NeurIPS 2022 Papers

Monte Carlo integration is a key technique for designing randomized approximation schemes for counting problems, with applications, e.g., in machine learning and statistical physics. The technique typically enables massively parallel computation, however, with the risk that some of the delegated computations contain spontaneous or adversarial errors. We present an orchestration of the computations such that the outcome is accompanied with a proof of correctness that can be verified with substantially less computational resources than it takes to run the computations from scratch with state-of-the-art algorithms. Specifically, we adopt an algebraic proof system developed in computational complexity theory, in which the proof is represented by a polynomial; evaluating the polynomial at a random point amounts to a verification of the proof with probabilistic guarantees. We give examples of known Monte Carlo estimators that admit verifiable extensions with moderate computational overhead: for the permanent of zero--one matrices, for the model count of disjunctive normal form formulas, and for the gradient of logistic regression models. We also discuss the prospects and challenges of engineering efficient verifiable approximation schemes more generally.

Laplace approximation (LA) and its linearized variant (LLA) enable effortless adaptation of pretrained deep neural networks to Bayesian neural networks. The generalized Gauss-Newton (GGN) approximation is typically introduced to improve their tractability. However, LA and LLA are still confronted with non-trivial inefficiency issues and should rely on Kronecker-factored, diagonal, or even last-layer approximate GGN matrices in practical use. These approximations are likely to harm the fidelity of learning outcomes. To tackle this issue, inspired by the connections between LLA and neural target kernels (NTKs), we develop a Nystrom approximation to NTKs to accelerate LLA. Our method benefits from the capability of popular deep learning libraries for forward mode automatic differentiation, and enjoys reassuring theoretical guarantees. Extensive studies reflect the merits of the proposed method in aspects of both scalability and performance. Our method can even scale up to architectures like vision transformers. We also offer valuable ablation studies to diagnose our method. Code is available at https://github.com/thudzj/ELLA.

In this paper, we derive upper bounds on generalization errors for deep neural networks with Markov datasets. These bounds are developed based on Koltchinskii and Panchenko's approach for bounding the generalization error of combined classifiers with i.i.d. datasets. The development of new symmetrization inequalities in high-dimensional probability for Markov chains is a key element in our extension, where the spectral gap of the infinitesimal generator of the Markov chain plays a key parameter in these inequalities. We also propose a simple method to convert these bounds and other similar ones in traditional deep learning and machine learning to Bayesian counterparts for both i.i.d. and Markov datasets. Extensions to $m$-order homogeneous Markov chains such as AR and ARMA models and mixtures of several Markov data services are given.

Sparsely-activated Mixture-of-experts (MoE) models allow the number of parameters to greatly increase while keeping the amount of computation for a given token or a given sample unchanged. However, a poor expert routing strategy (e.g. one resulting in load imbalance) can cause certain experts to be under-trained, leading to an expert being under or over-specialized. Prior work allocates a fixed number of experts to each token using a top-k function regardless of the relative importance of different tokens. To address this, we propose a heterogeneous mixture-of-experts employing an expert choice method. Instead of letting tokens select the top-k experts, we have experts selecting the top-k tokens. As a result, each token can be routed to a variable number of experts and each expert can have a fixed bucket size. We systematically study pre-training speedups using the same computational resources of the Switch Transformer top-1 and GShard top-2 gating of prior work and find that our method improves training convergence time by more than 2×. For the same computational cost, our method demonstrates higher performance in fine-tuning 11 selected tasks in the GLUE and SuperGLUE benchmarks. For a smaller activation cost, our method outperforms the T5 dense model in 7 out of the 11 tasks.

We present a family $\{\widehat{\pi}_p\}_{p\ge 1}$ of pessimistic learning rules for offline learning of linear contextual bandits, relying on confidence sets with respect to different $\ell_p$ norms, where $\widehat{\pi}_2$ corresponds to Bellman-consistent pessimism (BCP), while $\widehat{\pi}_\infty$ is a novel generalization of lower confidence bound (LCB) to the linear setting. We show that the novel $\widehat{\pi}_\infty$ learning rule is, in a sense, adaptively optimal, as it achieves the minimax performance (up to log factors) against all $\ell_q$-constrained problems, and as such it strictly dominates all other predictors in the family, including $\widehat{\pi}_2$.

In recent years, deep neural networks have demonstrated increasingly strong abilities to recognize objects and activities in videos. However, as video understanding becomes widely used in real-world applications, a key consideration is developing human-centric systems that understand not only the content of the video but also how it would affect the wellbeing and emotional state of viewers. To facilitate research in this setting, we introduce two large-scale datasets with over 60,000 videos manually annotated for emotional response and subjective wellbeing. The Video Cognitive Empathy (VCE) dataset contains annotations for distributions of fine-grained emotional responses, allowing models to gain a detailed understanding of affective states. The Video to Valence (V2V) dataset contains annotations of relative pleasantness between videos, which enables predicting a continuous spectrum of wellbeing. In experiments, we show how video models that are primarily trained to recognize actions and find contours of objects can be repurposed to understand human preferences and the emotional content of videos. Although there is room for improvement, predicting wellbeing and emotional response is on the horizon for state-of-the-art models. We hope our datasets can help foster further advances at the intersection of commonsense video understanding and human preference learning.

Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number. This result leads to a general standpoint that deep quantum circuits would not be feasible for practical tasks. In this work, we propose an initialization strategy with theoretical guarantees for the vanishing gradient problem in general deep quantum circuits. Specifically, we prove that under proper Gaussian initialized parameters, the norm of the gradient decays at most polynomially when the qubit number and the circuit depth increase. Our theoretical results hold for both the local and the global observable cases, where the latter was believed to have vanishing gradients even for very shallow circuits. Experimental results verify our theoretical findings in quantum simulation and quantum chemistry.

We study the fundamental task of outlier-robust mean estimation for heavy-tailed distributions in the presence of sparsity. Specifically, given a small number of corrupted samples from a high-dimensional heavy-tailed distribution whose mean $\mu$ is guaranteed to be sparse, the goal is to efficiently compute a hypothesis that accurately approximates $\mu$ with high probability. Prior work had obtained efficient algorithms for robust sparse mean estimation of light-tailed distributions. In this work, we give the first sample-efficient and polynomial-time robust sparse mean estimator for heavy-tailed distributions under mild moment assumptions. Our algorithm achieves the optimal asymptotic error using a number of samples scaling logarithmically with the ambient dimension. Importantly, the sample complexity of our method is optimal as a function of the failure probability $\tau$, having an {\em additive} $\log(1/\tau)$ dependence. Our algorithm leverages the stability-based approach from the algorithmic robust statistics literature, with crucial (and necessary) adaptations required in our setting. Our analysis may be of independent interest, involving the delicate design of a (non-spectral) decomposition for positive semi-definite matrices satisfying certain sparsity properties.

Antibodies are immune system proteins that protect the host by binding to specific antigens such as viruses and bacteria. The binding between antibodies and antigens is mainly determined by the complementarity-determining regions (CDR) of the antibodies. In this work, we develop a deep generative model that jointly models sequences and structures of CDRs based on diffusion probabilistic models and equivariant neural networks. Our method is the first deep learning-based method that generates antibodies explicitly targeting specific antigen structures and is one of the earliest diffusion probabilistic models for protein structures. The model is a "Swiss Army Knife" capable of sequence-structure co-design, sequence design for given backbone structures, and antibody optimization. We conduct extensive experiments to evaluate the quality of both sequences and structures of designed antibodies. We find that our model could yield competitive results in binding affinity measured by biophysical energy functions and other protein design metrics.

Recent work has shown that a simple, fast method called Simple Graph Convolution (SGC) (Wu et al., 2019), which eschews deep learning, is competitive with deep methods like graph convolutional networks (GCNs) (Kipf & Welling, 2017) in common graph machine learning benchmarks. The use of graph data in SGC implicitly assumes the common but not universal graph characteristic of homophily, wherein nodes link to nodes which are similar. Here we confirm that SGC is indeed ineffective for heterophilous (i.e., non-homophilous) graphs via experiments on synthetic and real-world datasets. We propose Adaptive Simple Graph Convolution (ASGC), which we show can adapt to both homophilous and heterophilous graph structure. Like SGC, ASGC is not a deep model, and hence is fast, scalable, and interpretable; further, we can prove performance guarantees on natural synthetic data models. Empirically, ASGC is often competitive with recent deep models at node classification on a benchmark of real-world datasets. The SGC paper questioned whether the complexity of graph neural networks is warranted for common graph problems involving homophilous networks; our results similarly suggest that, while deep learning often achieves the highest performance, heterophilous structure alone does not necessitate these more involved methods.

Self-Supervised Learning (SSL) surmises that inputs and pairwise positive relationships are enough to learn meaningful representations. Although SSL has recently reached a milestone: outperforming supervised methods in many modalities\dots the theoretical foundations are limited, method-specific, and fail to provide principled design guidelines to practitioners. In this paper, we propose a unifying framework under the helm of spectral manifold learning. Through the course of this study, we will demonstrate that VICReg, SimCLR, BarlowTwins et al. correspond to eponymous spectral methods such as Laplacian Eigenmaps, ISOMAP et al. From this unified viewpoint, we obtain (i) the close-form optimal representation, (ii) the close-form optimal network parameters in the linear regime, (iii) the impact of the pairwise relations used during training on each of those quantities and on downstream task performances, and most importantly, (iv) the first theoretical bridge between contrastive and non-contrastive methods to global and local spectral methods respectively hinting at the benefits and limitations of each. For example, if the pairwise relation is aligned with the downstream task, all SSL methods produce optimal representations for that downstream task.

Knowledge distillation (KD) is essentially a process of transferring a teacher model's behavior, e.g., network response, to a student model. The network response serves as additional supervision to formulate the machine domain, which uses the data collected from the human domain as a transfer set. Traditional KD methods hold an underlying assumption that the data collected in both human domain and machine domain are both independent and identically distributed (IID). We point out that this naive assumption is unrealistic and there is indeed a transfer gap between the two domains. Although the gap offers the student model external knowledge from the machine domain, the imbalanced teacher knowledge would make us incorrectly estimate how much to transfer from teacher to student per sample on the non-IID transfer set. To tackle this challenge, we propose Inverse Probability Weighting Distillation (IPWD) that estimates the propensity of a training sample belonging to the machine domain, and assigns its inverse amount to compensate for under-represented samples. Experiments on CIFAR-100 and ImageNet demonstrate the effectiveness of \ours~for both two-stage distillation and one-stage self-distillation.

The spectacular successes of recurrent neural network models where key parameters are adjusted via backpropagation-based gradient descent have inspired much thought as to how biological neuronal networks might solve the corresponding synaptic credit assignment problem [1, 2, 3]. There is so far little agreement, however, as to how biological networks could implement the necessary backpropagation through time, given widely recognized constraints of biological synaptic network signaling architectures. Here, we propose that extra-synaptic diffusion of local neuromodulators such as neuropeptides may afford an effective mode of backpropagation lying within the bounds of biological plausibility. Going beyond existing temporal truncation-based gradient approximations [4, 5, 6], our approximate gradient-based update rule, ModProp, propagates credit information through arbitrary time steps. ModProp suggests that modulatory signals can act on receiving cells by convolving their eligibility traces via causal, time-invariant and synapse-type-specific filter taps. Our mathematical analysis of ModProp learning, together with simulation results on benchmark temporal tasks, demonstrate the advantage of ModProp over existing biologically-plausible temporal credit assignment rules. These results suggest a potential neuronal mechanism for signaling credit information related to recurrent interactions over a longer time horizon. Finally, we derive an in-silico implementation of ModProp that could serve as a low-complexity and causal alternative to backpropagation through time.

In this paper, we consider the problem of differentially private (DP) algorithms for isotonic regression. For the most general problem of isotonic regression over a partially ordered set (poset) $\mathcal{X}$ and for any Lipschitz loss function, we obtain a pure-DP algorithm that, given $n$ input points, has an expected excess empirical risk of roughly $\mathrm{width}(\mathcal{X}) \cdot \log|\mathcal{X}| / n$, where $\mathrm{width}(\mathcal{X})$ is the width of the poset. In contrast, we also obtain a near-matching lower bound of roughly $(\mathrm{width}(\mathcal{X}) + \log |\mathcal{X}|) / n$, that holds even for approximate-DP algorithms. Moreover, we show that the above bounds are essentially the best that can be obtained without utilizing any further structure of the poset. In the special case of a totally ordered set and for $\ell_1$ and $\ell_2^2$ losses, our algorithm can be implemented in near-linear running time; we also provide extensions of this algorithm to the problem of private isotonic regression with additional structural constraints on the output function.

Offline reinforcement learning (RL) aims at learning effective policies from historical data without extra environment interactions. During our experience of applying offline RL, we noticed that previous offline RL benchmarks commonly involve significant reality gaps, which we have identified include rich and overly exploratory datasets, degraded baseline, and missing policy validation. In many real-world situations, to ensure system safety, running an overly exploratory policy to collect various data is prohibited, thus only a narrow data distribution is available. The resulting policy is regarded as effective if it is better than the working behavior policy; the policy model can be deployed only if it has been well validated, rather than accomplished the training. In this paper, we present a Near real-world offline RL benchmark, named NeoRL, to reflect these properties. NeoRL datasets are collected with a more conservative strategy. Moreover, NeoRL contains the offline training and offline validation pipeline before the online test, corresponding to real-world situations. We then evaluate recent state-of-the-art offline RL algorithms in NeoRL. The empirical results demonstrate that some offline RL algorithms are less competitive to the behavior cloning and the deterministic behavior policy, implying that they could be less effective in real-world tasks than in the previous benchmarks. We also disclose that current offline policy evaluation methods could hardly select the best policy. We hope this work will shed some light on future research and deploying RL in real-world systems.

Reinforcement learning typically relies heavily on a well-designed reward signal, which gets more challenging in cooperative multi-agent reinforcement learning. Alternatively, unsupervised reinforcement learning (URL) has delivered on its promise in the recent past to learn useful skills and explore the environment without external supervised signals. These approaches mainly aimed for the single agent to reach distinguishable states, insufficient for multi-agent systems due to that each agent interacts with not only the environment, but also the other agents. We propose Synergy Pattern Diversifying Oriented Unsupervised Multi-agent Reinforcement Learning (SPD) to learn generic coordination policies for agents with no extrinsic reward. Specifically, we devise the Synergy Pattern Graph (SPG), a graph depicting the relationships of agents at each time step. Furthermore, we propose an episode-wise divergence measurement to approximate the discrepancy of synergy patterns. To overcome the challenge of sparse return, we decompose the discrepancy of synergy patterns to per-time-step pseudo-reward. Empirically, we show the capacity of SPD to acquire meaningful coordination policies, such as maintaining specific formations in Multi-Agent Particle Environment and pass-and-shoot in Google Research Football. Furthermore, we demonstrate that the same instructive pretrained policy's parameters can serve as a good initialization for a series of downstream tasks' policies, achieving higher data efficiency and outperforming state-of-the-art approaches in Google Research Football.

Automatic action identification from video and kinematic data is an important machine learning problem with applications ranging from robotics to smart health. Most existing works focus on identifying coarse actions such as running, climbing, or cutting vegetables, which have relatively long durations and a complex series of motions. This is an important limitation for applications that require identification of more elemental motions at high temporal resolution. For example, in the rehabilitation of arm impairment after stroke, quantifying the training dose (number of repetitions) requires differentiating motions with sub-second durations. Our goal is to bridge this gap. To this end, we introduce a large-scale, multimodal dataset, StrokeRehab, as a new action-recognition benchmark that includes elemental short-duration actions labeled at a high temporal resolution. StrokeRehab consists of a high-quality inertial measurement unit sensor and video data of 51 stroke-impaired patients and 20 healthy subjects performing activities of daily living like feeding, brushing teeth, etc. Because it contains data from both healthy and impaired individuals, StrokeRehab can be used to study the influence of distribution shift in action-recognition tasks. When evaluated on StrokeRehab, current state-of-the-art models for action segmentation produce noisy predictions, which reduces their accuracy in identifying the corresponding sequence of actions. To address this, we propose a novel approach for high-resolution action identification, inspired by speech-recognition techniques, which is based on a sequence-to-sequence model that directly predicts the sequence of actions. This approach outperforms current state-of-the-art methods on StrokeRehab, as well as on the standard benchmark datasets 50Salads, Breakfast, and Jigsaws.

We provide new insights on eluder dimension, a complexity measure that has been extensively used to bound the regret of algorithms for online bandits and reinforcement learning with function approximation. First, we study the relationship between the eluder dimension for a function class and a generalized notion of \emph{rank}, defined for any monotone ``activation'' $\sigma : \mathbb{R}\to \mathbb{R}$, which corresponds to the minimal dimension required to represent the class as a generalized linear model. It is known that when $\sigma$ has derivatives bounded away from $0$, $\sigma$-rank gives rise to an upper bound on eluder dimension for any function class; we show however that eluder dimension can be exponentially smaller than $\sigma$-rank. We also show that the condition on the derivative is necessary; namely, when $\sigma$ is the $\mathsf{relu}$ activation, the eluder dimension can be exponentially larger than $\sigma$-rank. For Boolean-valued function classes, we obtain a characterization of the eluder dimension in terms of star number and threshold dimension, quantities which are relevant in active learning and online learning respectively.

We study Model Predictive Control (MPC) and propose a general analysis pipeline to bound its dynamic regret. The pipeline first requires deriving a perturbation bound for a finite-time optimal control problem. Then, the perturbation bound is used to bound the per-step error of MPC, which leads to a bound on the dynamic regret. Thus, our pipeline reduces the study of MPC to the well-studied problem of perturbation analysis, enabling the derivation of regret bounds of MPC under a variety of settings. To demonstrate the power of our pipeline, we use it to generalize existing regret bounds on MPC in linear time-varying (LTV) systems to incorporate prediction errors on costs, dynamics, and disturbances. Further, our pipeline leads to regret bounds on MPC in systems with nonlinear dynamics and constraints.