NeurIPS 2022 Papers

Training convolutional neural networks (CNNs) with a strict 1-Lipschitz constraint under the l_{2} norm is useful for adversarial robustness, interpretable gradients and stable training. 1-Lipschitz CNNs are usually designed by enforcing each layer to have an orthogonal Jacobian matrix (for all inputs) to prevent the gradients from vanishing during backpropagation. However, their performance often significantly lags behind that of heuristic methods to enforce Lipschitz constraints where the resulting CNN is not provably 1-Lipschitz. In this work, we reduce this gap by introducing (a) a procedure to certify robustness of 1-Lipschitz CNNs by replacing the last linear layer with a 1-hidden layer MLP that significantly improves their performance for both standard and provably robust accuracy, (b) a method to significantly reduce the training time per epoch for Skew Orthogonal Convolution (SOC) layers (>30\% reduction for deeper networks) and (c) a class of pooling layers using the mathematical property that the l_{2} distance of an input to a manifold is 1-Lipschitz. Using these methods, we significantly advance the state-of-the-art for standard and provable robust accuracies on CIFAR-10 (gains of +1.79\% and +3.82\%) and similarly on CIFAR-100 (+3.78\% and +4.75\% across all networks.

Variational Bayesian posterior inference often requires simplifying approximations such as mean-field parametrisation to ensure tractability. However, prior work has associated the variational mean-field approximation for Bayesian neural networks with underfitting in the case of small datasets or large model sizes. In this work, we show that invariances in the likelihood function of over-parametrised models contribute to this phenomenon because these invariances complicate the structure of the posterior by introducing discrete and/or continuous modes which cannot be well approximated by Gaussian mean-field distributions. In particular, we show that the mean-field approximation has an additional gap in the evidence lower bound compared to a purpose-built posterior that takes into account the known invariances. Importantly, this invariance gap is not constant; it vanishes as the approximation reverts to the prior. We proceed by first considering translation invariances in a linear model with a single data point in detail. We show that, while the true posterior can be constructed from a mean-field parametrisation, this is achieved only if the objective function takes into account the invariance gap. Then, we transfer our analysis of the linear model to neural networks. Our analysis provides a framework for future work to explore solutions to the invariance problem.

Due to the widespread use of complex machine learning models in real-world applications, it is becoming critical to explain model predictions. However, these models are typically black-box deep neural networks, explained post-hoc via methods with known faithfulness limitations. Generalized Additive Models (GAMs) are an inherently interpretable class of models that address this limitation by learning a non-linear shape function for each feature separately, followed by a linear model on top. However, these models are typically difficult to train, require numerous parameters, and are difficult to scale. We propose an entirely new subfamily of GAMs that utilizes basis decomposition of shape functions. A small number of basis functions are shared among all features, and are learned jointly for a given task, thus making our model scale much better to large-scale data with high-dimensional features, especially when features are sparse. We propose an architecture denoted as the Neural Basis Model (NBM) which uses a single neural network to learn these bases. On a variety of tabular and image datasets, we demonstrate that for interpretable machine learning, NBMs are the state-of-the-art in accuracy, model size, and, throughput and can easily model all higher-order feature interactions. Source code is available at \href{https://github.com/facebookresearch/nbm-spam}{\ttfamily github.com/facebookresearch/nbm-spam}.

Mean-Field Game (MFG) serves as a crucial mathematical framework in modeling the collective behavior of individual agents interacting stochastically with a large population. In this work, we aim at solving a challenging class of MFGs in which the differentiability of these interacting preferences may not be available to the solver, and the population is urged to converge exactly to some desired distribution. These setups are, despite being well-motivated for practical purposes, complicated enough to paralyze most (deep) numerical solvers. Nevertheless, we show that Schrödinger Bridge — as an entropy-regularized optimal transport model — can be generalized to accepting mean-field structures, hence solving these MFGs. This is achieved via the application of Forward-Backward Stochastic Differential Equations theory, which, intriguingly, leads to a computational framework with a similar structure to Temporal Difference learning. As such, it opens up novel algorithmic connections to Deep Reinforcement Learning that we leverage to facilitate practical training. We show that our proposed objective function provides necessary and sufficient conditions to the mean-field problem. Our method, named Deep Generalized Schrödinger Bridge (DeepGSB), not only outperforms prior methods in solving classical population navigation MFGs, but is also capable of solving 1000-dimensional opinion depolarization, setting a new state-of-the-art numerical solver for high-dimensional MFGs. Our code will be made available at https://github.com/ghliu/DeepGSB.

Next Best View computation (NBV) is a long-standing problem in robotics, and consists in identifying the next most informative sensor position(s) for reconstructing a 3D object or scene efficiently and accurately. Like most current methods, we consider NBV prediction from a depth sensor like Lidar systems. Learning-based methods relying on a volumetric representation of the scene are suitable for path planning, but have lower accuracy than methods using a surface-based representation. However, the latter do not scale well with the size of the scene and constrain the camera to a small number of poses. To obtain the advantages of both representations, we show that we can maximize surface metrics by Monte Carlo integration over a volumetric representation. In particular, we propose an approach, SCONE, that relies on two neural modules: The first module predicts occupancy probability in the entire volume of the scene. Given any new camera pose, the second module samples points in the scene based on their occupancy probability and leverages a self-attention mechanism to predict the visibility of the samples. Finally, we integrate the visibility to evaluate the gain in surface coverage for the new camera pose. NBV is selected as the pose that maximizes the gain in total surface coverage. Our method scales to large scenes and handles free camera motion: It takes as input an arbitrarily large point cloud gathered by a depth sensor as well as camera poses to predict NBV. We demonstrate our approach on a novel dataset made of large and complex 3D scenes.

Given a long list of anomaly detection algorithms developed in the last few decades, how do they perform with regard to (i) varying levels of supervision, (ii) different types of anomalies, and (iii) noisy and corrupted data? In this work, we answer these key questions by conducting (to our best knowledge) the most comprehensive anomaly detection benchmark with 30 algorithms on 57 benchmark datasets, named ADBench. Our extensive experiments (98,436 in total) identify meaningful insights into the role of supervision and anomaly types, and unlock future directions for researchers in algorithm selection and design. With ADBench, researchers can easily conduct comprehensive and fair evaluations for newly proposed methods on the datasets (including our contributed ones from natural language and computer vision domains) against the existing baselines. To foster accessibility and reproducibility, we fully open-source ADBench and the corresponding results.

In-context learning is the ability of a model to condition on a prompt sequence consisting of in-context examples (input-output pairs corresponding to some task) along with a new query input, and generate the corresponding output. Crucially, in-context learning happens only at inference time without any parameter updates to the model. While large language models such as GPT-3 exhibit some ability to perform in-context learning, it is unclear what the relationship is between tasks on which this succeeds and what is present in the training data. To investigate this, we consider the problem of training a model to in-context learn a function class (e.g., linear functions): given data derived from some functions in the class, can we train a model (e.g., a Transformer) to in-context learn most functions from that class? We show empirically that standard Transformers can be trained from scratch to perform in-context learning of linear functions---that is, the trained model is able to learn unseen linear functions from in-context examples with performance comparable to the optimal least squares estimator. In fact, in-context learning is possible even under two forms of distribution shift: (i) between the training data of the Transformer and inference-time prompts, and (ii) between the in-context examples and the query input during inference. We also show that we can train Transformers to in-context learn more complex function classes: sparse linear functions where the model outperforms least squares and nearly matches the performance of Lasso, and two-layer neural networks where the model performs comparably to neural networks trained on in-context examples using gradient descent.

Recently, model-based agents have achieved better performance than model-free ones using the same computational budget and training time in single-agent environments. However, due to the complexity of multi-agent systems, it is tough to learn the model of the environment. The significant compounding error may hinder the learning process when model-based methods are applied to multi-agent tasks. This paper proposes an implicit model-based multi-agent reinforcement learning method based on value decomposition methods. Under this method, agents can interact with the learned virtual environment and evaluate the current state value according to imagined future states in the latent space, making agents have the foresight. Our approach can be applied to any multi-agent value decomposition method. The experimental results show that our method improves the sample efficiency in different partially observable Markov decision process domains.

Massive amounts of data are naturally dispersed over different clients in many real-world applications, collaborative learning has been a promising paradigm that allows to learn models through collaboration among the clients. However, leveraging these dispersed data to learn good models is still challenging since data over different clients are heterogeneous. Previous works mainly focus on learning the centralized model for all clients or learning a personalized model for each client. When there are numerous clients, the centralized model performs badly on some clients, while learning a personalized model for each client costs unaffordable computational resources. In this paper, we propose the collaborative learning method to detect collaboration partners and adaptively learn $K$ models for numerous heterogeneous clients. We theoretically prove that the model learned for each client is a good approximation of its personalized model. Experimental results on real-world datasets verify the effectiveness of our method.

Federated learning is a learning paradigm to enable collaborative learning across different parties without revealing raw data. Notably, vertical federated learning (VFL), where parties share the same set of samples but only hold partial features, has a wide range of real-world applications. However, most existing studies in VFL disregard the "record linkage'' process. They design algorithms either assuming the data from different parties can be exactly linked or simply linking each record with its most similar neighboring record. These approaches may fail to capture the key features from other less similar records. Moreover, such improper linkage cannot be corrected by training since existing approaches provide no feedback on linkage during training. In this paper, we design a novel coupled training paradigm, FedSim, that integrates one-to-many linkage into the training process. Besides enabling VFL in many real-world applications with fuzzy identifiers, FedSim also achieves better performance in traditional VFL tasks. Moreover, we theoretically analyze the additional privacy risk incurred by sharing similarities. Our experiments on eight datasets with various similarity metrics show that FedSim outperforms other state-of-the-art baselines. The codes of FedSim are available at https://github.com/Xtra-Computing/FedSim.

We rigorously prove that deep Gaussian process priors can outperform Gaussian process priors if the target function has a compositional structure. To this end, we study information-theoretic lower bounds for posterior contraction rates for Gaussian process regression in a continuous regression model. We show that if the true function is a generalized additive function, then the posterior based on any mean-zero Gaussian process can only recover the truth at a rate that is strictly slower than the minimax rate by a factor that is polynomially suboptimal in the sample size $n$.

With the advent of deep learning over the last decade, a considerable amount of effort has gone into better understanding and enhancing Stochastic Gradient Descent so as to improve the performance and stability of artificial neural network training. Active research fields in this area include exploiting second order information of the loss landscape and improving the understanding of chaotic dynamics in optimization. This paper exploits the theoretical connection between the curvature of the loss landscape and chaotic dynamics in neural network training to propose a modified SGD ensuring non-chaotic training dynamics to study the importance thereof in NN training. Building on this, we present empirical evidence suggesting that the negative eigenspectrum - and thus directions of local chaos - cannot be removed from SGD without hurting training performance. Extending our empirical analysis to long-term chaos dynamics, we challenge the widespread understanding of convergence against a confined region in parameter space. Our results show that although chaotic network behavior is mostly confined to the initial training phase, models perturbed upon initialization do diverge at a slow pace even after reaching top training performance, and that their divergence can be modelled through a composition of a random walk and a linear divergence. The tools and insights developed as part of our work contribute to improving the understanding of neural network training dynamics and provide a basis for future improvements of optimization methods.

Active learning methods have shown great promise in reducing the number of samples necessary for learning. As automated learning systems are adopted into real-time, real-world decision-making pipelines, it is increasingly important that such algorithms are designed with safety in mind. In this work we investigate the complexity of learning the best safe decision in interactive environments. We reduce this problem to a safe linear bandits problem, where our goal is to find the best arm satisfying certain (unknown) safety constraints. We propose an adaptive experimental design-based algorithm, which we show efficiently trades off between the difficulty of showing an arm is unsafe vs suboptimal. To our knowledge, our results are the first on best-arm identification in linear bandits with safety constraints. In practice, we demonstrate that this approach performs well on synthetic and real world datasets.

Large language models generate complex, open-ended outputs: instead of outputting a class label they write summaries, generate dialogue, or produce working code. In order to asses the reliability of these open-ended generation systems, we aim to identify qualitative categories of erroneous behavior, beyond identifying individual errors. To hypothesize and test for such qualitative errors, we draw inspiration from human cognitive biases---systematic patterns of deviation from rational judgement. Specifically, we use cognitive biases as motivation to (i) generate hypotheses for problems that models may have, and (ii) develop experiments that elicit these problems. Using code generation as a case study, we find that OpenAI’s Codex errs predictably based on how the input prompt is framed, adjusts outputs towards anchors, and is biased towards outputs that mimic frequent training examples. We then use our framework to elicit high-impact errors such as incorrectly deleting files. Our results indicate that experimental methodology from cognitive science can help characterize how machine learning systems behave.

Given an $n \times n$ non-negative rank-$K$ matrix $\Omega$ where $m$ eigenvalues are negative, when can we write $\Omega = Z P Z'$ for non-negative matrices $Z \in \mathbb{R}^{n, K}$ and $P \in \mathbb{R}^{K, K}$? While most existing works focused on the case of $m = 0$, our primary interest is on the case of general $m$. With new proof ideas we develop, we present sharp results on when the NMF problem is solvable, which significantly extend existing results on this topic. The NMF problem is partially motivated by applications in network modeling. For a network with $K$ communities, rank-$K$ models are popular, with many proposals. The DCMM model is a recent rank-$K$ model which is especially useful and interpretable in practice. To enjoy such properties, it is of interest to study when a rank-$K$ model can be rewritten as a DCMM model. Using our NMF results, we show that for a rank-$K$ model with parameters in the most interesting range, we can always rewrite it as a DCMM model.

The lottery ticket hypothesis (LTH) has attracted attention because it can explain why over-parameterized models often show high generalization ability. It is known that when we use iterative magnitude pruning (IMP), which is an algorithm to find sparse networks with high generalization ability that can be trained from the initial weights independently, called winning tickets, the initial large learning rate does not work well in deep neural networks such as ResNet. However, since the initial large learning rate generally helps the optimizer to converge to flatter minima, we hypothesize that the winning tickets have relatively sharp minima, which is considered a disadvantage in terms of generalization ability. In this paper, we confirm this hypothesis and show that the PAC-Bayesian theory can provide an explicit understanding of the relationship between LTH and generalization behavior. On the basis of our experimental findings that IMP with a small learning rate finds relatively sharp minima and that the distance from the initial weights is deeply involved in winning tickets, we offer the PAC-Bayes bound using a spike-and-slab distribution to analyze winning tickets. Finally, we revisit existing algorithms for finding winning tickets from a PAC-Bayesian perspective and provide new insights into these methods.

Graph contrastive learning (GCL), leveraging graph augmentations to convert graphs into different views and further train graph neural networks (GNNs), has achieved considerable success on graph benchmark datasets. Yet, there are still some gaps in directly applying existing GCL methods to real-world data. First, handcrafted graph augmentations require trials and errors, but still can not yield consistent performance on multiple tasks. Second, most real-world graph data present class-imbalanced distribution but existing GCL methods are not immune to data imbalance. Therefore, this work proposes to explicitly tackle these challenges, via a principled framework called \textit{\textbf{C}o-\textbf{M}odality \textbf{G}raph \textbf{C}ontrastive \textbf{L}earning} (\textbf{CM-GCL}) to automatically generate contrastive pairs and further learn balanced representation over unlabeled data. Specifically, we design inter-modality GCL to automatically generate contrastive pairs (e.g., node-text) based on rich node content. Inspired by the fact that minority samples can be ``forgotten'' by pruning deep neural networks, we naturally extend network pruning to our GCL framework for mining minority nodes. Based on this, we co-train two pruned encoders (e.g., GNN and text encoder) in different modalities by pushing the corresponding node-text pairs together and the irrelevant node-text pairs away. Meanwhile, we propose intra-modality GCL by co-training non-pruned GNN and pruned GNN, to ensure node embeddings with similar attribute features stay closed. Last, we fine-tune the GNN encoder on downstream class-imbalanced node classification tasks. Extensive experiments demonstrate that our model significantly outperforms state-of-the-art baseline models and learns more balanced representations on real-world graphs. Our source code is available at https://github.com/graphprojects/CM-GCL.

Intensive algorithmic efforts have been made to enable the rapid improvements of certificated robustness for complex ML models recently. However, current robustness certification methods are only able to certify under a limited perturbation radius. Given that existing pure data-driven statistical approaches have reached a bottleneck, in this paper, we propose to integrate statistical ML models with knowledge (expressed as logical rules) as a reasoning component using Markov logic networks (MLN), so as to further improve the overall certified robustness. This opens new research questions about certifying the robustness of such a paradigm, especially the reasoning component (e.g., MLN). As the first step towards understanding these questions, we first prove that the computational complexity of certifying the robustness of MLN is #P-hard. Guided by this hardness result, we then derive the first certified robustness bound for MLN by carefully analyzing different model regimes. Finally, we conduct extensive experiments on five datasets including both high-dimensional images and natural language texts, and we show that the certified robustness with knowledge-based logical reasoning indeed significantly outperforms that of the state-of-the-arts.

We present new algorithms for online convex optimization over unbounded domains that obtain parameter-free regret in high-probability given access only to potentially heavy-tailed subgradient estimates. Previous work in unbounded domains con- siders only in-expectation results for sub-exponential subgradients. Unlike in the bounded domain case, we cannot rely on straight-forward martingale concentration due to exponentially large iterates produced by the algorithm. We develop new regularization techniques to overcome these problems. Overall, with probability at most δ, for all comparators u our algorithm achieves regret O ̃(∥u∥T 1/p log(1/δ)) for subgradients with bounded pth moments for some p ∈ (1, 2].