Representation Learning on Heterophilic Graph with Directional Neighborhood Attention

Graph Attention Network (GAT) is one of the most popular Graph Neural Network (GNN) architecture, which employs the attention mechanism to learn edge weights and has demonstrated promising performance in various applications. However, since it only incorporates information from immediate neighborhood, it lacks the ability to capture long-range and global graph information, leading to unsatisfactory performance on some datasets, particularly on heterophilic graphs. To address this limitation, we propose the Directional Graph Attention Network (DGAT) in this paper. DGAT is able to combine the feature-based attention with the global directional information extracted from the graph topology. To this end, a new class of Laplacian matrices is proposed which can provably reduce the diffusion distance between nodes. Based on the new Laplacian, topology-guided neighbour pruning and edge adding mechanisms are proposed to remove the noisy and capture the helpful long-range neighborhood information. Besides, a global directional attention is designed to enable a topological-aware information propagation. The superiority of the proposed DGAT over the baseline GAT has also been verified through experiments on real-world benchmarks and synthetic data sets. It also outperforms the state-of-the-art (SOTA) models on 6 out of 7 real-world benchmark datasets.

On Addressing the Limitations of Graph Neural Networks

This report gives a summary of two problems about graph convolutional networks (GCNs): over-smoothing and heterophily challenges, and outlines future directions to explore.

MUDiff: Unified Diffusion for Complete Molecule Generation

We present a new model for generating molecular data by combining discrete and continuous diffusion processes. Our model generates a comprehensive representation of molecules, including atom features, 2D discrete molecule structures, and 3D continuous molecule coordinates. The use of diffusion processes allows for capturing the probabilistic nature of molecular processes and the ability to explore the effect of different factors on molecular structures and properties. Additionally, we propose a novel graph transformer architecture to denoise the diffusion process. The transformer is equivariant to Euclidean transformations, allowing it to learn invariant atom and edge representations while preserving the equivariance of atom coordinates. This transformer can be used to learn molecular representations robust to geometric transformations. We evaluate the performance of our model through experiments and comparisons with existing methods, showing its ability to generate more stable and valid molecules with good properties. Our model is a promising approach for designing molecules with desired properties and can be applied to a wide range of tasks in molecular modeling.

When Do Graph Neural Networks Help with Node Classification: Investigating the Homophily Principle on Node Distinguishability

Homophily principle, i.e. nodes with the same labels are more likely to be connected, was believed to be the main reason for the performance superiority of Graph Neural Networks (GNNs) over Neural Networks (NNs) on Node Classification (NC) tasks. Recently, people have developed theoretical results arguing that, even though the homophily principle is broken, the advantage of GNNs can still hold as long as nodes from the same class share similar neighborhood patterns, which questions the validity of homophily. However, this argument only considers intra-class Node Distinguishability (ND) and ignores inter-class ND, which is insufficient to study the effect of homophily. In this paper, we first demonstrate the aforementioned insufficiency with examples and argue that an ideal situation for ND is to have smaller intra-class ND than inter-class ND. To formulate this idea and have a better understanding of homophily, we propose Contextual Stochastic Block Model for Homophily (CSBM-H) and define two metrics, Probabilistic Bayes Error (PBE) and Expected Negative KL-divergence (ENKL), to quantify ND, through which we can also find how intra- and inter-class ND influence ND together. We visualize the results and give detailed analysis. Through experiments, we verified that the superiority of GNNs is indeed closely related to both intra- and inter-class ND regardless of homophily levels, based on which we define Kernel Performance Metric (KPM). KPM is a new non-linear, feature-based metric, which is tested to be more effective than the existing homophily metrics on revealing the advantage and disadvantage of GNNs on synthetic and real-world datasets.

Complete the Missing Half: Augmenting Aggregation Filtering with Diversification for Graph Convolutional Neural Networks

The core operation of current Graph Neural Networks (GNNs) is the aggregation enabled by the graph Laplacian or message passing, which filters the neighborhood information of nodes. Though effective for various tasks, in this paper, we show that they are potentially a problematic factor underlying all GNN models for learning on certain datasets, as they force the node representations similar, making the nodes gradually lose their identity and become indistinguishable. Hence, we augment the aggregation operations with their dual, i.e. diversification operators that make the node more distinct and preserve the identity. Such augmentation replaces the aggregation with a two-channel filtering process that, in theory, is beneficial for enriching the node representations. In practice, the proposed two-channel filters can be easily patched on existing GNN methods with diverse training strategies, including spectral and spatial (message passing) methods. In the experiments, we observe desired characteristics of the models and significant performance boost upon the baselines on 9 node classification tasks.

When Do We Need GNN for Node Classification?

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by additionally making use of graph structure based on the relational inductive bias (edge bias), rather than treating the nodes as collections of independent and identically distributed (\iid) samples. Though GNNs are believed to outperform basic NNs in real-world tasks, it is found that in some cases, GNNs have little performance gain or even underperform graph-agnostic NNs. To identify these cases, based on graph signal processing and statistical hypothesis testing, we propose two measures which analyze the cases in which the edge bias in features and labels does not provide advantages. Based on the measures, a threshold value can be given to predict the potential performance advantages of graph-aware models over graph-agnostic models.

Revisiting Heterophily For Graph Neural Networks

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using graph structures based on the relational inductive bias (homophily assumption). While GNNs have been commonly believed to outperform NNs in real-world tasks, recent work has identified a non-trivial set of datasets where their performance compared to NNs is not satisfactory. Heterophily has been considered the main cause of this empirical observation and numerous works have been put forward to address it. In this paper, we first revisit the widely used homophily metrics and point out that their consideration of only graph-label consistency is a shortcoming. Then, we study heterophily from the perspective of post-aggregation node similarity and define new homophily metrics, which are potentially advantageous compared to existing ones. Based on this investigation, we prove that some harmful cases of heterophily can be effectively addressed by local diversification operation. Then, we propose the Adaptive Channel Mixing (ACM), a framework to adaptively exploit aggregation, diversification and identity channels node-wisely to extract richer localized information for diverse node heterophily situations. ACM is more powerful than the commonly used uni-channel framework for node classification tasks on heterophilic graphs and is easy to be implemented in baseline GNN layers. When evaluated on 10 benchmark node classification tasks, ACM-augmented baselines consistently achieve significant performance gain, exceeding state-of-the-art GNNs on most tasks without incurring significant computational burden.

Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using the graph structures based on the relational inductive bias (homophily assumption). Though GNNs are believed to outperform NNs in real-world tasks, performance advantages of GNNs over graph-agnostic NNs seem not generally satisfactory. Heterophily has been considered as a main cause and numerous works have been put forward to address it. In this paper, we first show that not all cases of heterophily are harmful for GNNs with aggregation operation. Then, we propose new metrics based on a similarity matrix which considers the influence of both graph structure and input features on GNNs. The metrics demonstrate advantages over the commonly used homophily metrics by tests on synthetic graphs. From the metrics and the observations, we find some cases of harmful heterophily can be addressed by diversification operation. With this fact and knowledge of filterbanks, we propose the Adaptive Channel Mixing (ACM) framework to adaptively exploit aggregation, diversification and identity channels in each GNN layer to address harmful heterophily. We validate the ACM-augmented baselines with 10 real-world node classification tasks. They consistently achieve significant performance gain and exceed the state-of-the-art GNNs on most of the tasks without incurring significant computational burden.

A Consciousness-Inspired Planning Agent for Model-Based Reinforcement Learning

We present an end-to-end, model-based deep reinforcement learning agent which dynamically attends to relevant parts of its state, in order to plan and to generalize better out-of-distribution. The agent's architecture uses a set representation and a bottleneck mechanism, forcing the number of entities to which the agent attends at each planning step to be small. In experiments with customized MiniGrid environments with different dynamics, we observe that the design allows agents to learn to plan effectively, by attending to the relevant objects, leading to better out-of-distribution generalization.