Search

Typically, the Time-Delay Neural Network (TDNN) and Transformer can serve as a backbone for Speaker Verification (SV). Both of them have advantages and disadvantages from the perspective of global and local feature modeling. How to effectively integrate these two style features is still an open issue. In this paper, we explore a Parallel-coupled TDNN/Transformer Network (p-vectors) to replace the serial hybrid networks. The p-vectors allows TDNN and Transformer to learn the complementary information from each other through Soft Feature Alignment Interaction (SFAI) under the premise of preserving local and global features. Also, p-vectors uses the Spatial Frequency-channel Attention (SFA) to enhance the spatial interdependence modeling for input features. Finally, the outputs of dual branches of p-vectors are combined by Embedding Aggregation Layer (EAL). Experiments show that p-vectors outperforms MACCIF-TDNN and MFA-Conformer with relative improvements of 11.5% and 13.9% in EER on VoxCeleb1-O., Accepted by INTERSPEECH 2023

Relational pooling is a framework for building more expressive and permutation-invariant graph neural networks. However, there is limited understanding of the exact enhancement in the expressivity of RP and its connection with the Weisfeiler Lehman hierarchy. Starting from RP, we propose to explicitly assign labels to nodes as additional features to improve expressive power of message passing neural networks. The method is then extended to higher dimensional WL, leading to a novel $k,l$-WL algorithm, a more general framework than $k$-WL. Theoretically, we analyze the expressivity of $k,l$-WL with respect to $k$ and $l$ and unifies it with a great number of subgraph GNNs. Complexity reduction methods are also systematically discussed to build powerful and practical $k,l$-GNN instances. We theoretically and experimentally prove that our method is universally compatible and capable of improving the expressivity of any base GNN model. Our $k,l$-GNNs achieve superior performance on many synthetic and real-world datasets, which verifies the effectiveness of our framework., To be published in ICML 2023. 27 pages, 5 figures

In this paper, we provide a theory of using graph neural networks (GNNs) for \textit{multi-node representation learning}, where we are interested in learning a representation for a set of more than one node such as a link. Existing GNNs are mainly designed to learn single-node representations. When we want to learn a node-set representation involving multiple nodes, a common practice in previous works is to directly aggregate the single-node representations obtained by a GNN. In this paper, we show a fundamental limitation of such an approach, namely the inability to capture the dependence among multiple nodes in a node set, and argue that directly aggregating individual node representations fails to produce an effective joint representation for multiple nodes. A straightforward solution is to distinguish target nodes from others. Formalizing this idea, we propose \text{labeling trick}, which first labels nodes in the graph according to their relationships with the target node set before applying a GNN and then aggregates node representations obtained in the labeled graph for multi-node representations. The labeling trick also unifies a few previous successful works for multi-node representation learning, including SEAL, Distance Encoding, ID-GNN, and NBFNet. Besides node sets in graphs, we also extend labeling tricks to posets, subsets and hypergraphs. Experiments verify that the labeling trick technique can boost GNNs on various tasks, including undirected link prediction, directed link prediction, hyperedge prediction, and subgraph prediction. Our work explains the superior performance of previous node-labeling-based methods and establishes a theoretical foundation for using GNNs for multi-node representation learning.

Despite its outstanding performance in various graph tasks, vanilla Message Passing Neural Network (MPNN) usually fails in link prediction tasks, as it only uses representations of two individual target nodes and ignores the pairwise relation between them. To capture the pairwise relations, some models add manual features to the input graph and use the output of MPNN to produce pairwise representations. In contrast, others directly use manual features as pairwise representations. Though this simplification avoids applying a GNN to each link individually and thus improves scalability, these models still have much room for performance improvement due to the hand-crafted and unlearnable pairwise features. To upgrade performance while maintaining scalability, we propose Neural Common Neighbor (NCN), which uses learnable pairwise representations. To further boost NCN, we study the unobserved link problem. The incompleteness of the graph is ubiquitous and leads to distribution shifts between the training and test set, loss of common neighbor information, and performance degradation of models. Therefore, we propose two intervention methods: common neighbor completion and target link removal. Combining the two methods with NCN, we propose Neural Common Neighbor with Completion (NCNC). NCN and NCNC outperform recent strong baselines by large margins. NCNC achieves state-of-the-art performance in link prediction tasks. Our code is available at https://github.com/GraphPKU/NeuralCommonNeighbor.

Graph Neural Networks (GNNs) are often used for tasks involving the 3D geometry of a given graph, such as molecular dynamics simulation. Although the distance matrix of a geometric graph contains complete geometric information, it has been demonstrated that Message Passing Neural Networks (MPNNs) are insufficient for learning this geometry. In this work, we expand on the families of counterexamples that MPNNs are unable to distinguish from their distance matrices, by constructing families of novel and symmetric geometric graphs, to better understand the inherent limitations of MPNNs. We then propose $k$-DisGNNs, which can effectively exploit the rich geometry contained in the distance matrix. We demonstrate the high expressive power of $k$-DisGNNs from three perspectives: 1. They can learn high-order geometric information that cannot be captured by MPNNs. 2. They can unify some existing well-designed geometric models. 3. They are universal function approximators from geometric graphs to scalars (when $k\geq 2$) and vectors (when $k\geq 3$). Most importantly, we establish a connection between geometric deep learning (GDL) and traditional graph representation learning (GRL), showing that those highly expressive GNN models originally designed for GRL can also be applied to GDL with impressive performance, and that existing complex, equivariant models are not the only solution. Experiments verify our theory.

Modeling molecular potential energy surface is of pivotal importance in science. Graph Neural Networks have shown great success in this field. However, their message passing schemes need special designs to capture geometric information and fulfill symmetry requirement like rotation equivariance, leading to complicated architectures. To avoid these designs, we introduce a novel local frame method to molecule representation learning and analyze its expressivity. Projected onto a frame, equivariant features like 3D coordinates are converted to invariant features, so that we can capture geometric information with these projections and decouple the symmetry requirement from GNN design. Theoretically, we prove that given non-degenerate frames, even ordinary GNNs can encode molecules injectively and reach maximum expressivity with coordinate projection and frame-frame projection. In experiments, our model uses a simple ordinary GNN architecture yet achieves state-of-the-art accuracy. The simpler architecture also leads to higher scalability. Our model only takes about 30% inference time and 10% GPU memory compared to the most efficient baselines., Learning on Graphs (LoG) 2022

Link prediction is one important application of graph neural networks (GNNs). Most existing GNNs for link prediction are based on one-dimensional Weisfeiler-Lehman (1-WL) test. 1-WL-GNNs first compute node representations by iteratively passing neighboring node features to the center, and then obtain link representations by aggregating the pairwise node representations. As pointed out by previous works, this two-step procedure results in low discriminating power, as 1-WL-GNNs by nature learn node-level representations instead of link-level. In this paper, we study a completely different approach which can directly obtain node pair (link) representations based on \textit{two-dimensional Weisfeiler-Lehman (2-WL) tests}. 2-WL tests directly use links (2-tuples) as message passing units instead of nodes, and thus can directly obtain link representations. We theoretically analyze the expressive power of 2-WL tests to discriminate non-isomorphic links, and prove their superior link discriminating power than 1-WL. Based on different 2-WL variants, we propose a series of novel 2-WL-GNN models for link prediction. Experiments on a wide range of real-world datasets demonstrate their competitive performance to state-of-the-art baselines and superiority over plain 1-WL-GNNs.

Spectral Graph Neural Network is a kind of Graph Neural Network (GNN) based on graph signal filters. Some models able to learn arbitrary spectral filters have emerged recently. However, few works analyze the expressive power of spectral GNNs. This paper studies spectral GNNs' expressive power theoretically. We first prove that even spectral GNNs without nonlinearity can produce arbitrary graph signals and give two conditions for reaching universality. They are: 1) no multiple eigenvalues of graph Laplacian, and 2) no missing frequency components in node features. We also establish a connection between the expressive power of spectral GNNs and Graph Isomorphism (GI) testing, the latter of which is often used to characterize spatial GNNs' expressive power. Moreover, we study the difference in empirical performance among different spectral GNNs with the same expressive power from an optimization perspective, and motivate the use of an orthogonal basis whose weight function corresponds to the graph signal density in the spectrum. Inspired by the analysis, we propose JacobiConv, which uses Jacobi basis due to its orthogonality and flexibility to adapt to a wide range of weight functions. JacobiConv deserts nonlinearity while outperforming all baselines on both synthetic and real-world datasets., Comment: To be published in ICML2022