ICLR 2023 Papers

Many works show that node-level predictions of Graph Neural Networks (GNNs) are unrobust to small, often termed adversarial, changes to the graph structure. However, because manual inspection of a graph is difficult, it is unclear if the studied perturbations always preserve a core assumption of adversarial examples: that of unchanged semantic content. To address this problem, we introduce a more principled notion of an adversarial graph, which is aware of semantic content change. Using Contextual Stochastic Block Models (CSBMs) and real-world graphs, our results suggest: $i)$ for a majority of nodes the prevalent perturbation models include a large fraction of perturbed graphs violating the unchanged semantics assumption; $ii)$ surprisingly, all assessed GNNs show over-robustness - that is robustness beyond the point of semantic change. We find this to be a complementary phenomenon to adversarial examples and show that including the label-structure of the training graph into the inference process of GNNs significantly reduces over-robustness, while having a positive effect on test accuracy and adversarial robustness. Theoretically, leveraging our new semantics-aware notion of robustness, we prove that there is no robustness-accuracy tradeoff for inductively classifying a newly added node.

Gaussian processes (GPs) are an attractive class of machine learning models because of their simplicity and flexibility as building blocks of more complex Bayesian models. Meanwhile, graph neural networks (GNNs) emerged recently as a promising class of models for graph-structured data in semi-supervised learning and beyond. Their competitive performance is often attributed to a proper capturing of the graph inductive bias. In this work, we introduce this inductive bias into GPs to improve their predictive performance for graph-structured data. We show that a prominent example of GNNs, the graph convolutional network, is equivalent to some GP when its layers are infinitely wide; and we analyze the kernel universality and the limiting behavior in depth. We further present a programmable procedure to compose covariance kernels inspired by this equivalence and derive example kernels corresponding to several interesting members of the GNN family. We also propose a computationally efficient approximation of the covariance matrix for scalable posterior inference with large-scale data. We demonstrate that these graph-based kernels lead to competitive classification and regression performance, as well as advantages in computation time, compared with the respective GNNs.

Lottery Ticket Hypothesis (LTH) claims the existence of a winning ticket (i.e., a properly pruned sub-network together with original weight initialization) that can achieve competitive performance to the original dense network. A recent work, called UGS, extended LTH to prune graph neural networks (GNNs) for effectively accelerating GNN inference. UGS simultaneously prunes the graph adjacency matrix and the model weights using the same masking mechanism, but since the roles of the graph adjacency matrix and the weight matrices are very different, we find that their sparsifications lead to different performance characteristics. Specifically, we find that the performance of a sparsified GNN degrades significantly when the graph sparsity goes beyond a certain extent. Therefore, we propose two techniques to improve GNN performance when the graph sparsity is high. First, UGS prunes the adjacency matrix using a loss formulation which, however, does not properly involve all elements of the adjacency matrix; in contrast, we add a new auxiliary loss head to better guide the edge pruning by involving the entire adjacency matrix. Second, by regarding unfavorable graph sparsification as adversarial data perturbations, we formulate the pruning process as a min-max optimization problem to gain the robustness of lottery tickets when the graph sparsity is high. We further investigate the question: Can the ``retrainable'' winning ticket of a GNN be also effective for graph transferring learning? We call it the transferable graph lottery ticket (GLT) hypothesis. Extensive experiments were conducted which demonstrate the superiority of our proposed sparsification method over UGS, and which empirically verified our transferable GLT hypothesis.

With the adoption of recent laws ensuring the ``right to be forgotten'', the problem of machine unlearning has become of significant importance. This is particularly the case for graph-structured data, and learning tools specialized for such data, including graph neural networks (GNNs). This work introduces the first known approach for \emph{approximate graph unlearning} with provable theoretical guarantees. The challenges in addressing the problem are two-fold. First, there exist multiple different types of unlearning requests that need to be considered, including node feature, edge and node unlearning. Second, to establish provable performance guarantees, one needs to carefully evaluate the process of feature mixing during propagation. We focus on analyzing Simple Graph Convolutions (SGC) and their generalized PageRank (GPR) extensions, thereby laying the theoretical foundations for unlearning GNNs. Empirical evaluations of six benchmark datasets demonstrate excellent performance/complexity/privacy trade-offs of our approach compared to complete retraining and general methods that do not leverage graph information. For example, unlearning $200$ out of $1208$ training nodes of the Cora dataset only leads to a $0.1\%$ loss in test accuracy, but offers a $4$-fold speed-up compared to complete retraining with a $(\epsilon,\delta)=(1,10^{-4})$ ``privacy cost''. We also exhibit a $12\%$ increase in test accuracy for the same dataset when compared to unlearning methods that do not leverage graph information, with comparable time complexity and the same privacy guarantee.

Learning to optimize is a rapidly growing area that aims to solve optimization problems or improve existing optimization algorithms using machine learning (ML). In particular, the graph neural network (GNN) is considered a suitable ML model for optimization problems whose variables and constraints are permutation--invariant, for example, the linear program (LP). While the literature has reported encouraging numerical results, this paper establishes the theoretical foundation of applying GNNs to solving LPs. Given any size limit of LPs, we construct a GNN that maps different LPs to different outputs. We show that properly built GNNs can reliably predict feasibility, boundedness, and an optimal solution for each LP in a broad class. Our proofs are based upon the recently--discovered connections between the Weisfeiler--Lehman isomorphism test and the GNN. To validate our results, we train a simple GNN and present its accuracy in mapping LPs to their feasibilities and solutions.

Recurrent neural network (RNN) and self-attention mechanism (SAM) are the de facto methods to extract spatial-temporal information for temporal graph learning. Interestingly, we found that although both RNN and SAM could lead to a good performance, in practice neither of them is always necessary. In this paper, we propose GraphMixer, a conceptually and technically simple architecture that consists of three components: (1) a link-encoder that is only based on multi-layer perceptrons (MLP) to summarize the information from temporal links, (2) a node-encoder that is only based on neighbor mean-pooling to summarize node information, and (3) an MLP-based link classifier that performs link prediction based on the outputs of the encoders. Despite its simplicity, GraphMixer attains an outstanding performance on temporal link prediction benchmarks with faster convergence and better generalization performance. These results motivate us to rethink the importance of simpler model architecture.

This work establishes rigorous, novel and widely applicable stability guarantees and transferability bounds for general graph convolutional networks -- without reference to any underlying limit object or statistical distribution. Crucially, utilized graph-shift operators are not necessarily assumed to be normal, allowing for the treatment of networks on both directed- and undirected graphs within the developed framework. In the undirected setting, stability to node-level perturbations is related to an 'adequate spectral covering' property of the filters in each layer. Stability to edge-level perturbations is discussed and related to properties of the utilized filters such as their Lipschitz constants. Results on stability to vertex-set non-preserving perturbations are obtained by utilizing recently developed mathematical-physics based tools. As an exemplifying application of the developed theory, it is showcased that general graph convolutional networks utilizing the un-normalized graph Laplacian as graph-shift-operator can be rendered stable to collapsing strong edges in the underlying graph if filters are mandated to be constant at infinity. These theoretical results are supported by corresponding numerical investigations showcasing the response of filters and networks to such perturbations.

Existing Graph Neural Networks (GNNs) compute the message exchange between nodes by either aggregating uniformly (convolving) the features of all the neighbor- ing nodes, or by applying a non-uniform score (attending) to the features. Recent works have shown the strengths and weaknesses of the resulting GNN architectures, respectively, GCNs and GATs. In this work, we aim at exploiting the strengths of both approaches to their full extent. To this end, we first introduce the graph convolutional attention layer (CAT), which relies on convolutions to compute the attention scores. Unfortunately, as in the case of GCNs and GATs, we show that there exists no clear winner between the three—neither theoretically nor in practice—as their performance directly depends on the nature of the data (i.e., of the graph and features). This result brings us to the main contribution of our work, the learnable graph convolutional attention network (L-CAT): a GNN architecture that automatically interpolates between GCN, GAT and CAT in each layer, by adding only two scalar parameters. Our results demonstrate that L-CAT is able to efficiently combine different GNN layers along the network, outperforming competing methods in a wide range of datasets, and resulting in a more robust model that reduces the need of cross-validating.

Strategic classification studies learning in settings where users can modify their features to obtain favorable predictions. Most current works focus on simple classifiers that trigger independent user responses. Here we examine the implications of learning with more elaborate models that break the independence assumption. Motivated by the idea that applications of strategic classification are often social in nature, we focus on graph neural networks, which make use of social relations between users to improve predictions. Using a graph for learning introduces inter-user dependencies in prediction; our key point is that strategic users can exploit these to promote their goals. As we show through analysis and simulation, this can work either against the system---or for it. Based on this, we propose a differentiable framework for strategically-robust learning of graph-based classifiers. Experiments on several real networked datasets demonstrate the utility of our approach.

Serving a GNN model online is challenging --- in many applications when testing nodes are connected to training nodes, one has to propagate information from training nodes to testing nodes to achieve the best performance, and storing the whole training set (including training graph and node features) during inference stage is prohibitive for large-scale problems. In this paper, we study graph compression to reduce the storage requirement for GNN in serving. Given a GNN model to be served, we propose to construct a compressed graph with a smaller number of nodes. In serving time, one just needs to replace the original training set graph by this compressed graph, without the need of changing the actual GNN model and the forward pass. We carefully analyze the error in the forward pass and derive simple ways to construct the compressed graph to minimize the approximation error. Experimental results on semi-supervised node classification demonstrate that the proposed method can significantly reduce the serving space requirement for GNN inference.

Complex Query Answering (CQA) over Knowledge Graphs (KGs) has attracted a lot of attention to potentially support many applications. Given that KGs are usually incomplete, neural models are proposed to answer the logical queries by parameterizing set operators with complex neural networks. However, such methods usually train neural set operators with a large number of entity and relation embeddings from the zero, where whether and how the embeddings or the neural set operators contribute to the performance remains not clear. In this paper, we propose a simple framework for complex query answering that decomposes the KG embeddings from neural set operators. We propose to represent the complex queries into the query graph. On top of the query graph, we propose the Logical Message Passing Neural Network (LMPNN) that connects the local one-hop inferences on atomic formulas to the global logical reasoning for complex query answering. We leverage existing effective KG embeddings to conduct one-hop inferences on atomic formulas, the results of which are regarded as the messages passed in LMPNN. The reasoning process over the overall logical formulas is turned into the forward pass of LMPNN that incrementally aggregates local information to finally predict the answers' embeddings. The complex logical inference across different types of queries will then be learned from training examples based on the LMPNN architecture. Theoretically, our query-graph represenation is more general than the prevailing operator-tree formulation, so our approach applies to a broader range of complex KG queries. Empirically, our approach yields the new state-of-the-art neural CQA model. Our research bridges the gap between complex KG query answering tasks and the long-standing achievements of knowledge graph representation learning. Our implementation can be found at https://github.com/HKUST-KnowComp/LMPNN.

Graph matching (GM) has been a building block in various areas including computer vision and pattern recognition. Despite recent impressive progress, existing deep GM methods often have obvious difficulty in handling outliers, which are ubiquitous in practice. We propose a deep reinforcement learning based approach RGM, whose sequential node matching scheme naturally fits the strategy for selective inlier matching against outliers. A revocable action framework is devised to improve the agent's flexibility against the complex constrained GM. Moreover, we propose a quadratic approximation technique to regularize the affinity score, in the presence of outliers. As such, the agent can finish inlier matching timely when the affinity score stops growing, for which otherwise an additional parameter i.e. the number of inliers is needed to avoid matching outliers. In this paper, we focus on learning the back-end solver under the most general form of GM: the Lawler's QAP, whose input is the affinity matrix. Especially, our approach can also boost existing GM methods that use such input. Experiments on multiple real-world datasets demonstrate its performance regarding both accuracy and robustness.

In the field of skeleton-based action recognition, current top-performing graph convolutional networks (GCNs) exploit intra-sequence context to construct adaptive graphs for feature aggregation. However, we argue that such context is still $\textit{local}$ since the rich cross-sequence relations have not been explicitly investigated. In this paper, we propose a graph contrastive learning framework for skeleton-based action recognition ($\textit{SkeletonGCL}$) to explore the $\textit{global}$ context across all sequences. In specific, SkeletonGCL associates graph learning across sequences by enforcing graphs to be class-discriminative, i.e., intra-class compact and inter-class dispersed, which improves the GCN capacity to distinguish various action patterns. Besides, two memory banks are designed to enrich cross-sequence context from two complementary levels, i.e., instance and semantic levels, enabling graph contrastive learning in multiple context scales. Consequently, SkeletonGCL establishes a new training paradigm, and it can be seamlessly incorporated into current GCNs. Without loss of generality, we combine SkeletonGCL with three GCNs (2S-ACGN, CTR-GCN, and InfoGCN), and achieve consistent improvements on NTU60, NTU120, and NW-UCLA benchmarks.

Graph Convolutional Networks (GCNs) are one of the most popular architectures that are used to solve classification problems accompanied by graphical information. We present a rigorous theoretical understanding of the effects of graph convolutions in multi-layer networks. We study these effects through the node classification problem of a non-linearly separable Gaussian mixture model coupled with a stochastic block model. First, we show that a single graph convolution expands the regime of the distance between the means where multi-layer networks can classify the data by a factor of at least $1/\sqrt[4]{\rm deg}$, where ${\rm deg}$ denotes the expected degree of a node. Second, we show that with a slightly stronger graph density, two graph convolutions improve this factor to at least $1/\sqrt[4]{n}$, where $n$ is the number of nodes in the graph. Finally, we provide both theoretical and empirical insights into the performance of graph convolutions placed in different combinations among the layers of a neural network, concluding that the performance is mutually similar for all combinations of the placement. We present extensive experiments on both synthetic and real-world data that illustrate our results.

Graph neural networks (GNNs) for temporal graphs have recently attracted increasing attentions, where a common assumption is that the class set for nodes is closed. However, in real-world scenarios, it often faces the open set problem with the dynamically increased class set as the time passes by. This will bring two big challenges to the existing dynamic GNN methods: (i) How to dynamically propagate appropriate information in an open temporal graph, where new class nodes are often linked to old class nodes. This case will lead to a sharp contradiction. This is because typical GNNs are prone to make the embeddings of connected nodes become similar, while we expect the embeddings of these two interactive nodes to be distinguishable since they belong to different classes. (ii) How to avoid catastrophic knowledge forgetting over old classes when learning new classes occurred in temporal graphs. In this paper, we propose a general and principled learning approach for open temporal graphs, called OTGNet, with the goal of addressing the above two challenges. We assume the knowledge of a node can be disentangled into class-relevant and class-agnostic one, and thus explore a new message passing mechanism by extending the information bottleneck principle to only propagate class-agnostic knowledge between nodes of different classes, avoiding aggregating conflictive information. Moreover, we devise a strategy to select both important and diverse triad sub-graph structures for effective class-incremental learning. Extensive experiments on three real-world datasets of different domains demonstrate the superiority of our method, compared to the baselines.

Non-autoregressive translation (NAT) reduces the decoding latency but suffers from performance degradation due to the multi-modality problem. Recently, the structure of directed acyclic graph has achieved great success in NAT, which tackles the multi-modality problem by introducing dependency between vertices. However, training it with negative log-likelihood loss implicitly requires a strict alignment between reference tokens and vertices, weakening its ability to handle multiple translation modalities. In this paper, we hold the view that all paths in the graph are fuzzily aligned with the reference sentence. We do not require the exact alignment but train the model to maximize a fuzzy alignment score between the graph and reference, which takes captured translations in all modalities into account. Extensive experiments on major WMT benchmarks show that our method substantially improves translation performance and increases prediction confidence, setting a new state of the art for NAT on the raw training data.

Despite their widespread success in various domains, Transformer networks have yet to perform well across datasets in the domain of 3D atomistic graphs such as molecules even when 3D-related inductive biases like translational invariance and rotational equivariance are considered. In this paper, we demonstrate that Transformers can generalize well to 3D atomistic graphs and present Equiformer, a graph neural network leveraging the strength of Transformer architectures and incorporating SE(3)/E(3)-equivariant features based on irreducible representations (irreps). First, we propose a simple and effective architecture by only replacing original operations in Transformers with their equivariant counterparts and including tensor products. Using equivariant operations enables encoding equivariant information in channels of irreps features without complicating graph structures. With minimal modifications to Transformers, this architecture has already achieved strong empirical results. Second, we propose a novel attention mechanism called equivariant graph attention, which improves upon typical attention in Transformers through replacing dot product attention with multi-layer perceptron attention and including non-linear message passing. With these two innovations, Equiformer achieves competitive results to previous models on QM9, MD17 and OC20 datasets.

Graph Neural Networks usually rely on the assumption that the graph topology is available to the network as well as optimal for the downstream task. Latent graph inference allows models to dynamically learn the intrinsic graph structure of problems where the connectivity patterns of data may not be directly accessible. In this work, we generalize the discrete Differentiable Graph Module (dDGM) for latent graph learning. The original dDGM architecture used the Euclidean plane to encode latent features based on which the latent graphs were generated. By incorporating Riemannian geometry into the model and generating more complex embedding spaces, we can improve the performance of the latent graph inference system. In particular, we propose a computationally tractable approach to produce product manifolds of constant curvature model spaces that can encode latent features of varying structure. The latent representations mapped onto the inferred product manifold are used to compute richer similarity measures that are leveraged by the latent graph learning model to obtain optimized latent graphs. Moreover, the curvature of the product manifold is learned during training alongside the rest of the network parameters and based on the downstream task, rather than it being a static embedding space. Our novel approach is tested on a wide range of datasets, and outperforms the original dDGM model.

Simulating rigid collisions among arbitrary shapes is notoriously difficult due to complex geometry and the strong non-linearity of the interactions. While graph neural network (GNN)-based models are effective at learning to simulate complex physical dynamics, such as fluids, cloth and articulated bodies, they have been less effective and efficient on rigid-body physics, except with very simple shapes. Existing methods that model collisions through the meshes' nodes are often inaccurate because they struggle when collisions occur on faces far from nodes. Alternative approaches that represent the geometry densely with many particles are prohibitively expensive for complex shapes. Here we introduce the ``Face Interaction Graph Network'' (FIGNet) which extends beyond GNN-based methods, and computes interactions between mesh faces, rather than nodes. Compared to learned node- and particle-based methods, FIGNet is around 4x more accurate in simulating complex shape interactions, while also 8x more computationally efficient on sparse, rigid meshes. Moreover, FIGNet can learn frictional dynamics directly from real-world data, and can be more accurate than analytical solvers given modest amounts of training data. FIGNet represents a key step forward in one of the few remaining physical domains which have seen little competition from learned simulators, and offers allied fields such as robotics, graphics and mechanical design a new tool for simulation and model-based planning.