ICLR 2023 Papers

What is an image, and how to extract latent features? Convolutional Networks (ConvNets) consider an image as organized pixels in a rectangular shape and extract features via convolutional operation in a local region; Vision Transformers (ViTs) treat an image as a sequence of patches and extract features via attention mechanism in a global range. In this work, we introduce a straightforward and promising paradigm for visual representation, which is called Context Clusters. Context clusters (CoCs) view an image as a set of unorganized points and extract features via a simplified clustering algorithm. In detail, each point includes the raw feature (e.g., color) and positional information (e.g., coordinates), and a simplified clustering algorithm is employed to group and extract deep features hierarchically. Our CoCs are convolution- and attention-free, only relying on clustering algorithm for spatial interaction. Owing to the simple design, we show CoCs endow gratifying interpretability via the visualization of the clustering process. Our CoCs aim at providing a new perspective on image and visual representation, which may enjoy broad applications in different domains and exhibit profound insights. Even though we are not targeting SOTA performance, COCs still achieve comparable or even better performance than ConvNets or ViTs on several benchmarks.

Empirical risk minimization (ERM) is known to be non-robust in practice to distributional shift where the training and the test distributions are different. A suite of approaches, such as importance weighting, and variants of distributionally robust optimization (DRO), have been proposed to solve this problem. But a line of recent work has empirically shown that these approaches do not significantly improve over ERM in real applications with distribution shift. The goal of this work is to obtain a comprehensive theoretical understanding of this intriguing phenomenon. We first posit the class of Generalized Reweighting (GRW) algorithms, as a broad category of approaches that iteratively update model parameters based on iterative reweighting of the training samples. We show that when overparameterized models are trained under GRW, the resulting models are close to that obtained by ERM. We also show that adding small regularization which does not greatly affect the empirical training accuracy does not help. Together, our results show that a broad category of what we term GRW approaches are not able to achieve distributionally robust generalization. Our work thus has the following sobering takeaway: to make progress towards distributionally robust generalization, we either have to develop non-GRW approaches, or perhaps devise novel classification/regression loss functions that are adapted to GRW approaches.

Large-scale linear models are ubiquitous throughout machine learning, with contemporary application as surrogate models for neural network uncertainty quantification; that is, the linearised Laplace method. Alas, the computational cost associated with Bayesian linear models constrains this method's application to small networks, small output spaces and small datasets. We address this limitation by introducing a scalable sample-based Bayesian inference method for conjugate Gaussian multi-output linear models, together with a matching method for hyperparameter (regularisation) selection. Furthermore, we use a classic feature normalisation method (the g-prior) to resolve a previously highlighted pathology of the linearised Laplace method. Together, these contributions allow us to perform linearised neural network inference with ResNet-18 on CIFAR100 (11M parameters, 100 output dimensions × 50k datapoints) and with a U-Net on a high-resolution tomographic reconstruction task (2M parameters, 251k output dimensions).

The robustness of a deep classifier can be characterized by its margins: the decision boundary's distances to natural data points. However, it is unclear whether existing robust training methods effectively increase the margin for each vulnerable point during training. To understand this, we propose a continuous-time framework for quantifying the relative speed of the decision boundary with respect to each individual point. Through visualizing the moving speed of the decision boundary under Adversarial Training, one of the most effective robust training algorithms, a surprising moving-behavior is revealed: the decision boundary moves away from some vulnerable points but simultaneously moves closer to others, decreasing their margins. To alleviate these conflicting dynamics of the decision boundary, we propose Dynamics-aware Robust Training (DyART), which encourages the decision boundary to engage in movement that prioritizes increasing smaller margins. In contrast to prior works, DyART directly operates on the margins rather than their indirect approximations, allowing for more targeted and effective robustness improvement. Experiments on the CIFAR-10 and Tiny-ImageNet datasets verify that DyART alleviates the conflicting dynamics of the decision boundary and obtains improved robustness under various perturbation sizes compared to the state-of-the-art defenses. Our code is available at https://github.com/Yuancheng-Xu/Dynamics-Aware-Robust-Training.

We consider the problem of computing the $1$-Wasserstein distance $\mathcal{W}(\mu,\nu)$ between two $d$-dimensional discrete distributions $\mu$ and $\nu$ whose support lie within the unit hypercube. There are several algorithms that estimate $\mathcal{W}(\mu,\nu)$ within an additive error of $\varepsilon$. However, when $\mathcal{W}(\mu,\nu)$ is small, the additive error $\varepsilon$ dominates, leading to noisy results. Consider any additive approximation algorithm with execution time $T(n,\varepsilon)$. We propose an algorithm that runs in $O(T(n,\varepsilon/d) \log n)$ time and boosts the accuracy of estimating $\mathcal{W}(\mu,\nu)$ from $\varepsilon$ to an expected additive error of $\min\{\varepsilon, (d\log_{\sqrt{d}/\varepsilon} n)\mathcal{W}(\mu,\nu)\}$. For the special case where every point in the support of $\mu$ and $\nu$ has a mass of $1/n$ (also called the Euclidean Bipartite Matching problem), we describe an algorithm to boost the accuracy of any additive approximation algorithm from $\varepsilon$ to an expected additive error of $\min\{\varepsilon, (d\log\log n)\mathcal{W}(\mu,\nu)\}$ in $O(T(n, \varepsilon/d)\log\log n)$ time.

Identifying nonlinear causal relationships in high-dimensional biological data is an important task. However, current neural network based causality detection approaches for such data suffer from poor interpretability and cannot scale well to the high dimensional regime. Here we present GEASS (Granger fEAture Selection of Spatiotemporal data), which identifies sparse Granger causality mechanisms of high dimensional spatiotemporal data by a single neural network. GEASS maximizes sparsity-regularized modified transfer entropy with a theoretical guarantee of recovering features with spatial/temporal Granger causal relationships. The sparsity regularization is achieved by a novel combinatorial stochastic gate layer to select sparse non-overlapping feature subsets. We demonstrate the efficacy of GEASS in several synthetic datasets and real biological data from single-cell RNA sequencing and spatial transcriptomics.

In this paper, we explore learning statistically consistent classifiers under label noise by estimating the noise transition matrix T. We first provide a holistic view of existing T-estimation methods including those with or without anchor point assumptions. We unified them into the Minimum Geometric Envelope Operator (MGEO) framework, which tries to find the smallest T (in terms of a certain metric) that elicits a convex hull to enclose the posteriors of all the training data. Although MGEO methods show appealing theoretical properties and empirical results, we find them prone to failing when the noisy posterior estimation is imperfect, which is inevitable in practice. Specifically, we show that MGEO methods are in-consistent even with infinite samples if the noisy posterior is not estimated accurately. In view of this, we make the first effort to address this issue by proposing a novel T-estimation framework via the lens of bilevel optimization, and term it RObust Bilevel OpTimzation (ROBOT). ROBOT paves a new road beyond MGEO framework, which enjoys strong theoretical properties: identifibility, consistency and finite-sample generalization guarantees. Notably, ROBOT neither requires the perfect posterior estimation nor assumes the existence of anchor points. We further theoretically demonstrate that ROBOT is more robust in the case where MGEO methods fail. Experimentally, our framework also shows superior performance across multiple benchmarks.

Out-of-distribution (OOD) detection is a critical task for reliable machine learning. Recent advances in representation learning give rise to distance-based OOD detection, where testing samples are detected as OOD if they are relatively far away from the centroids or prototypes of in-distribution (ID) classes. However, prior methods directly take off-the-shelf contrastive losses that suffice for classifying ID samples, but are not optimally designed when test inputs contain OOD samples. In this work, we propose CIDER, a novel representation learning framework that exploits hyperspherical embeddings for OOD detection. CIDER jointly optimizes two losses to promote strong ID-OOD separability: a dispersion loss that promotes large angular distances among different class prototypes, and a compactness loss that encourages samples to be close to their class prototypes. We analyze and establish the unexplored relationship between OOD detection performance and the embedding properties in the hyperspherical space, and demonstrate the importance of dispersion and compactness. CIDER establishes superior performance, outperforming the latest rival by 13.33% in FPR95. Code is available at https://github.com/deeplearning-wisc/cider.

Semi-supervised learning and weakly supervised learning are important paradigms that aim to reduce the growing demand for labeled data in current machine learning applications. In this paper, we introduce a novel analysis of the classical label propagation algorithm (LPA) (Zhu & Ghahramani, 2002) that moreover takes advantage of useful prior information, specifically probabilistic hypothesized labels on the unlabeled data. We provide an error bound that exploits both the local geometric properties of the underlying graph and the quality of the prior information. We also propose a framework to incorporate multiple sources of noisy information. In particular, we consider the setting of weak supervision, where our sources of information are weak labelers. We demonstrate the ability of our approach on multiple benchmark weakly supervised classification tasks, showing improvements upon existing semi-supervised and weakly supervised methods.

To reduce the human annotation efforts, the programmatic weak supervision (PWS) paradigm abstracts weak supervision sources as labeling functions (LFs) and involves a label model to aggregate the output of multiple LFs to produce training labels. Most existing label models require a parameter learning step for each dataset. In this work, we present a hyper label model that (once learned) infers the ground-truth labels for each dataset in a single forward pass without dataset-specific parameter learning. The hyper label model approximates an optimal analytical (yet computationally intractable) solution of the ground-truth labels. We train the model on synthetic data generated in the way that ensures the model approximates the analytical optimal solution, and build the model upon Graph Neural Network (GNN) to ensure the model prediction being invariant (or equivariant) to the permutation of LFs (or data points). On 14 real-world datasets, our hyper label model outperforms the best existing methods in both accuracy (by 1.4 points on average) and efficiency (by six times on average). Our code is available at https://github.com/wurenzhi/hyper_label_model

Kohn-Sham Density Functional Theory (KS-DFT) has been traditionally solved by the Self-Consistent Field (SCF) method. Behind the SCF loop is the physics intuition of solving a system of non-interactive single-electron wave functions under an effective potential. In this work, we propose a deep learning approach to KS-DFT. First, in contrast to the conventional SCF loop, we propose to directly minimize the total energy by reparameterizing the orthogonal constraint as a feed-forward computation. We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity from O(N^4) to O(N^3). Second, the numerical integration which involves a summation over the quadrature grids can be amortized to the optimization steps. At each step, stochastic gradient descent (SGD) is performed with a sampled minibatch of the grids. Extensive experiments are carried out to demonstrate the advantage of our approach in terms of efficiency and stability. In addition, we show that our approach enables us to explore more complex neural-based wave functions.

This work pursues the optimization of over-parameterized deep models for superior training efficiency and test performance. We first theoretically emphasize the importance of two properties of over-parameterized models, i.e., the convergence gap and the generalization gap. Subsequent analyses unveil that these two gaps can be upper-bounded by the ratio of the Lipschitz constant and the Polyak-{\L}ojasiewicz (PL) constant, a crucial term abbreviated as the \emph{condition number}. Such discoveries have led to a structured pruning method with a novel pruning criterion. That is, we devise a gating network that dynamically detects and masks out those poorly-behaved nodes of a deep model during the training session. To this end, this gating network is learned via minimizing the \emph{condition number} of the target model, and this process can be implemented as an extra regularization loss term. Experimental studies demonstrate that the proposed method outperforms the baselines in terms of both training efficiency and test performance, exhibiting the potential of generalizing to a variety of deep network architectures and tasks.

Large language models distill broad knowledge from text corpora. However, they can be inconsistent when it comes to completing user specified tasks. This issue can be addressed by finetuning such models via supervised learning on curated datasets, or via reinforcement learning. In this work, we propose a novel offline RL method, implicit language Q-learning (ILQL), designed for use on language models, that combines both the flexible utility maximization framework of RL algorithms with the ability of supervised learning to leverage previously collected data, as well as its simplicity and stability. Our method employs a combination of value conservatism alongside an implicit dataset support constraint in learning value functions, which are then used to guide language model generations towards maximizing user-specified utility functions. In addition to empirically validating ILQL, we present a detailed empirical analysis of situations where offline RL can be useful in natural language generation settings, demonstrating how it can be a more effective utility optimizer than prior approaches for end-to-end dialogue, and how it can effectively optimize high variance reward functions based on subjective judgement, such as whether to label a comment as toxic or not.

In a backdoor attack, an attacker injects corrupted examples into the training set. The goal of the attacker is to cause the final trained model to predict the attacker's desired target label when a predefined trigger is added to test inputs. Central to these attacks is the trade-off between the success rate of the attack and the number of corrupted training examples injected. We pose this attack as a novel bilevel optimization problem: construct strong poison examples that maximize the attack success rate of the trained model. We use neural tangent kernels to approximate the training dynamics of the model being attacked and automatically learn strong poison examples. We experiment on subclasses of CIFAR-10 and ImageNet with WideResNet-34 and ConvNeXt architectures on periodic and patch trigger attacks and show that NTBA-designed poisoned examples achieve, for example, an attack success rate of 90% with ten times smaller number of poison examples injected compared to the baseline. We provided an interpretation of the NTBA-designed attacks using the analysis of kernel linear regression. We further demonstrate a vulnerability in overparametrized deep neural networks, which is revealed by the shape of the neural tangent kernel.

Incorporating equivariance to symmetry groups as a constraint during neural network training can improve performance and generalization for tasks exhibiting those symmetries, but such symmetries are often not perfectly nor explicitly present. This motivates algorithmically optimizing the architectural constraints imposed by equivariance. We propose the equivariance relaxation morphism, which preserves functionality while reparameterizing a group equivariant layer to operate with equivariance constraints on a subgroup, as well as the $[G]$-mixed equivariant layer, which mixes layers constrained to different groups to enable within-layer equivariance optimization. We further present evolutionary and differentiable neural architecture search (NAS) algorithms that utilize these mechanisms respectively for equivariance-aware architectural optimization. Experiments across a variety of datasets show the benefit of dynamically constrained equivariance to find effective architectures with approximate equivariance.

The success of the Adam optimizer on a wide array of architectures has made it the default in settings where stochastic gradient descent (SGD) performs poorly. However, our theoretical understanding of this discrepancy is lagging, preventing the development of significant improvements on either algorithm. Recent work advances the hypothesis that Adam and other heuristics like gradient clipping outperform SGD on language tasks because the distribution of the error induced by sampling has heavy tails. This suggests that Adam outperform SGD because it uses a more robust gradient estimate. We evaluate this hypothesis by varying the batch size, up to the entire dataset, to control for stochasticity. We present evidence that stochasticity and heavy-tailed noise are not major factors in the performance gap between SGD and Adam. Rather, Adam performs better as the batch size increases, while SGD is less effective at taking advantage of the reduction in noise. This raises the question as to why Adam outperforms SGD in the full-batch setting. Through further investigation of simpler variants of SGD, we find that the behavior of Adam with large batches is similar to sign descent with momentum.

Offline reinforcement learning algorithms still lack trust in practice due to the risk that the learned policy performs worse than the original policy that generated the dataset or behaves in an unexpected way that is unfamiliar to the user. At the same time, offline RL algorithms are not able to tune their most important hyperparameter - the proximity of the learned policy to the original policy. We propose an algorithm that allows the user to tune this hyperparameter at runtime, thereby addressing both of the above mentioned issues simultaneously. This allows users to start with the original behavior and grant successively greater deviation, as well as stopping at any time when the policy deteriorates or the behavior is too far from the familiar one.

Fully-parametric language models generally require a huge number of model parameters to store the necessary knowledge for solving multiple natural language tasks in zero/few-shot settings. In addition, it is hard to adapt to the evolving world knowledge without the costly model re-training. In this paper, we develop a novel semi-parametric language model architecture, Knowledge-in-Context (KiC), which empowers a parametric text-to-text language model with a knowledge-rich external memory. Specifically, the external memory contains six different types of knowledge: entity, dictionary, commonsense, event, script, and causality knowledge. For each input instance, the KiC model adaptively selects a knowledge type and retrieves the most helpful pieces of knowledge. The input instance along with its knowledge augmentation is fed into a text-to-text model (e.g., T5) to generate the output answer, where both the input and the output are in natural language forms after prompting. Interestingly, we find that KiC can be identified as a special mixture-of-experts (MoE) model, where the knowledge selector plays the role of a router that is used to determine the sequence-to-expert assignment in MoE. This key observation inspires us to develop a novel algorithm for training KiC with an instance-adaptive knowledge selector. As a knowledge-rich semi-parametric language model, KiC only needs a much smaller parametric part to achieve superior zero-shot performance on unseen tasks. By evaluating on 40+ different tasks, we show that KiC-Large with 770M parameters easily outperforms large language models that are 4-39x larger. In addition, KiC also exhibits emergent abilities at a much smaller model scale compared to the fully-parametric models.

We propose a general-purpose variational algorithm that forms a natural analogue of Stein variational gradient descent (SVGD) in function space. While SVGD successively updates a set of particles to match a target density, the method introduced here of Stein functional variational gradient descent (SFVGD) updates a set of particle functions to match a target stochastic process (SP). The update step is found by minimizing the functional derivative of the Kullback-Leibler divergence between SPs. SFVGD can either be used to train Bayesian neural networks (BNNs) or for ensemble gradient boosting. We show the efficacy of training BNNs with SFVGD on various real-world datasets.