ICML 2023 Papers

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).

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.

We introduce in this paper the mechanism of graph random features (GRFs). GRFs can be used to construct unbiased randomized estimators of several important kernels defined on graphs' nodes, in particular the regularized Laplacian kernel. As regular RFs for non-graph kernels, they provide means to scale up kernel methods defined on graphs to larger networks. Importantly, they give substantial computational gains also for smaller graphs, while applied in downstream applications. Consequently, GRFs address the notoriously difficult problem of cubic (in the number of the nodes of the graph) time complexity of graph kernels algorithms. We provide a detailed theoretical analysis of GRFs and an extensive empirical evaluation: from speed tests, through Frobenius relative error analysis to kmeans graph-clustering with graph kernels. We show that the computation of GRFs admits an embarrassingly simple distributed algorithm that can be applied if the graph under consideration needs to be split across several machines. We also introduce a (still unbiased) quasi Monte Carlo variant of GRFs, q-GRFs, relying on the so-called reinforced random walks that might be used to optimize the variance of GRFs. As a byproduct, we obtain a novel approach to solve certain classes of linear equations with positive and symmetric matrices.

Training graph neural networks (GNNs) is extremely time consuming because sparse graph-based operations are hard to be accelerated by community hardware. Prior art successfully reduces the computation cost of dense matrix based operations (e.g., convolution and linear) via sampling-based approximation. However, unlike dense matrices, sparse matrices are stored in the irregular data format such that each row/column may have different number of non-zero entries. Thus, compared to the dense counterpart, approximating sparse operations has two unique challenges (1) we cannot directly control the efficiency of approximated sparse operation since the computation is only executed on non-zero entries; (2) sampling sparse matrices is much more inefficient due to the irregular data format. To address the issues, our key idea is to control the accuracy-efficiency trade off by optimizing computation resource allocation layer-wisely and epoch-wisely. For the first challenge, we customize the computation resource to different sparse operations, while limit the total used resource below a certain budget. For the second challenge, we cache previous sampled sparse matrices to reduce the epoch-wise sampling overhead. Finally, we propose a switching mechanisms to improve the generalization of GNNs trained with approximated operations. To this end, we propose Randomized Sparse Computation. In practice, rsc can achieve up to 11.6X speedup for a single sparse operation and 1.6X end-to-end wall-clock time speedup with almost no accuracy drop.

Spiking neural networks (SNNs) with biologically inspired spatio-temporal dynamics demonstrate superior energy efficiency on neuromorphic architectures. Error backpropagation in SNNs is prohibited by the all-or-none nature of spikes. The existing solution circumvents this problem by a relaxation on the gradient calculation using a continuous function with a constant relaxation de- gree, so-called surrogate gradient learning. Nevertheless, such a solution introduces additional smoothing error on spike firing which leads to the gradients being estimated inaccurately. Thus, how to adaptively adjust the relaxation degree and eliminate smoothing error progressively is crucial. Here, we propose a methodology such that training a prototype neural network will evolve into training an SNN gradually by fusing the learnable relaxation degree into the network with random spike noise. In this way, the network learns adaptively the accurate gradients of loss landscape in SNNs. The theoretical analysis further shows optimization on such a noisy network could be evolved into optimization on the embedded SNN with shared weights progressively. Moreover, The experiments on static images, dynamic event streams, speech, and instrumental sounds show the proposed method achieves state-of-the-art performance across all the datasets with remarkable robustness on different relaxation degrees.

The deployment and training of neural networks on edge computing devices pose many challenges. The low memory nature of edge devices is often one of the biggest limiting factors encountered in the deployment of large neural network models. Tensor rematerialization or recompute is a way to address high memory requirements for neural network training and inference. In this paper we consider the problem of execution time minimization of compute graphs subject to a memory budget. In particular, we develop a new constraint programming formulation called Moccasin with only $O(n)$ integer variables, where $n$ is the number of nodes in the compute graph. This is a significant improvement over the works in the recent literature that propose formulations with $O(n^2)$ Boolean variables. We present numerical studies that show that our approach is up to an order of magnitude faster than recent work especially for large-scale graphs.

Graph neural networks (GNNs) learn the representation of graph-structured data, and their expressiveness can be further enhanced by inferring node relations for propagation. Attention-based GNNs infer neighbor importance to manipulate the weight of its propagation. Despite their popularity, the discussion on deep graph attention and its unique challenges has been limited. In this work, we investigate some problematic phenomena related to deep graph attention, including vulnerability to over-smoothed features and smooth cumulative attention. Through theoretical and empirical analyses, we show that various attention-based GNNs suffer from these problems. Motivated by our findings, we propose AERO-GNN, a novel GNN architecture designed for deep graph attention. AERO-GNN provably mitigates the proposed problems of deep graph attention, which is further empirically demonstrated with (a) its adaptive and less smooth attention functions and (b) higher performance at deep layers (up to 64). On 9 out of 12 node classification benchmarks, AERO-GNN outperforms the baseline GNNs, highlighting the advantages of deep graph attention. Our code is available at https://github.com/syleeheal/AERO-GNN.

In federated learning (FL), weighted aggregation of local models is conducted to generate a global model, and the aggregation weights are normalized (the sum of weights is 1) and proportional to the local data sizes. In this paper, we revisit the weighted aggregation process and gain new insights into the training dynamics of FL. First, we find that the sum of weights can be smaller than 1, causing global weight shrinking effect (analogous to weight decay) and improving generalization. We explore how the optimal shrinking factor is affected by clients' data heterogeneity and local epochs. Second, we dive into the relative aggregation weights among clients to depict the clients' importance. We develop client coherence to study the learning dynamics and find a critical point that exists. Before entering the critical point, more coherent clients play more essential roles in generalization. Based on the above insights, we propose an effective method for Federated Learning with Learnable Aggregation Weights, named as FedLAW. Extensive experiments verify that our method can improve the generalization of the global model by a large margin on different datasets and models.

The successes of artificial neural networks (ANNs) are largely attributed to mimicking the human brain structures. Recent advances in neuroscience revealed that neurons interact with each other through various kinds of connectivity patterns to process information, in which the common connectivity patterns are also called circuit motifs. However, many existing ANNs can only model one or two circuit motifs in their architectures, so that their performance may drastically vary among different types of machine learning tasks. In this paper, we propose a new type of neural network inspired by the architectures of neuronal circuits, namely Circuit Neural Network (CircuitNet). In CircuitNet, a group of densely connected neurons, namely circuit motif unit (CMU), form the basic unit of the network, which is capable of modeling universal circuit motifs by adjusting the weights within the CMUs. Compared with traditional feed-forward networks, CircuitNet has the ability to model more types of neuron connections such as feed-back and lateral motifs. Inspired by the locally dense and globally sparse structure of the human brain, several iterations of signal transmission among different CMUs are achieved by sparse connections through the input ports and output ports of different CMUs. Experiments have demonstrated that CircuitNet can outperform popular neural network architectures in function approximation, reinforcement learning, image classification, and time series forecasting tasks.

In this work we perform symbolic discovery of differential operators in a situation where there is sparse experimental data. This small data regime in machine learning can be made tractable by providing our algorithms with prior information about the underlying dynamics. Physics Informed Neural Networks (PINNs) have been very successful in this regime (reconstructing entire ODE solutions using only a single point or entire PDE solutions with very few measurements of the initial condition). The Universal PINN approach (UPINN) adds a neural network that learns a representation of unknown hidden terms in the differential equation. The algorithm yields both a surrogate solution to the differential equation and a black-box representation of the hidden terms. These hidden term neural networks can then be converted into symbolic equations using symbolic regression techniques like AI Feynman. In order to achieve convergence of the neural networks, we provide our algorithms with (noisy) measurements of both the initial condition as well as (synthetic) experimental data obtained at later times. We demonstrate strong performance of UPINNs even when provided with very few measurements of noisy data in both the ODE and PDE regime.

While graph neural networks (GNNs) dominate the state-of-the-art for exploring graphs in real-world applications, they have been shown to be vulnerable to a growing number of privacy attacks. For instance, link stealing is a well-known membership inference attack (MIA) on edges that infers the presence of an edge in a GNN's training graph. Recent studies on independent and identically distributed data (e.g., images) have empirically demonstrated that individuals from different groups suffer from different levels of privacy risks to MIAs, i.e., uneven vulnerability. However, theoretical evidence of such uneven vulnerability is missing. In this paper, we first present theoretical evidence of the uneven vulnerability of GNNs to link stealing attacks, which lays the foundation for demystifying such uneven risks among different groups of edges. We further demonstrate a group-based attack paradigm to expose the practical privacy harm to GNN users derived from the uneven vulnerability of edges. Finally, we empirically validate the existence of obvious uneven vulnerability on nine real-world datasets (e.g., about 25% AUC difference between different groups in the Credit graph). Compared with existing methods, the outperformance of our group-based attack paradigm confirms that customising different strategies for different groups results in more effective privacy attacks.

A neural network consisting of piecewise affine building blocks, such as fully-connected layers and ReLU activations, is itself a piecewise affine function supported on a polyhedral complex. This complex has been previously studied to characterize theoretical properties of neural networks, but, in practice, extracting it remains a challenge due to its high combinatorial complexity. A natural idea described in previous works is to subdivide the regions via intersections with hyperplanes induced by each neuron. However, we argue that this view leads to computational redundancy. Instead of regions, we propose to subdivide edges, leading to a novel method for polyhedral complex extraction. A key to this are sign-vectors, which encode the combinatorial structure of the complex. Our approach allows to use standard tensor operations on a GPU, taking seconds for millions of cells on a consumer grade machine. Motivated by the growing interest in neural shape representation, we use the speed and differentiablility of our method to optimize geometric properties of the complex. The code is available at https://github.com/arturs-berzins/relu_edge_subdivision.

Graph neural networks (GNNs) achieve remarkable performance in graph machine learning tasks but can be hard to train on large-graph data, where their learning dynamics are not well understood. We investigate the training dynamics of large-graph GNNs using graph neural tangent kernels (GNTKs) and graphons. In the limit of large width, optimization of an overparametrized NN is equivalent to kernel regression on the NTK. Here, we investigate how the GNTK evolves as another independent dimension is varied: the graph size. We use graphons to define limit objects---graphon NNs for GNNs, and graphon NTKs for GNTKs---, and prove that, on a sequence of graphs, the GNTKs converge to the graphon NTK. We further prove that the spectrum of the GNTK, which is related to the problem's learning directions, converges to the spectrum of the GNTK. This implies that in the large-graph limit, the GNTK fitted on a graph of moderate size can be used to solve the same task on the large graph, and to infer the learning dynamics of the large-graph GNN. These results are verified empirically on node regression and classification tasks.

Graph neural networks (GNNs) based methods have achieved impressive performance on node clustering task. However, they are designed on the homophilic assumption of graph and clustering on heterophilic graph is overlooked. Due to the lack of labels, it is impossible to first identify a graph as homophilic or heterophilic before a suitable GNN model can be found. Hence, clustering on real-world graph with various levels of homophily poses a new challenge to the graph research community. To fill this gap, we propose a novel graph clustering method, which contains three key components: graph reconstruction, a mixed filter, and dual graph clustering network. To be graph-agnostic, we empirically construct two graphs which are high homophily and heterophily from each data. The mixed filter based on the new graphs extracts both low-frequency and high-frequency information. To reduce the adverse coupling between node attribute and topological structure, we separately map them into two subspaces in dual graph clustering network. Extensive experiments on 11 benchmark graphs demonstrate our promising performance. In particular, our method dominates others on heterophilic graphs.

The main aim of this paper is to conduct the convergence analysis of the gradient descent for two-layer physics-informed neural networks (PINNs). Here, the loss function involves derivatives of neural network outputs with respect to its inputs, so the interaction between the trainable parameters is more complicated compared with simple regression and classification tasks. We first develop the positive definiteness of Gram matrices and prove that the gradient flow finds the global optima of the empirical loss under over-parameterization. Then, we demonstrate that the standard gradient descent converges to the global optima of the loss with proper choices of learning rates. The framework of our analysis works for various categories of PDEs (e.g., linear second-order PDEs) and common types of network initialization (LecunUniform etc.). Our theoretical results do not need a very strict hypothesis for training samples and have a looser requirement on the network width compared with some previous works.

We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the $\mathrm{Pin}(p,q,r)$ group. We then propose the concept of group action layers, which linearly combine object transformations using pre-specified group actions. Together with a new activation and normalization scheme, these layers serve as adjustable geometric templates that can be refined via gradient descent. Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods.

Encoding constraints into neural networks is attractive. This paper studies how to introduce the popular positive linear satisfiability to neural networks. We propose the first differentiable satisfiability layer based on an extension of the classic Sinkhorn algorithm for jointly encoding multiple sets of marginal distributions. We further theoretically characterize the convergence property of the Sinkhorn algorithm for multiple marginals, and the underlying formulation is also derived. In contrast to the sequential decision e.g. reinforcement learning-based solvers, we showcase our technique in solving constrained (specifically satisfiability) problems by one-shot neural networks, including i) a neural routing solver learned without supervision of optimal solutions; ii) a partial graph matching network handling graphs with unmatchable outliers on both sides; iii) a predictive network for financial portfolios with continuous constraints. To our knowledge, there exists no one-shot neural solver for these scenarios when they are formulated as satisfiability problems. Source code is available at https://github.com/Thinklab-SJTU/LinSATNet.

Batching has a fundamental influence on the efficiency of deep neural network (DNN) execution. However, for dynamic DNNs, efficient batching is particularly challenging as the dataflow graph varies per input instance. As a result, state-of-the-art frameworks use heuristics that result in suboptimal batching decisions. Further, batching puts strict restrictions on memory adjacency and can lead to high data movement costs. In this paper, we provide an approach for batching dynamic DNNs based on finite state machines, which enables the automatic discovery of batching policies specialized for each DNN via reinforcement learning. Moreover, we find that memory planning that is aware of the batching policy can save significant data movement overheads, which is automated by a PQ tree-based algorithm we introduce. Experimental results show that our framework speeds up state-of-the-art frameworks by on average 1.15x, 1.39x, and 2.45x for chain-based, tree-based, and lattice-based DNNs across CPU and GPU. The framework is open-sourced at https://github.com/gulang2019/ED-Batch.git.