NeurIPS 2023 Papers

Wasserstein distributionally robust estimators have emerged as powerful models for prediction and decision-making under uncertainty. These estimators provide attractive generalization guarantees: the robust objective obtained from the training distribution is an exact upper bound on the true risk with high probability. However, existing guarantees either suffer from the curse of dimensionality, are restricted to specific settings, or lead to spurious error terms. In this paper, we show that these generalization guarantees actually hold on general classes of models, do not suffer from the curse of dimensionality, and can even cover distribution shifts at testing. We also prove that these results carry over to the newly-introduced regularized versions of Wasserstein distributionally robust problems.

We propose an algorithm for robust recovery of the spherical harmonic expansion of functions defined on the $d$-dimensional unit sphere $\mathbb{S}^{d-1}$ using a near-optimal number of function evaluations. We show that for any $f\in L^2(\mathbb{S}^{d-1})$, the number of evaluations of $f$ needed to recover its degree-$q$ spherical harmonic expansion equals the dimension of the space of spherical harmonics of degree at most $q$, up to a logarithmic factor. Moreover, we develop a simple yet efficient kernel regression-based algorithm to recover degree-$q$ expansion of $f$ by only evaluating the function on uniformly sampled points on $\mathbb{S}^{d-1}$. Our algorithm is built upon the connections between spherical harmonics and Gegenbauer polynomials. Unlike the prior results on fast spherical harmonic transform, our proposed algorithm works efficiently using a nearly optimal number of samples in any dimension $d$. Furthermore, we illustrate the empirical performance of our algorithm on numerical examples.

Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world applications, a theoretical understanding of their generalization capabilities remains underdeveloped. This work embarks on a comprehensive theoretical exploration of the generalization attributes of diffusion models. We establish the theoretical estimates of the generalization gap that evolves in tandem with the training dynamics of score-based diffusion models, suggesting a polynomially small generalization error ($O(n^{-2/5}+m^{-4/5})$) on both the sample size $n$ and the model capacity $m$, evading the curse of dimensionality (i.e., independent of the data dimension) when *early-stopped*. Furthermore, we extend our quantitative analysis to a *data-dependent* scenario, wherein target distributions are portrayed as a succession of densities with progressively increasing distances between modes. This precisely elucidates the *adverse* effect of "*modes shift*'' in ground truths on the model generalization. Furthermore, these estimates are not solely theoretical constructs but have also been confirmed through numerical simulations. Our findings contribute to the rigorous understanding of diffusion models' generalization properties and provide insights that may guide practical applications.

Predicting upcoming events is critical to our ability to effectively interact with our environment and conspecifics. In natural language processing, transformer models, which are trained on next-word prediction, appear to construct a general-purpose representation of language that can support diverse downstream tasks. However, we still lack an understanding of how a predictive objective shapes such representations. Inspired by recent work in vision neuroscience Hénaff et al. (2019), here we test a hypothesis about predictive representations of autoregressive transformer models. In particular, we test whether the neural trajectory of a sequence of words in a sentence becomes progressively more straight as it passes through the layers of the network. The key insight behind this hypothesis is that straighter trajectories should facilitate prediction via linear extrapolation. We quantify straightness using a 1- dimensional curvature metric, and present four findings in support of the trajectory straightening hypothesis: i) In trained models, the curvature progressively decreases from the first to the middle layers of the network. ii) Models that perform better on the next-word prediction objective, including larger models and models trained on larger datasets, exhibit greater decreases in curvature, suggesting that this improved ability to straighten sentence neural trajectories may be the underlying driver of better language modeling performance. iii) Given the same linguistic context, the sequences that are generated by the model have lower curvature than the ground truth (the actual continuations observed in a language corpus), suggesting that the model favors straighter trajectories for making predictions. iv) A consistent relationship holds between the average curvature and the average surprisal of sentences in the middle layers of models, such that sentences with straighter neural trajectories also have lower surprisal. Importantly, untrained models don’t exhibit these behaviors. In tandem, these results support the trajectory straightening hypothesis and provide a possible mechanism for how the geometry of the internal representations of autoregressive models supports next word prediction.

By universal formulas we understand parameterized analytic expressions that have a fixed complexity, but nevertheless can approximate any continuous function on a compact set. There exist various examples of such formulas, including some in the form of neural networks. In this paper we analyze the essential structural elements of these highly expressive models. We introduce a hierarchy of expressiveness classes connecting the global approximability property to the weaker property of infinite VC dimension, and prove a series of classification results for several increasingly complex functional families. In particular, we introduce a general family of polynomially-exponentially-algebraic functions that, as we prove, is subject to polynomial constraints. As a consequence, we show that fixed-size neural networks with not more than one layer of neurons having transcendental activations (e.g., sine or standard sigmoid) cannot in general approximate functions on arbitrary finite sets. On the other hand, we give examples of functional families, including two-hidden-layer neural networks, that approximate functions on arbitrary finite sets, but fail to do that on the whole domain of definition.

The advancements in generative modeling, particularly the advent of diffusion models, have sparked a fundamental question: how can these models be effectively used for discriminative tasks? In this work, we find that generative models can be great test-time adapters for discriminative models. Our method, Diffusion-TTA, adapts pre-trained discriminative models such as image classifiers, segmenters and depth predictors, to each unlabelled example in the test set using generative feedback from a diffusion model. We achieve this by modulating the conditioning of the diffusion model using the output of the discriminative model. We then maximize the image likelihood objective by backpropagating the gradients to discriminative model’s parameters. We show Diffusion-TTA significantly enhances the accuracy of various large-scale pre-trained discriminative models, such as, ImageNet classifiers, CLIP models, image pixel labellers and image depth predictors. Diffusion-TTA outperforms existing test-time adaptation methods, including TTT-MAE and TENT, and particularly shines in online adaptation setups, where the discriminative model is continually adapted to each example in the test set. We provide access to code, results, and visualizations on our website: diffusion-tta.github.io/

Nonlinear independent component analysis (ICA) aims to uncover the true latent sources from their observable nonlinear mixtures. Despite its significance, the identifiability of nonlinear ICA is known to be impossible without additional assumptions. Recent advances have proposed conditions on the connective structure from sources to observed variables, known as Structural Sparsity, to achieve identifiability in an unsupervised manner. However, the sparsity constraint may not hold universally for all sources in practice. Furthermore, the assumptions of bijectivity of the mixing process and independence among all sources, which arise from the setting of ICA, may also be violated in many real-world scenarios. To address these limitations and generalize nonlinear ICA, we propose a set of new identifiability results in the general settings of undercompleteness, partial sparsity and source dependence, and flexible grouping structures. Specifically, we prove identifiability when there are more observed variables than sources (undercomplete), and when certain sparsity and/or source independence assumptions are not met for some changing sources. Moreover, we show that even in cases with flexible grouping structures (e.g., part of the sources can be divided into irreducible independent groups with various sizes), appropriate identifiability results can also be established. Theoretical claims are supported empirically on both synthetic and real-world datasets.

Image generation techniques have been gaining increasing attention recently, but concerns have been raised about the potential misuse and intellectual property (IP) infringement associated with image generation models. It is, therefore, necessary to analyze the origin of images by inferring if a specific image was generated by a particular model, i.e., origin attribution. Existing methods only focus on specific types of generative models and require additional procedures during the training phase or generation phase. This makes them unsuitable for pre-trained models that lack these specific operations and may impair generation quality. To address this problem, we first develop an alteration-free and model-agnostic origin attribution method via reverse-engineering on image generation models, i.e., inverting the input of a particular model for a specific image. Given a particular model, we first analyze the differences in the hardness of reverse-engineering tasks for generated samples of the given model and other images. Based on our analysis, we then propose a method that utilizes the reconstruction loss of reverse-engineering to infer the origin. Our proposed method effectively distinguishes between generated images of a specific generative model and other images, i.e., images generated by other models and real images.

Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. However, existing methods are difficult to reproduce or build on, due to private code, data, and large compute requirements. This has created substantial barriers to research on machine learning methods for theorem proving. This paper removes these barriers by introducing LeanDojo: an open-source Lean playground consisting of toolkits, data, models, and benchmarks. LeanDojo extracts data from Lean and enables interaction with the proof environment programmatically. It contains fine-grained annotations of premises in proofs, providing valuable data for premise selection—a key bottleneck in theorem proving. Using this data, we develop ReProver (Retrieval-Augmented Prover): an LLM-based prover augmented with retrieval for selecting premises from a vast math library. It is inexpensive and needs only one GPU week of training. Our retriever leverages LeanDojo's program analysis capability to identify accessible premises and hard negative examples, which makes retrieval much more effective. Furthermore, we construct a new benchmark consisting of 98,734 theorems and proofs extracted from Lean's math library. It features challenging data split requiring the prover to generalize to theorems relying on novel premises that are never used in training. We use this benchmark for training and evaluation, and experimental results demonstrate the effectiveness of ReProver over non-retrieval baselines and GPT-4. We thus provide the first set of open-source LLM-based theorem provers without any proprietary datasets and release it under a permissive MIT license to facilitate further research.

Language instructions and demonstrations are two natural ways for users to teach robots personalized tasks. Recent progress in Large Language Models (LLMs) has shown impressive performance in translating language instructions into code for robotic tasks. However, translating demonstrations into task code continues to be a challenge due to the length and complexity of both demonstrations and code, making learning a direct mapping intractable. This paper presents Demo2Code, a novel framework that generates robot task code from demonstrations via an extended chain-of-thought and defines a common latent specification to connect the two. Our framework employs a robust two-stage process: (1) a recursive summarization technique that condenses demonstrations into concise specifications, and (2) a code synthesis approach that expands each function recursively from the generated specifications. We conduct extensive evaluation on various robot task benchmarks, including a novel game benchmark Robotouille, designed to simulate diverse cooking tasks in a kitchen environment.

Neural Radiance Fields (NeRF) is a novel implicit 3D reconstruction method that shows immense potential and has been gaining increasing attention. It enables the reconstruction of 3D scenes solely from a set of photographs. However, its real-time rendering capability, especially for interactive real-time rendering of large-scale scenes, still has significant limitations. To address these challenges, in this paper, we propose a novel neural rendering system called UE4-NeRF, specifically designed for real-time rendering of large-scale scenes. We partitioned each large scene into different sub-NeRFs. In order to represent the partitioned independent scene, we initialize polygonal meshes by constructing multiple regular octahedra within the scene and the vertices of the polygonal faces are continuously optimized during the training process. Drawing inspiration from Level of Detail (LOD) techniques, we trained meshes of varying levels of detail for different observation levels. Our approach combines with the rasterization pipeline in Unreal Engine 4 (UE4), achieving real-time rendering of large-scale scenes at 4K resolution with a frame rate of up to 43 FPS. Rendering within UE4 also facilitates scene editing in subsequent stages. Furthermore, through experiments, we have demonstrated that our method achieves rendering quality comparable to state-of-the-art approaches. Project page: https://jamchaos.github.io/UE4-NeRF/.

Humans and animals have a rich and flexible understanding of the physical world, which enables them to infer the underlying dynamical trajectories of objects and events, plausible future states, and use that to plan and anticipate the consequences of actions. However, the neural mechanisms underlying these computations are unclear. We combine a goal-driven modeling approach with dense neurophysiological data and high-throughput human behavioral readouts that contain thousands of comparisons to directly impinge on this question. Specifically, we construct and evaluate several classes of sensory-cognitive networks to predict the future state of rich, ethologically-relevant environments, ranging from self-supervised end-to-end models with pixel-wise or object-slot objectives, to models that future predict in the latent space of purely static image-pretrained or dynamic video-pretrained foundation models. We find that ``scale is \emph{not} all you need'', and that many state-of-the-art machine learning models fail to perform well on our neural and behavioral benchmarks for future prediction. In fact, only one class of models matches these data well overall. We find that neural responses are currently best predicted by models trained to predict the future state of their environment in the \emph{latent} space of pretrained foundation models optimized for \emph{dynamic} scenes in a self-supervised manner. These models also approach the neurons' ability to predict the environmental state variables that are visually hidden from view, despite not being explicitly trained to do so. Finally, we find that not all foundation model latents are equal. Notably, models that future predict in the latent space of video foundation models that are optimized to support a \emph{diverse} range of egocentric sensorimotor tasks, reasonably match \emph{both} human behavioral error patterns and neural dynamics across all environmental scenarios that we were able to test. Overall, these findings suggest that the neural mechanisms and behaviors of primate mental simulation have strong inductive biases associated with them, and are thus far most consistent with being optimized to future predict on \emph{reusable} visual representations that are useful for Embodied AI more generally.

Intelligent agents use internal world models to reason and make predictions about different courses of their actions at many scales. Devising learning paradigms and architectures that allow machines to learn world models that operate at multiple levels of temporal abstractions while dealing with complex uncertainty predictions is a major technical hurdle. In this work, we propose a probabilistic formalism to learn multi-time scale world models which we call the Multi Time Scale State Space (MTS3) model. Our model uses a computationally efficient inference scheme on multiple time scales for highly accurate long-horizon predictions and uncertainty estimates over several seconds into the future. Our experiments, which focus on action conditional long horizon future predictions, show that MTS3 outperforms recent methods on several system identification benchmarks including complex simulated and real-world dynamical systems. Code is available at this repository: https://github.com/ALRhub/MTS3.

An important problem in time-series analysis is modeling systems with time-varying dynamics. Probabilistic models with joint continuous and discrete latent states offer interpretable, efficient, and experimentally useful descriptions of such data. Commonly used models include autoregressive hidden Markov models (ARHMMs) and switching linear dynamical systems (SLDSs), each with its own advantages and disadvantages. ARHMMs permit exact inference and easy parameter estimation, but are parameter intensive when modeling long dependencies, and hence are prone to overfitting. In contrast, SLDSs can capture long-range dependencies in a parameter efficient way through Markovian latent dynamics, but present an intractable likelihood and a challenging parameter estimation task. In this paper, we propose _switching autoregressive low-rank tensor_ SALT models, which retain the advantages of both approaches while ameliorating the weaknesses. SALT parameterizes the tensor of an ARHMM with a low-rank factorization to control the number of parameters and allow longer range dependencies without overfitting. We prove theoretical and discuss practical connections between SALT, linear dynamical systems, and SLDSs. We empirically demonstrate quantitative advantages of SALT models on a range of simulated and real prediction tasks, including behavioral and neural datasets. Furthermore, the learned low-rank tensor provides novel insights into temporal dependencies within each discrete state.

Diffusion Probabilistic Models (DPMs) have achieved considerable success in generation tasks. As sampling from DPMs is equivalent to solving diffusion SDE or ODE which is time-consuming, numerous fast sampling methods built upon improved differential equation solvers are proposed. The majority of such techniques consider solving the diffusion ODE due to its superior efficiency. However, stochastic sampling could offer additional advantages in generating diverse and high-quality data. In this work, we engage in a comprehensive analysis of stochastic sampling from two aspects: variance-controlled diffusion SDE and linear multi-step SDE solver. Based on our analysis, we propose SA-Solver, which is an improved efficient stochastic Adams method for solving diffusion SDE to generate data with high quality. Our experiments show that SA-Solver achieves: 1) improved or comparable performance compared with the existing state-of-the-art (SOTA) sampling methods for few-step sampling; 2) SOTA FID on substantial benchmark datasets under a suitable number of function evaluations (NFEs).

Despite substantial advancements, Natural Language Processing (NLP) models often require post-training adjustments to enforce business rules, rectify undesired behavior, and align with user values. These adjustments involve operationalizing "concepts"—dictating desired model responses to certain inputs. However, it's difficult for a single entity to enumerate and define all possible concepts, indicating a need for a multi-user, collaborative model alignment framework. Moreover, the exhaustive delineation of a concept is challenging, and an improper approach can create shortcuts or interfere with original data or other concepts. To address these challenges, we introduce CoAlign, a framework that enables multi-user interaction with the model, thereby mitigating individual limitations. CoAlign aids users in operationalizing their concepts using Large Language Models, and relying on the principle that NLP models exhibit simpler behaviors in local regions. Our main insight is learning a \emph{local} model for each concept, and a \emph{global} model to integrate the original data with all concepts. We then steer a large language model to generate instances within concept boundaries where local and global disagree. Our experiments show CoAlign is effective at helping multiple users operationalize concepts and avoid interference for a variety of scenarios, tasks, and models.

Recently, large-scale pre-trained Vision and Language (VL) models have set a new state-of-the-art (SOTA) in zero-shot visual classification enabling open-vocabulary recognition of potentially unlimited set of categories defined as simple language prompts. However, despite these great advances, the performance of these zero-shot classifiers still falls short of the results of dedicated (closed category set) classifiers trained with supervised fine-tuning. In this paper we show, for the first time, how to reduce this gap without any labels and without any paired VL data, using an unlabeled image collection and a set of texts auto-generated using a Large Language Model (LLM) describing the categories of interest and effectively substituting labeled visual instances of those categories. Using our label-free approach, we are able to attain significant performance improvements over the zero-shot performance of the base VL model and other contemporary methods and baselines on a wide variety of datasets, demonstrating absolute improvement of up to $11.7\%$ ($3.8\%$ on average) in the label-free setting. Moreover, despite our approach being label-free, we observe $1.3\%$ average gains over leading few-shot prompting baselines that do use 5-shot supervision.

The storage of continuous variables in working memory is hypothesized to be sustained in the brain by the dynamics of recurrent neural networks (RNNs) whose steady states form continuous manifolds. In some cases, it is thought that the synaptic connectivity supports multiple attractor manifolds, each mapped to a different context or task. For example, in hippocampal area CA3, positions in distinct environments are represented by distinct sets of population activity patterns, each forming a continuum. It has been argued that the embedding of multiple continuous attractors in a single RNN inevitably causes detrimental interference: quenched noise in the synaptic connectivity disrupts the continuity of each attractor, replacing it by a discrete set of steady states that can be conceptualized as lying on local minima of an abstract energy landscape. Consequently, population activity patterns exhibit systematic drifts towards one of these discrete minima, thereby degrading the stored memory over time. Here we show that it is possible to dramatically attenuate these detrimental interference effects by adjusting the synaptic weights. Synaptic weight adjustment are derived from a loss function that quantifies the roughness of the energy landscape along each of the embedded attractor manifolds. By minimizing this loss function, the stability of states can be dramatically improved, without compromising the capacity.

We characterise the learning of a mixture of two clouds of data points with generic centroids via empirical risk minimisation in the high dimensional regime, under the assumptions of generic convex loss and convex regularisation. Each cloud of data points is obtained via a double-stochastic process, where the sample is obtained from a Gaussian distribution whose variance is itself a random parameter sampled from a scalar distribution $\varrho$. As a result, our analysis covers a large family of data distributions, including the case of power-law-tailed distributions with no covariance, and allows us to test recent ''Gaussian universality'' claims. We study the generalisation performance of the obtained estimator, we analyse the role of regularisation, and we analytically characterise the separability transition.