Spectral graph convolution, an important tool of data filtering on graphs, relies on two essential decisions; selecting spectral bases for signal transformation and parameterizing the kernel for frequency analysis. While recent techniques mainly focus on standard Fourier transform and vector-valued spectral functions, they fall short in flexibility to describe specific signal distribution for each node, and expressivity of spectral function. In this paper, we present a novel wavelet-based graph convolution network, namely WaveGC, which integrates multi-resolution spectral bases and a matrix-valued filter kernel. Theoretically, we establish that WaveGC can effectively capture and decouple short-range and long-range information, providing superior filtering flexibility, surpassing existing graph convolutional networks and graph Transformers (GTs). To instantiate WaveGC, we introduce a novel technique for learning general graph wavelets by separately combining odd and even terms of Chebyshev polynomials. This approach strictly satisfies wavelet admissibility criteria. Our numerical experiments showcase the capabilities of the new network. By replacing the Transformer part in existing architectures with WaveGC, we consistently observe improvements in both short-range and long-range tasks. This underscores the effectiveness of the proposed model in handling different scenarios. Our code is available at https://github.com/liun-online/WaveGC.

Given a graph with textual attributes, we enable users to `chat with their graph': that is, to ask questions about the graph using a conversational interface. In response to a user's questions, our method provides textual replies and highlights the relevant parts of the graph. While existing works integrate large language models (LLMs) and graph neural networks (GNNs) in various ways, they mostly focus on either conventional graph tasks (such as node, edge, and graph classification), or on answering simple graph queries on small or synthetic graphs. In contrast, we develop a flexible question-answering framework targeting real-world textual graphs, applicable to multiple applications including scene graph understanding, common sense reasoning, and knowledge graph reasoning. Toward this goal, we first develop our Graph Question Answering (GraphQA) benchmark with data collected from different tasks. Then, we propose our G-Retriever approach, which integrates the strengths of GNNs, LLMs, and Retrieval-Augmented Generation (RAG), and can be fine-tuned to enhance graph understanding via soft prompting. To resist hallucination and to allow for textual graphs that greatly exceed the LLM's context window size, G-Retriever performs RAG over a graph by formulating this task as a Prize-Collecting Steiner Tree optimization problem. Empirical evaluations show that our method outperforms baselines on textual graph tasks from multiple domains, scales well with larger graph sizes, and resists hallucination. (Our codes and datasets are available at: https://github.com/XiaoxinHe/G-Retriever.)

Graph condensation aims to reduce the size of a large-scale graph dataset by synthesizing a compact counterpart without sacrificing the performance of Graph Neural Networks (GNNs) trained on it, which has shed light on reducing the computational cost for training GNNs. Nevertheless, existing methods often fall short of accurately replicating the original graph for certain datasets, thereby failing to achieve the objective of lossless condensation. To understand this phenomenon, we investigate the potential reasons and reveal that the previous state-of-the-art trajectory matching method provides biased and restricted supervision signals from the original graph when optimizing the condensed one. This significantly limits both the scale and efficacy of the condensed graph. In this paper, we make the first attempt toward \textit{lossless graph condensation} by bridging the previously neglected supervision signals. Specifically, we employ a curriculum learning strategy to train expert trajectories with more diverse supervision signals from the original graph, and then effectively transfer the information into the condensed graph with expanding window matching. Moreover, we design a loss function to further extract knowledge from the expert trajectories. Theoretical analysis justifies the design of our method and extensive experiments verify its superiority across different datasets. Code is released at https://github.com/NUS-HPC-AI-Lab/GEOM.

Graph Neural Networks (GNNs) have become the preferred tool to process graph data, with their efficacy being boosted through graph data augmentation techniques. Despite the evolution of augmentation methods, issues like graph property distortions and restricted structural changes persist. This leads to the question: Is it possible to develop more property-conserving and structure-sensitive augmentation methods? Through a spectral lens, we investigate the interplay between graph properties, their augmentation, and their spectral behavior, and found that keeping the low-frequency eigenvalues unchanged can preserve the critical properties at a large scale when generating augmented graphs. These observations inform our introduction of the Dual-Prism (DP) augmentation method, comprising DP-Noise and DP-Mask, which adeptly retains essential graph properties while diversifying augmented graphs. Graph structures, modeling complex systems through nodes and edges, are ubiquitous across various domains, including social networks (Newman et al., 2002), bioinformatics (Yi et al., 2022), and transportation systems (Jin et al., 2023a). Graph Neural Networks (GNNs) (Kipf & Welling, 2016a) elegantly handle this relational information, paving the way for tasks such as accurate predictions. Their capabilities are further enhanced by graph data augmentation techniques. These methods artificially diversify the dataset through strategic manipulations, thereby bolstering the performance and generalization of GNNs (Rong et al., 2019; Feng et al., 2020; You et al., 2020). Graph data augmentation has progressed from early random topological modifications, exemplified by DropEdge (Rong et al., 2019) and DropNode (Feng et al., 2020), to sophisticated learning-centric approaches like InfoMin (Suresh et al., 2021). Furthermore, techniques inspired by image augmentation's mixup principle (Zhang et al., 2017) have emerged as prominent contenders in this domain (Verma et al., 2019; Wang et al., 2021; Guo & Mao, 2021). Though promising, these augmentation methods are challenged by three key issues as follows. Before the era of deep learning, graph properties, e.g., graph connectivity and diameter, served as vital features for classification for decades (Childs et al., 2009). While now they seem to be ignored, many aforementioned contemporary augmentation methods appear to sidestep this tradition and overlook the graph properties.

Transformers have recently emerged as powerful neural networks for graph learning, showcasing state-of-the-art performance on several graph property prediction tasks. However, these results have been limited to small-scale graphs, where the computational feasibility of the global attention mechanism is possible. The next goal is to scale up these architectures to handle very large graphs on the scale of millions or even billions of nodes. With large-scale graphs, global attention learning is proven impractical due to its quadratic complexity w.r.t. the number of nodes. On the other hand, neighborhood sampling techniques become essential to manage large graph sizes, yet finding the optimal trade-off between speed and accuracy with sampling techniques remains challenging. This work advances representation learning on single large-scale graphs with a focus on identifying model characteristics and critical design constraints for developing scalable graph transformer (GT) architectures. We argue such GT requires layers that can adeptly learn both local and global graph representations while swiftly sampling the graph topology. As such, a key innovation of this work lies in the creation of a fast neighborhood sampling technique coupled with a local attention mechanism that encompasses a 4-hop reception field, but achieved through just 2-hop operations. This local node embedding is then integrated with a global node embedding, acquired via another self-attention layer with an approximate global codebook, before finally sent through a downstream layer for node predictions. The proposed GT framework, named LargeGT, overcomes previous computational bottlenecks and is validated on three large-scale node classification benchmarks. We report a 3x speedup and 16.8% performance gain on ogbn-products and snap-patents, while we also scale LargeGT on ogbn-papers100M with a 5.9% performance improvement.

Representation learning on text-attributed graphs (TAGs) has become a critical research problem in recent years. A typical example of a TAG is a paper citation graph, where the text of each paper serves as node attributes. Initial graph neural network (GNN) pipelines handled these text attributes by transforming them into shallow or hand-crafted features, such as skip-gram or bag-of-words features. Recent efforts have focused on enhancing these pipelines with language models (LMs), which typically demand intricate designs and substantial computational resources. With the advent of powerful large language models (LLMs) such as GPT or Llama2, which demonstrate an ability to reason and to utilize general knowledge, there is a growing need for techniques which combine the textual modelling abilities of LLMs with the structural learning capabilities of GNNs. Hence, in this work, we focus on leveraging LLMs to capture textual information as features, which can be used to boost GNN performance on downstream tasks. A key innovation is our use of explanations as features: we prompt an LLM to perform zero-shot classification, request textual explanations for its decision-making process, and design an LLM-to-LM interpreter to translate these explanations into informative features that enhance downstream GNNs. Our experiments demonstrate that our method achieves state-of-the-art results on well-established TAG datasets, including Cora, PubMed, ogbn-arxiv, as well as our newly introduced dataset, tape-arxiv23. Furthermore, our method significantly speeds up training, achieving a 2.88 times improvement over the closest baseline on ogbn-arxiv.

We formalize and study a phenomenon called feature collapse that makes precise the intuitive idea that entities playing a similar role in a learning task receive similar representations. As feature collapse requires a notion of task, we leverage a simple but prototypical NLP task to study it. We start by showing experimentally that feature collapse goes hand in hand with generalization. We then prove that, in the large sample limit, distinct words that play identical roles in this NLP task receive identical local feature representations in a neural network. This analysis reveals the crucial role that normalization mechanisms, such as LayerNorm, play in feature collapse and in generalization.

Part of the motivation for deploying a neural network arises from the belief that algorithms that learn features/representations generalize better than algorithms that do not. We try to give some mathematical ballast to this notion by studying a data model where, at an intuitive level, a learner succeeds if and only if it manages to learn the correct features. The data model itself attempts to capture two key structures observed in natural data such as text or images. First, it is endowed with a latent structure at the patch or word level that is directly tied to a classification task. Second, the data distribution has a long-tail, in the sense that rare and uncommon instances collectively form a significant fraction of the data. We derive non-asymptotic generalization error bounds that quantify, within our framework, the penalty that one must pay for not learning features.

With the emergence of social media, voluminous video clips are uploaded every day, and retrieving the most relevant visual content with a language query becomes critical. Most approaches aim to learn a joint embedding space for plain textual and visual contents without adequately exploiting their intra-modality structures and inter-modality correlations. This paper proposes a novel transformer that explicitly disentangles the text and video into semantic roles of objects, spatial contexts and temporal contexts with an attention scheme to learn the intra- and inter-role correlations among the three roles to discover discriminative features for matching at different levels. The preliminary results on popular YouCook2 indicate that our approach surpasses a current state-of-the-art method, with a high margin in all metrics. It also overpasses two SOTA methods in terms of two metrics.

The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current works look at utilizing deep learning to construct reasonable solutions. Such efforts have been very successful, but tend to be slow and compute intensive. This paper exemplifies the integration of entropic regularized optimal transport techniques as a layer in a deep reinforcement learning network. We show that we can construct a model capable of learning without supervision and inferences significantly faster than current autoregressive approaches. We also empirically evaluate the benefits of including optimal transport algorithms within deep learning models to enforce assignment constraints during end-to-end training.