ICLR 2023 Papers

AutoML has demonstrated remarkable success in finding an effective neural architecture for a given machine learning task defined by a specific dataset and an evaluation metric. However, most present AutoML techniques consider each task independently from scratch, which requires exploring many architectures, leading to high computational cost. Here we propose AutoTransfer, an AutoML solution that improves search efficiency by transferring the prior architectural design knowledge to the novel task of interest. Our key innovation includes a task-model bank that captures the model performance over a diverse set of GNN architectures and tasks, and a computationally efficient task embedding that can accurately measure the similarity among different tasks. Based on the task-model bank and the task embeddings, we estimate the design priors of desirable models of the novel task, by aggregating a similarity-weighted sum of the top-K design distributions on tasks that are similar to the task of interest. The computed design priors can be used with any AutoML search algorithm. We evaluate AutoTransfer on six datasets in the graph machine learning domain. Experiments demonstrate that (i) our proposed task embedding can be computed efficiently, and that tasks with similar embeddings have similar best-performing architectures; (ii) AutoTransfer significantly improves search efficiency with the transferred design priors, reducing the number of explored architectures by an order of magnitude. Finally, we release GNN-Bank-101, a large-scale dataset of detailed GNN training information of 120,000 task-model combinations to facilitate and inspire future research.

Knowledge graphs are inherently incomplete. Therefore substantial research has been directed toward knowledge graph completion (KGC), i.e., predicting missing triples from the information represented in the knowledge graph (KG). KG embedding models (KGEs) have yielded promising results for KGC, yet any current KGE is incapable of: (1) fully capturing vital inference patterns (e.g., composition), (2) capturing prominent patterns jointly (e.g., hierarchy and composition), and (3) providing an intuitive interpretation of captured patterns. In this work, we propose ExpressivE, a fully expressive spatio-functional KGE that solves all these challenges simultaneously. ExpressivE embeds pairs of entities as points and relations as hyper-parallelograms in the virtual triple space $\mathbb{R}^{2d}$. This model design allows ExpressivE not only to capture a rich set of inference patterns jointly but additionally to display any supported inference pattern through the spatial relation of hyper-parallelograms, offering an intuitive and consistent geometric interpretation of ExpressivE embeddings and their captured patterns. Experimental results on standard KGC benchmarks reveal that ExpressivE is competitive with state-of-the-art KGEs and even significantly outperforms them on WN18RR.

In the past decades, many large graphs with millions of nodes have been collected/constructed. The high computational cost and significant visualization difficulty hinder the analysis of large graphs. To overcome the difficulties, researchers have developed many graph subsampling approaches to provide a rough sketch that preserves global properties. By selecting representative nodes, these graph subsampling methods can help researchers estimate the graph statistics, e.g., the number of communities, of the large graph from the subsample. However, the available subsampling methods, e.g., degree node sampler and random walk sampler, tend to leave out minority communities because nodes with high degrees are more likely to be sampled. To overcome the shortcomings of the existing methods, we are motivated to apply the community information hidden in the graph to the subsampling method. Though the community structure is unavailable, community structure information can be obtained by applying geometric methods to a graph. An analog of Ricci curvature in the manifold is defined for the graph, i.e., Ollivier Ricci curvature. Based on the asymptotic results about the within-community edge and between-community edge's OR curvature, we propose a subsampling algorithm based on our theoretical results, the Ollivier-Ricci curvature Gradient-based subsampling (ORG-sub) algorithm. The proposed ORG-sub algorithm has two main contributions: First, ORG-sub provides a rigorous theoretical guarantee that the probability of ORG-sub taking all communities into the final subgraph converges to one. Second, extensive experiments on synthetic and benchmark datasets demonstrate the advantages of our algorithm.

Data augmentations are effective in improving the invariance of learning machines. We argue that the core challenge of data augmentations lies in designing data transformations that preserve labels. This is relatively straightforward for images, but much more challenging for graphs. In this work, we propose GraphAug, a novel automated data augmentation method aiming at computing label-invariant augmentations for graph classification. Instead of using uniform transformations as in existing studies, GraphAug uses an automated augmentation model to avoid compromising critical label-related information of the graph, thereby producing label-invariant augmentations at most times. To ensure label-invariance, we develop a training method based on reinforcement learning to maximize an estimated label-invariance probability. Experiments show that GraphAug outperforms previous graph augmentation methods on various graph classification tasks.

Despite that going deep has proven successful in many neural architectures, the existing graph transformers are relatively shallow. In this work, we explore whether more layers are beneficial to graph transformers, and find that current graph transformers suffer from the bottleneck of improving performance by increasing depth. Our further analysis reveals the reason is that deep graph transformers are limited by the vanishing capacity of global attention, restricting the graph transformer from focusing on the critical substructure and obtaining expressive features. To this end, we propose a novel graph transformer model named DeepGraph that explicitly employs substructure tokens in the encoded representation, and applies local attention on related nodes to obtain substructure based attention encoding. Our model enhances the ability of the global attention to focus on substructures and promotes the expressiveness of the representations, addressing the limitation of self-attention as the graph transformer deepens. Experiments show that our method unblocks the depth limitation of graph transformers and results in state-of-the-art performance across various graph benchmarks with deeper models.

Pruning neural networks at initialization (PaI) has received an upsurge of interest due to its end-to-end saving potential. PaI is able to find sparse subnetworks at initialization that can achieve comparable performance to the full networks. These methods can surpass the trivial baseline of random pruning but suffer from a significant performance gap compared to post-training pruning. Previous approaches firmly rely on weights, gradients, and sanity checks as primary signals when conducting PaI analysis. To better understand the underlying mechanism of PaI, we propose to interpret it through the lens of the Ramanujan Graph - a class of expander graphs that are sparse while being highly connected. It is often believed there should be a strong correlation between the Ramanujan graph and PaI since both are about finding sparse and well-connected neural networks. However, the finer-grained link relating highly sparse and connected networks to their relative performance (i.e., ranking of difference sparse structures at the same specific global sparsity) is still missing. We observe that not only the Ramanujan property for sparse networks shows no significant relationship to PaI’s relative performance, but maximizing it can also lead to the formation of pseudo-random graphs with no structural meanings. We reveal the underlying cause to be Ramanujan Graph’s strong assumption on the upper bound of the largest nontrivial eigenvalue (µˆ) of layers belonging to highly sparse networks. We hence propose Iterative Mean Difference of Bound (IMDB) as a mean to relax the µˆ upper bound. Likewise, we also show there exists a lower bound for µˆ, which we call the Normalized Random Coefficient (NaRC), that gives us an accurate assessment for when sparse but highly connected structure degenerates into naive randomness. Finally, we systematically analyze the behavior of various PaI methods and demonstrate the utility of our proposed metrics in characterizing PaI performance. We show that subnetworks preserving better the IMDB property correlate higher in performance, while NaRC provides us with a possible mean to locate the region where highly connected, highly sparse, and non-trivial Ramanujan expanders exist. Our code is available at: https://github.com/VITA-Group/ramanujan-on-pai.

Node classification is a classical graph representation learning task on which Graph Neural Networks (GNNs) have recently achieved strong results. However, it is often believed that standard GNNs only work well for homophilous graphs, i.e., graphs where edges tend to connect nodes of the same class. Graphs without this property are called heterophilous, and it is typically assumed that specialized methods are required to achieve strong performance on such graphs. In this work, we challenge this assumption. First, we show that the standard datasets used for evaluating heterophily-specific models have serious drawbacks, making results obtained by using them unreliable. The most significant of these drawbacks is the presence of a large number of duplicate nodes in the datasets Squirrel and Chameleon, which leads to train-test data leakage. We show that removing duplicate nodes strongly affects GNN performance on these datasets. Then, we propose a set of heterophilous graphs of varying properties that we believe can serve as a better benchmark for evaluating the performance of GNNs under heterophily. We show that standard GNNs achieve strong results on these heterophilous graphs, almost always outperforming specialized models. Our datasets and the code for reproducing our experiments are available at https://github.com/yandex-research/heterophilous-graphs

Recently, Graph Neural Networks (GNNs) have significantly advanced the performance of machine learning tasks on graphs. However, this technological breakthrough makes people wonder: how does a GNN make such decisions, and can we trust its prediction with high confidence? When it comes to some critical fields, such as biomedicine, where making wrong decisions can have severe consequences, it is crucial to interpret the inner working mechanisms of GNNs before applying them. In this paper, we propose a model-agnostic model-level explanation method for different GNNs that follow the message passing scheme, GNNInterpreter, to explain the high-level decision-making process of the GNN model. More specifically, GNNInterpreter learns a probabilistic generative graph distribution that produces the most discriminative graph pattern the GNN tries to detect when making a certain prediction by optimizing a novel objective function specifically designed for the model-level explanation for GNNs. Compared to existing works, GNNInterpreter is more flexible and computationally efficient in generating explanation graphs with different types of node and edge features, without introducing another blackbox or requiring manually specified domain-specific rules. In addition, the experimental studies conducted on four different datasets demonstrate that the explanation graphs generated by GNNInterpreter match the desired graph pattern if the model is ideal; otherwise, potential model pitfalls can be revealed by the explanation.

Recent years have witnessed the success of applying seq2seq models to graph parsing tasks, where the outputs are compositionally structured (e.g., a graph or a tree). However, these seq2seq approaches pose a challenge in quantifying the model’s compositional uncertainty on graph structures due to the gap between seq2seq output probability and structural probability on the graph. This work is the first to quantify and evaluate compositional uncertainty for seq2seq graph parsing tasks. First, we proposed a generic, probabilistically interpretable framework that allows correspondences between seq2seq output probability to structural probability on the graph. This framework serves as a powerful medium for quantifying a seq2seq model's compositional uncertainty on graph elements (i.e., nodes or edges). Second, to evaluate uncertainty quality in terms of calibration, we propose a novel metric called Compositional Expected Calibration Error (CECE) which can measure a model’s calibration behavior in predicting graph structures. By a thorough evaluation for compositional uncertainty on three different tasks across ten domains, we demonstrate that CECE is a better reflection for distributional shift compared to vanilla sequence ECE. Finally, we validate the effectiveness of compositional uncertainty considering the task of collaborative semantic parsing, where the model is allowed to send limited subgraphs for human review. The results show that the collaborative performance based on uncertain subgraph selection consistently outperforms random subgraph selection (30% average error reduction rate) and performs comparably to oracle subgraph selection (only 0.33 difference in average prediction error), indicating that compositional uncertainty is an ideal signal for model errors and can benefit various downstream tasks.

Designing expressive Graph Neural Networks (GNNs) is a central topic in learning graph-structured data. While numerous approaches have been proposed to improve GNNs with respect to the Weisfeiler-Lehman (WL) test, for most of them, there is still a lack of deep understanding of what additional power they can systematically and provably gain. In this paper, we take a fundamentally different perspective to study the expressive power of GNNs beyond the WL test. Specifically, we introduce a novel class of expressivity metrics via graph biconnectivity and highlight their importance in both theory and practice. As biconnectivity can be easily calculated using simple algorithms that have linear computational costs, it is natural to expect that popular GNNs can learn it easily as well. However, after a thorough review of prior GNN architectures, we surprisingly find that most of them are not expressive for any of these metrics. The only exception is the ESAN framework (Bevilacqua et al., 2022), for which we give a theoretical justification of its power. We proceed to introduce a principled and more efficient approach, called the Generalized Distance Weisfeiler-Lehman (GD-WL), which is provably expressive for all biconnectivity metrics. Practically, we show GD-WL can be implemented by a Transformer-like architecture that preserves expressiveness and enjoys full parallelizability. A set of experiments on both synthetic and real datasets demonstrates that our approach can consistently outperform prior GNN architectures.

Traditional Dictionary Learning (DL) aims to approximate data vectors as sparse linear combinations of basis elements (atoms) and is widely used in machine learning, computer vision, and signal processing. To extend DL to graphs, Vincent-Cuaz et al. 2021 propose a method, called GDL, which describes the topology of each graph with a pairwise relation matrix (PRM) and compares PRMs via the Gromov-Wasserstein Discrepancy (GWD). However, the lack of robustness often excludes GDL from a variety of real-world applications since GWD is sensitive to the structural noise in graphs. This paper proposes an improved graph dictionary learning algorithm based on a robust Gromov-Wasserstein discrepancy (RGWD) which has theoretically sound properties and an efficient numerical scheme. Based on such a discrepancy, our dictionary learning algorithm can learn atoms from noisy graph data. Experimental results demonstrate that our algorithm achieves good performance on both simulated and real-world datasets.

Dynamical systems with interacting agents are universal in nature, commonly modeled by a graph of relationships between their constituents. Recently, various works have been presented to tackle the problem of inferring those relationships from the system trajectories via deep neural networks, but most of the studies assume binary or discrete types of interactions for simplicity. In the real world, the interaction kernels often involve continuous interaction strengths, which cannot be accurately approximated by discrete relations. In this work, we propose the relational attentive inference network (RAIN) to infer continuously weighted interaction graphs without any ground-truth interaction strengths. Our model employs a novel pairwise attention (PA) mechanism to refine the trajectory representations and a graph transformer to extract heterogeneous interaction weights for each pair of agents. We show that our RAIN model with the PA mechanism accurately infers continuous interaction strengths for simulated physical systems in an unsupervised manner. Further, RAIN with PA successfully predicts trajectories from motion capture data with an interpretable interaction graph, demonstrating the virtue of modeling unknown dynamics with continuous weights.

Odor perception in mammals is triggered by interactions between volatile organic compounds and a subset of hundreds of proteins called olfactory receptors (ORs). Molecules activate these receptors in a complex combinatorial coding allowing mammals to discriminate a vast number of chemical stimuli. Recently, ORs have gained attention as new therapeutic targets following the discovery of their involvement in other physiological processes and diseases. To date, predicting molecule-induced activation for ORs is highly challenging since $43\%$ of ORs have no identified active compound. In this work, we combine [CLS] token from protBERT with a molecular graph and propose a tailored GNN architecture incorporating inductive biases from the protein-molecule binding. We abstract the biological process of protein-molecule activation as the injection of a molecule into a protein-specific environment. On a newly gathered dataset of $46$ $700$ OR-molecule pairs, this model outperforms state-of-the-art models on drug-target interaction prediction as well as standard GNN baselines. Moreover, by incorporating non-bonded interactions the model is able to work with mixtures of compounds. Finally, our predictions reveal a similar activation pattern for molecules within a given odor family, which is in agreement with the theory of combinatorial coding in olfaction.

Estimating fluid dynamics is classically done through the simulation and integration of numerical models solving the Navier-Stokes equations, which is computationally complex and time-consuming even on high-end hardware. This is a notoriously hard problem to solve, which has recently been addressed with machine learning, in particular graph neural networks (GNN) and variants trained and evaluated on datasets of static objects in static scenes with fixed geometry. We attempt to go beyond existing work in complexity and introduce a new model, method and benchmark. We propose EAGLE: a large-scale dataset of ∼1.1 million 2D meshes resulting from simulations of unsteady fluid dynamics caused by a moving flow source interacting with nonlinear scene structure of varying geometries, with 600 different scenes of three different types in total. To perform future forecasting of pressure and velocity on the challenging EAGLE dataset, we introduce a new mesh transformer. It leverages node clustering, graph pooling and global attention to learn long-range dependencies between spatially distant data points without needing a large number of iterations, as existing GNN methods do. We show that our transformer outperforms state-of-the-art performance on, both, existing synthetic and real datasets and on EAGLE. Finally, we highlight that our approach learns to attend to airflow, integrating complex information in a single iteration.

Many Graph Neural Networks (GNNs) perform poorly compared to simple heuristics on Link Prediction (LP) tasks. This is due to limitations in expressive power such as the inability to count triangles (the backbone of most LP heuristics) and because they can not distinguish automorphic nodes (those having identical structural roles). Both expressiveness issues can be alleviated by learning link (rather than node) representations and incorporating structural features such as triangle counts. Since explicit link representations are often prohibitively expensive, recent works resorted to subgraph-based methods, which have achieved state-of-the-art performance for LP, but suffer from poor efficiency due to high levels of redundancy between subgraphs. We analyze the components of subgraph GNN (SGNN) methods for link prediction. Based on our analysis, we propose a novel full-graph GNN called ELPH (Efficient Link Prediction with Hashing) that passes subgraph sketches as messages to approximate the key components of SGNNs without explicit subgraph construction. ELPH is provably more expressive than Message Passing GNNs (MPNNs). It outperforms existing SGNN models on many standard LP benchmarks while being orders of magnitude faster. However, it shares the common GNN limitation that it is only efficient when the dataset fits in GPU memory. Accordingly, we develop a highly scalable model, called BUDDY, which uses feature precomputation to circumvent this limitation without sacrificing predictive performance. Our experiments show that BUDDY also outperforms SGNNs on standard LP benchmarks while being highly scalable and faster than ELPH.

Message Passing Neural Networks (MPNNs) are a widely used class of Graph Neural Networks (GNNs). The limited representational power of MPNNs inspires the study of provably powerful GNN architectures. However, knowing one model is more powerful than another gives little insight about what functions they can or cannot express. It is still unclear whether these models are able to approximate specific functions such as counting certain graph substructures, which is essential for applications in biology, chemistry and social network analysis. Motivated by this, we propose to study the counting power of Subgraph MPNNs, a recent and popular class of powerful GNN models that extract rooted subgraphs for each node, assign the root node a unique identifier and encode the root node's representation within its rooted subgraph. Specifically, we prove that Subgraph MPNNs fail to count more-than-4-cycles at node level, implying that node representations cannot correctly encode the surrounding substructures like ring systems with more than four atoms. To overcome this limitation, we propose I$^2$-GNNs to extend Subgraph MPNNs by assigning different identifiers for the root node and its neighbors in each subgraph. I$^2$-GNNs' discriminative power is shown to be strictly stronger than Subgraph MPNNs and partially stronger than the 3-WL test. More importantly, I$^2$-GNNs are proven capable of counting all 3, 4, 5 and 6-cycles, covering common substructures like benzene rings in organic chemistry, while still keeping linear complexity. To the best of our knowledge, it is the first linear-time GNN model that can count 6-cycles with theoretical guarantees. We validate its counting power in cycle counting tasks and demonstrate its competitive performance in molecular prediction benchmarks.

Physical simulations that accurately model reality are crucial for many engineering disciplines such as mechanical engineering and robotic motion planning. In recent years, learned Graph Network Simulators produced accurate mesh-based simulations while requiring only a fraction of the computational cost of traditional simulators. Yet, the resulting predictors are confined to learning from data generated by existing mesh-based simulators and thus cannot include real world sensory information such as point cloud data. As these predictors have to simulate complex physical systems from only an initial state, they exhibit a high error accumulation for long-term predictions. In this work, we integrate sensory information to ground Graph Network Simulators on real world observations. In particular, we predict the mesh state of deformable objects by utilizing point cloud data. The resulting model allows for accurate predictions over longer time horizons, even under uncertainties in the simulation, such as unknown material properties. Since point clouds are usually not available for every time step, especially in online settings, we employ an imputation-based model. The model can make use of such additional information only when provided, and resorts to a standard Graph Network Simulator, otherwise. We experimentally validate our approach on a suite of prediction tasks for mesh-based interactions between soft and rigid bodies. Our method results in utilization of additional point cloud information to accurately predict stable simulations where existing Graph Network Simulators fail.

Uncovering rationales behind predictions of graph neural networks (GNNs) has received increasing attention over the years. Existing literature mainly focus on selecting a subgraph, through combinatorial optimization, to provide faithful explanations. However, the exponential size of candidate subgraphs limits the applicability of state-of-the-art methods to large-scale GNNs. We enhance on this through a different approach: by proposing a generative structure – GFlowNets-based GNN Explainer (GFlowExplainer), we turn the optimization problem into a step-by-step generative problem. Our GFlowExplainer aims to learn a policy that generates a distribution of subgraphs for which the probability of a subgraph is proportional to its’ reward. The proposed approach eliminates the influence of node sequence and thus does not need any pre-training strategies. We also propose a new cut vertex matrix to efficiently explore parent states for GFlowNets structure, thus making our approach applicable in a large-scale setting. We conduct extensive experiments on both synthetic and real datasets, and both qualitative and quantitative results show the superiority of our GFlowExplainer.

Recent years have witnessed the prosperity of pre-training graph neural networks (GNNs) for molecules. Typically, atom types as node attributes are randomly masked, and GNNs are then trained to predict masked types as in AttrMask \citep{hu2020strategies}, following the Masked Language Modeling (MLM) task of BERT~\citep{devlin2019bert}. However, unlike MLM with a large vocabulary, the AttrMask pre-training does not learn informative molecular representations due to small and unbalanced atom `vocabulary'. To amend this problem, we propose a variant of VQ-VAE~\citep{van2017neural} as a context-aware tokenizer to encode atom attributes into chemically meaningful discrete codes. This can enlarge the atom vocabulary size and mitigate the quantitative divergence between dominant (e.g., carbons) and rare atoms (e.g., phosphorus). With the enlarged atom `vocabulary', we propose a novel node-level pre-training task, dubbed Masked Atoms Modeling (\textbf{MAM}), to mask some discrete codes randomly and then pre-train GNNs to predict them. MAM also mitigates another issue of AttrMask, namely the negative transfer. It can be easily combined with various pre-training tasks to improve their performance. Furthermore, we propose triplet masked contrastive learning (\textbf{TMCL}) for graph-level pre-training to model the heterogeneous semantic similarity between molecules for effective molecule retrieval. MAM and TMCL constitute a novel pre-training framework, \textbf{Mole-BERT}, which can match or outperform state-of-the-art methods in a fully data-driven manner. We release the code at \textcolor{magenta}{\url{https://github.com/junxia97/Mole-BERT}}.