ICML 2023 Papers

Transformers for graph data are increasingly widely studied and successful in numerous learning tasks. Graph inductive biases are crucial for Graph Transformers, and previous works incorporate them using message-passing modules and/or positional encodings. However, Graph Transformers that use message-passing inherit known issues of message-passing, and differ significantly from Transformers used in other domains, thus making transfer of research advances more difficult. On the other hand, Graph Transformers without message-passing often perform poorly on smaller datasets, where inductive biases are more crucial. To bridge this gap, we propose the Graph Inductive bias Transformer (GRIT) --- a new Graph Transformer that incorporates graph inductive biases without using message passing. GRIT is based on several architectural changes that are each theoretically and empirically justified, including: learned relative positional encodings initialized with random walk probabilities, a flexible attention mechanism that updates node and node-pair representations, and injection of degree information in each layer. We prove that GRIT is expressive --- it can express shortest path distances and various graph propagation matrices. GRIT achieves state-of-the-art empirical performance across a variety of graph datasets, thus showing the power that Graph Transformers without message-passing can deliver.

Unsupervised out-of-distribution detection (OOD) seeks to identify out-of-domain data by learning only from unlabeled in-domain data. We present a novel approach for this task -- Lift, Map, Detect (LMD) -- that leverages recent advancement in diffusion models. Diffusion models are one type of generative models. At their core, they learn an iterative denoising process that gradually maps a noisy image closer to their training manifolds. LMD leverages this intuition for OOD detection. Specifically, LMD lifts an image off its original manifold by corrupting it, and maps it towards the in-domain manifold with a diffusion model. For an OOD image, the mapped image would have a large distance away from its original manifold, and LMD would identify it as OOD accordingly. We show through extensive experiments that LMD achieves competitive performance across a broad variety of datasets. Code can be found at https://github.com/zhenzhel/lift_map_detect.

Spherical CNNs generalize CNNs to functions on the sphere, by using spherical convolutions as the main linear operation. The most accurate and efficient way to compute spherical convolutions is in the spectral domain (via the convolution theorem), which is still costlier than the usual planar convolutions. For this reason, applications of spherical CNNs have so far been limited to small problems that can be approached with low model capacity. In this work, we show how spherical CNNs can be scaled for much larger problems. To achieve this, we make critical improvements including novel variants of common model components, an implementation of core operations to exploit hardware accelerator characteristics, and application-specific input representations that exploit the properties of our model. Experiments show our larger spherical CNNs reach state-of-the-art on several targets of the QM9 molecular benchmark, which was previously dominated by equivariant graph neural networks, and achieve competitive performance on multiple weather forecasting tasks. Our code is available at https://github.com/google-research/spherical-cnn.

We show that taking the width and depth to infinity in a deep neural network with skip connections, when branches are scaled by $1/\sqrt{depth}$, result in the same covariance structure no matter how that limit is taken. This explains why the standard infinite-width-then-depth approach provides practical insights even for networks with depth of the same order as width. We also demonstrate that the pre-activations, in this case, have Gaussian distributions which has direct applications in Bayesian deep learning. We conduct extensive simulations that show an excellent match with our theoretical findings.

In node classification using graph neural networks (GNNs), a typical model generates logits for different class labels at each node. A softmax layer often outputs a label prediction based on the largest logit. We demonstrate that it is possible to infer hidden graph structural information from the dataset using these logits. We introduce the key notion of label non-uniformity, which is derived from the Wasserstein distance between the softmax distribution of the logits and the uniform distribution. We demonstrate that nodes with small label non-uniformity are harder to classify correctly. We theoretically analyze how the label non-uniformity varies across the graph, which provides insights into boosting the model performance: increasing training samples with high non-uniformity or dropping edges to reduce the maximal cut size of the node set of small non-uniformity. These mechanisms can be easily added to a base GNN model. Experimental results demonstrate that our approach improves the performance of many benchmark base models.

We study the problem of convergence to a stationary point in zero-sum games. We propose competitive gradient optimization (CGO), a gradient-based method that incorporates the interactions between two players in zero-sum games for its iterative updates. We provide a continuous-time analysis of CGO and its convergence properties while showing that in the continuous limit, previous methods degenerate to their gradient descent ascent (GDA) variants. We further provide a rate of convergence to stationary points in the discrete-time setting. We propose a generalized class of $\alpha$-coherent functions and show that for strictly $\alpha$-coherent functions, CGO ensures convergence to a saddle point. Moreover, we propose optimistic CGO (oCGO), an optimistic variant, for which we show a convergence rate of $O(\frac{1}{n})$ to saddle points for $\alpha$-coherent functions.

This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob's $h$-transforms that are typically intractable. We propose a computational framework to approximate these $h$-transforms by solving the underlying backward Kolmogorov equations using nonlinear Feynman-Kac formulas and neural networks. The methodology allows one to train a locally optimal particle filter prior to the data-assimilation procedure. Numerical experiments illustrate that the proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters in the regime of highly informative observations, when the observations are extreme under the model, and if the state dimension is large.

We consider the problem of solving large-scale instances of the Max-Cut semidefinite program (SDP), i.e., optimizing a linear function over $n\times n$ positive semidefinite (PSD) matrices with unit diagonal. When the cost matrix is PSD, we show how to exactly reformulate the problem as maximizing a smooth concave function over PSD matrices with unit trace. By applying the Frank-Wolfe method, we obtain a simple algorithm that is compatible with recent sampling-based techniques to solve SDPs using low memory. We demonstrate the practical performance of our method on $10^6\times 10^6$ instances of the max-cut SDP with costs having up to $5 \times 10^6$ non-zero entries. Theoretically, we show that our method solves problems with diagonally dominant costs to relative error $\epsilon$ in $O(n\epsilon^{-1})$ calls to a randomized approximate largest eigenvalue subroutine, each of which succeeds with high probability after $O(\log(n)\epsilon^{-1/2})$ matrix-vector multiplications with the cost matrix.

When trying to solve a computational problem, we are often faced with a choice between algorithms that are guaranteed to return the right answer but differ in their runtime distributions (e.g., SAT solvers, sorting algorithms). This paper aims to lay theoretical foundations for such choices by formalizing preferences over runtime distributions. It might seem that we should simply prefer the algorithm that minimizes expected runtime. However, such preferences would be driven by exactly how slow our algorithm is on bad inputs, whereas in practice we are typically willing to cut off occasional, sufficiently long runs before they finish. We propose a principled alternative, taking a utility-theoretic approach to characterize the scoring functions that describe preferences over algorithms. These functions depend on the way our value for solving our problem decreases with time and on the distribution from which captimes are drawn. We describe examples of realistic utility functions and show how to leverage a maximum-entropy approach for modeling underspecified captime distributions. Finally, we show how to efficiently estimate an algorithm's expected utility from runtime samples.

Pipeline parallelism is a key technique for training large language models within GPU clusters. However, it often leads to a memory imbalance problem, where certain GPUs face high memory pressure while others underutilize their capacity. This imbalance results in suboptimal training performance, even when the overall GPU memory capacity is sufficient for more efficient setups. To address this inefficiency, we propose BPipe, a novel approach for achieving memory balance in pipeline parallelism. BPipe employs an activation balancing method to transfer intermediate activations between GPUs during training, enabling all GPUs to utilize comparable amounts of memory. With balanced memory utilization, BPipe enhances the training efficiency of large language models like GPT-3 by eliminating redundant recomputations or increasing the micro-batch size. Our evaluation conducted on 48 A100 GPUs across six nodes interconnected with HDR InfiniBand shows that BPipe accelerates the training of GPT-3 96B and GPT-3 134B models by 1.25x-2.17x compared to Megatron-LM, a state-of-the-art framework for training large language models.

The Schrödinger bridge problem (SBP) is gaining increasing attention in generative modeling and showing promising potential even in comparison with the score-based generative models (SGMs). SBP can be interpreted as an entropy-regularized optimal transport problem, which conducts projections onto every other marginal alternatingly. However, in practice, only approximated projections are accessible and their convergence is not well understood. To fill this gap, we present a first convergence analysis of the Schrödinger bridge algorithm based on approximated projections. As for its practical applications, we apply SBP to probabilistic time series imputation by generating missing values conditioned on observed data. We show that optimizing the transport cost improves the performance and the proposed algorithm achieves the state-of-the-art result in healthcare and environmental data while exhibiting the advantage of exploring both temporal and feature patterns in probabilistic time series imputation.

Applications of machine learning techniques for materials modeling typically involve functions that are known to be equivariant or invariant to specific symmetries. While graph neural networks (GNNs) have proven successful in such applications, conventional GNN approaches that enforce symmetries via the model architecture often reduce expressivity, scalability or comprehensibility. In this paper, we introduce (1) a flexible, model-agnostic framework based on stochastic frame averaging that enforces E(3) equivariance or invariance, without any architectural constraints; (2) FAENet: a simple, fast and expressive GNN that leverages stochastic frame averaging to process geometric information without constraints. We prove the validity of our method theoretically and demonstrate its superior accuracy and computational scalability in materials modeling on the OC20 dataset (S2EF, IS2RE) as well as common molecular modeling tasks (QM9, QM7-X).

Machine learning force fields (MLFF) have been proposed to accelerate molecular dynamics (MD) simulation, which finds widespread applications in chemistry and biomedical research. Even for the most data-efficient MLFFs, reaching chemical accuracy can require hundreds of frames of force and energy labels generated by expensive quantum mechanical algorithms, which may scale as $O(n^3)$ to $O(n^7)$, with $n$ proportional to the number of basis functions. To address this issue, we propose a multi-stage computational framework -- ASTEROID, which lowers the data cost of MLFFs by leveraging a combination of cheap inaccurate data and expensive accurate data. The motivation behind ASTEROID is that inaccurate data, though incurring large bias, can help capture the sophisticated structures of the underlying force field. Therefore, we first train a MLFF model on a large amount of inaccurate training data, employing a bias-aware loss function to prevent the model from overfitting the potential bias of this data. We then fine-tune the obtained model using a small amount of accurate training data, which preserves the knowledge learned from the inaccurate training data while significantly improving the model's accuracy. Moreover, we propose a variant of ASTEROID based on score matching for the setting where the inaccurate training data are unlabeled. Extensive experiments on MD datasets and downstream tasks validate the efficacy of ASTEROID. Our code and data are available at https://github.com/abukharin3/asteroid.

We abstract the features (i.e. learned representations) of multi-modal data into 1) uni-modal features, which can be learned from uni-modal training, and 2) paired features, which can only be learned from cross-modal interactions. Multi-modal models are expected to benefit from cross-modal interactions on the basis of ensuring uni-modal feature learning. However, recent supervised multi-modal late-fusion training approaches still suffer from insufficient learning of uni-modal features on each modality. We prove that this phenomenon does hurt the model's generalization ability. To this end, we propose to choose a targeted late-fusion learning method for the given supervised multi-modal task from Uni-Modal Ensemble (UME) and the proposed Uni-Modal Teacher (UMT), according to the distribution of uni-modal and paired features. We demonstrate that, under a simple guiding strategy, we can achieve comparable results to other complex late-fusion or intermediate-fusion methods on various multi-modal datasets, including VGG-Sound, Kinetics-400, UCF101, and ModelNet40.

In real life, accurately annotating large-scale datasets is sometimes difficult. Datasets used for training deep learning models are likely to contain label noise. To make use of the dataset containing label noise, two typical methods have been proposed. One is to employ the semi-supervised method by exploiting labeled *confident examples* and unlabeled *unconfident examples*. The other one is to *model label noise* and design *statistically consistent* classifiers. A natural question remains unsolved: which one should be used for a specific real-world application? In this paper, we answer the question from the perspective of *causal data generative process*. Specifically, the performance of the semi-supervised based method depends heavily on the data generative process while the method modeling label-noise is not influenced by the generation process. For example, for a given dataset, if it has a causal generative structure that the features cause the label, the semi-supervised based method would not be helpful. When the causal structure is unknown, we provide an intuitive method to discover the causal structure for a given dataset containing label noise.

We study the variance of stochastic policy gradients (SPGs) with many action samples per state. We derive a many-actions optimality condition, which determines when many-actions SPG yields lower variance as compared to a single-action agent with proportionally extended trajectory. We propose Model-Based Many-Actions (MBMA), an approach leveraging dynamics models for many-actions sampling in the context of SPG. MBMA addresses issues associated with existing implementations of many-actions SPG and yields lower bias and comparable variance to SPG estimated from states in model-simulated rollouts. We find that MBMA bias and variance structure matches that predicted by theory. As a result, MBMA achieves improved sample efficiency and higher returns on a range of continuous action environments as compared to model-free, many-actions, and model-based on-policy SPG baselines.

Learning-based high-fidelity reconstruction of 3D shapes with varying topology is a fundamental problem in computer vision and computer graphics. Recent advances in learning 3D shapes using explicit and implicit representations have achieved impressive results in 3D modeling. However, the template-based explicit representation is limited by fixed topology, and the implicit representation, although flexible with arbitrary topology, requires a large number of sampled points to regress the surface, which is computationally expensive. In this work, we propose a novel 3D shape representation named NeuralSlice, which represents a 3D shape as the intersection of a 4D tetrahedral mesh and a 4D hyperplane. A novel network is designed to incorporate the proposed representation flexibly, which learns a deformable 4D template and a parameter for slicing 4D hyperplane to reconstruct the 3D object. To learn the local deformation of the 4D template, we further propose a spatial-aware network to locate the 4D points within the 3D feature volume of input shape via positional encoding, which leverages the local geometrical feature to guide the 4D deformation. By addressing the 3D problem in a higher 4D space, our method supports flexible topology changes while being highly efficient. Our method is guaranteed to produce manifold meshes. NeuralSlice outperforms the state-of-the-art explicit-based approaches in terms of reconstruction quality. Compared with implicit approaches, by avoiding point sampling, our method is 10 times faster than the implicit approaches, and better preserves thin structures. NeuralSlice has the capability of representing various shapes and topologies using a single 4D tetrahedral mesh. The corresponding code can be found on GitHub at https://github.com/IGLICT/NEURALSLICE

Prior-data fitted networks (PFNs) were recently proposed as a new paradigm for machine learning. Instead of training the network to an observed training set, a fixed model is pre-trained offline on small, simulated training sets from a variety of tasks. The pre-trained model is then used to infer class probabilities in-context on fresh training sets with arbitrary size and distribution. Empirically, PFNs achieve state-of-the-art performance on tasks with similar size to the ones used in pre-training. Surprisingly, their accuracy further improves when passed larger data sets during inference. This article establishes a theoretical foundation for PFNs and illuminates the statistical mechanisms governing their behavior. While PFNs are motivated by Bayesian ideas, a purely frequentistic interpretation of PFNs as pre-tuned, but untrained predictors explains their behavior. A predictor's variance vanishes if its sensitivity to individual training samples does and the bias vanishes only if it is appropriately localized around the test feature. The transformer architecture used in current PFN implementations ensures only the former. These findings shall prove useful for designing architectures with favorable empirical behavior.

Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features (outputs of the penultimate layer) of within-class samples decreases and the mean features of different classes approach a certain tight frame structure. Recent works analyze this behavior via idealized unconstrained features models where all the minimizers exhibit exact collapse. However, with practical networks and datasets, the features typically do not reach exact collapse, e.g., because deep layers cannot arbitrarily modify intermediate features that are far from being collapsed. In this paper, we propose a richer model that can capture this phenomenon by forcing the features to stay in the vicinity of a predefined features matrix (e.g., intermediate features). We explore the model in the small vicinity case via perturbation analysis and establish results that cannot be obtained by the previously studied models. For example, we prove reduction in the within-class variability of the optimized features compared to the predefined input features (via analyzing gradient flow on the "central-path" with minimal assumptions), analyze the minimizers in the near-collapse regime, and provide insights on the effect of regularization hyperparameters on the closeness to collapse. We support our theory with experiments in practical deep learning settings.