantities of gradients or Hessian vector products (HVPs). Traditional sketching methods struggle to scale under these memory constraints. We present a novel framework for scalable gradient and HVP sketching, tailored for modern hardware. We provide theoretical guarantees and demonstrate the power of our methods in applications like training data attribution, Hessian spectrum analysis, and intrinsic dimension computation for pre-trained language models. Our work sheds new light on the behavior of pre-trained language models, challenging assumptions about their intrinsic dimensionality and Hessian properties.

We consider the design of practically-implementable schemes for the task of channel simulation. Existing methods do not scale with the number of simultaneous uses of the channel and are therefore unable to harness the amortization gains associated with simulating many uses of the channel at once. We show how techniques from the theory of error-correcting codes can be applied to achieve scalability and hence improved performance. As an exemplar, we focus on how polar codes can be used to efficiently simulate i.i.d. copies of a class of binary-output channels.

Autoformalization, the task of automatically translating natural language descriptions into a formal language, poses a significant challenge across various domains, especially in mathematics. Recent advancements in large language models (LLMs) have unveiled their promising capabilities to formalize even competition-level math problems. However, we observe a considerable discrepancy between pass@1 and pass@k accuracies in LLM-generated formalizations. To address this gap, we introduce a novel framework that scores and selects the best result from k autoformalization candidates based on two complementary self-consistency methods: symbolic equivalence and semantic consistency. Elaborately, symbolic equivalence identifies the logical homogeneity among autoformalization candidates using automated theorem provers, and semantic consistency evaluates the preservation of the original meaning by informalizing the candidates and computing the similarity between the embeddings of the original and informalized texts. Our extensive experiments on the MATH and miniF2F datasets demonstrate that our approach significantly enhances autoformalization accuracy, achieving up to 0.22-1.35x relative improvements across various LLMs and baseline methods.

Minimum Bayes Risk (MBR) decoding is a powerful decoding strategy widely used for text generation tasks but its quadratic computational complexity limits its practical application. This paper presents a novel approach for approximating MBR decoding using matrix completion techniques, focusing on a machine translation task. We formulate MBR decoding as a matrix completion problem, where the utility metric scores between candidate hypotheses and reference translations form a low-rank matrix. First we empirically show that the scores matrices indeed have a low-rank structure. Then we exploit this by only computing a random subset of the scores and efficiently recover the missing entries in the matrix by applying the Alternating Least Squares (ALS) algorithm, thereby enabling fast approximation of the MBR decoding process. Our experimental results on machine translation tasks demonstrate that the proposed method requires 1/16 utility metric computations compared to the vanilla MBR decoding while achieving equal translation quality measured by COMET on the WMT22 dataset (en<>de, en<>ru). We also benchmark our method against other approximation methods and we show significant gains in quality.

Humans represent scenes and objects in rich feature spaces, carrying information that allows us to generalise about category memberships and abstract functions with few examples. What determines whether a neural network model generalises like a human? We tested how well the representations of $86$ pretrained neural network models mapped to human learning trajectories across two tasks where humans had to learn continuous relationships and categories of natural images. In these tasks, both human participants and neural networks successfully identified the relevant stimulus features within a few trials, demonstrating effective generalisation. We found that while training dataset size was a core determinant of alignment with human choices, contrastive training with multi-modal data (text and imagery) was a common feature of currently publicly available models that predicted human generalisation. Intrinsic dimensionality of representations had different effects on alignment for different model types. Lastly, we tested three sets of human-aligned representations and found no consistent improvements in predictive accuracy compared to the baselines. In conclusion, pretrained neural networks can serve to extract representations for cognitive models, as they appear to capture some fundamental aspects of cognition that are transferable across tasks. Both our paradigms and modelling approach offer a novel way to quantify alignment between neural networks and humans and extend cognitive science into more naturalistic domains.

Recent works have shown that large language model (LLM) agents are able to improve themselves from experience, which is an important ability for continuous enhancement post-deployment. However, existing benchmarks primarily evaluate their innate capabilities and do not assess their ability to improve over time. To address this gap, we introduce StreamBench, a pioneering benchmark designed to evaluate the continuous improvement of LLM agents over an input-feedback sequence. StreamBench simulates an online learning environment where LLMs receive a continuous flow of feedback stream and iteratively enhance their performance. In addition, we propose several simple yet effective baselines for improving LLMs on StreamBench, and provide a comprehensive analysis to identify critical components that contribute to successful streaming strategies. Our work serves as a stepping stone towards developing effective online learning strategies for LLMs, paving the way for more adaptive AI systems in streaming scenarios.