Xavier Bresson

ICML Conference 2025 Conference Paper

A General Graph Spectral Wavelet Convolution via Chebyshev Order Decomposition

• Nian Liu 0001
• Xiaoxin He
• Thomas Laurent 0001
• Francesco Di Giovanni
• Michael M. Bronstein
• Xavier Bresson

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 model signal distributions over large spatial ranges, and capacity 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 wavelet neural networks. 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 consistent improvements in both short-range and long-range tasks. This underscores the effectiveness of the proposed model in handling different scenarios.

AAAI Conference 2025 Conference Paper

Through the Dual-Prism: A Spectral Perspective on Graph Data Augmentation for Graph Classifications

• Yutong Xia
• Runpeng Yu
• Yuxuan Liang
• Xavier Bresson
• Xinchao Wang
• Roger Zimmermann

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. Extensive experiments validate the efficiency of our approach, providing a new and promising direction for graph data augmentation.

ICLR Conference 2024 Conference Paper

Feature Collapse

• Thomas Laurent 0001
• James von Brecht
• Xavier Bresson

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 synthetic task in which a learner must classify `sentences' constituted of $L$ tokens. We start by showing experimentally that feature collapse goes hand in hand with generalization. We then prove that, in the large sample limit, distinct tokens that play identical roles in the task receive identical local feature representations in the first layer of the network. This analysis shows that a neural network trained on this task provably learns interpretable and meaningful representations in its first layer.

NeurIPS Conference 2024 Conference Paper

G-Retriever: Retrieval-Augmented Generation for Textual Graph Understanding and Question Answering

• Xiaoxin He
• Yijun Tian
• Yifei Sun
• Nitesh V. Chawla
• Thomas Laurent
• Yann LeCun
• Xavier Bresson
• Bryan Hooi

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 a Graph Question Answering (GraphQA) benchmark with data collected from different tasks. Then, we propose our \textit{G-Retriever} method, introducing the first retrieval-augmented generation (RAG) approach for general textual graphs, which 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, \textit{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 mitigates hallucination. ~\footnote{Our codes and datasets are available at: \url{https: //github. com/XiaoxinHe/G-Retriever}}

ICLR Conference 2024 Conference Paper

Harnessing Explanations: LLM-to-LM Interpreter for Enhanced Text-Attributed Graph Representation Learning

• Xiaoxin He
• Xavier Bresson
• Thomas Laurent 0001
• Adam Perold
• Yann LeCun
• Bryan Hooi

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 \emph{explanations as features}: we prompt an LLM to perform zero-shot classification, request textual explanations for its decision-making process, and design an \emph{LLM-to-LM interpreter} to translate these explanations into informative features for downstream GNNs. Our experiments demonstrate that our method achieves state-of-the-art results on well-established TAG datasets, including \texttt{Cora}, \texttt{PubMed}, \texttt{ogbn-arxiv}, as well as our newly introduced dataset, \texttt{tape-arxiv23}. Furthermore, our method significantly speeds up training, achieving a 2.88 times improvement over the closest baseline on \texttt{ogbn-arxiv}. Lastly, we believe the versatility of the proposed method extends beyond TAGs and holds the potential to enhance other tasks involving graph-text data~\footnote{Our codes and datasets are available at: \url{https://github.com/XiaoxinHe/TAPE}}.

ICML Conference 2024 Conference Paper

Navigating Complexity: Toward Lossless Graph Condensation via Expanding Window Matching

• Yuchen Zhang
• Tianle Zhang
• Kai Wang 0036
• Ziyao Guo
• Yuxuan Liang 0002
• Xavier Bresson
• Wei Jin 0009
• Yang You 0001

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 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.

ICML Conference 2023 Conference Paper

A Generalization of ViT/MLP-Mixer to Graphs

• Xiaoxin He
• Bryan Hooi
• Thomas Laurent 0001
• Adam Perold
• Yann LeCun
• Xavier Bresson

Graph Neural Networks (GNNs) have shown great potential in the field of graph representation learning. Standard GNNs define a local message-passing mechanism which propagates information over the whole graph domain by stacking multiple layers. This paradigm suffers from two major limitations, over-squashing and poor long-range dependencies, that can be solved using global attention but significantly increases the computational cost to quadratic complexity. In this work, we propose an alternative approach to overcome these structural limitations by leveraging the ViT/MLP-Mixer architectures introduced in computer vision. We introduce a new class of GNNs, called Graph ViT/MLP-Mixer, that holds three key properties. First, they capture long-range dependency and mitigate the issue of over-squashing as demonstrated on Long Range Graph Benchmark and TreeNeighbourMatch datasets. Second, they offer better speed and memory efficiency with a complexity linear to the number of nodes and edges, surpassing the related Graph Transformer and expressive GNN models. Third, they show high expressivity in terms of graph isomorphism as they can distinguish at least 3-WL non-isomorphic graphs. We test our architecture on 4 simulated datasets and 7 real-world benchmarks, and show highly competitive results on all of them. The source code is available for reproducibility at: https: //github. com/XiaoxinHe/Graph-ViT-MLPMixer.

JMLR Journal 2023 Journal Article

Benchmarking Graph Neural Networks

• Vijay Prakash Dwivedi
• Chaitanya K. Joshi
• Anh Tuan Luu
• Thomas Laurent
• Yoshua Bengio
• Xavier Bresson

In the last few years, graph neural networks (GNNs) have become the standard toolkit for analyzing and learning from data on graphs. This emerging field has witnessed an extensive growth of promising techniques that have been applied with success to computer science, mathematics, biology, physics and chemistry. But for any successful field to become mainstream and reliable, benchmarks must be developed to quantify progress. This led us in March 2020 to release a benchmark framework that i) comprises of a diverse collection of mathematical and real-world graphs, ii) enables fair model comparison with the same parameter budget to identify key architectures, iii) has an open-source, easy-to use and reproducible code infrastructure, and iv) is flexible for researchers to experiment with new theoretical ideas. As of December 2022, the GitHub repository has reached 2,000 stars and 380 forks, which demonstrates the utility of the proposed open-source framework through the wide usage by the GNN community. In this paper, we present an updated version of our benchmark with a concise presentation of the aforementioned framework characteristics, an additional medium-sized molecular dataset AQSOL, similar to the popular ZINC, but with a real-world measured chemical target, and discuss how this framework can be leveraged to explore new GNN designs and insights. As a proof of value of our benchmark, we study the case of graph positional encoding (PE) in GNNs, which was introduced with this benchmark and has since spurred interest of exploring more powerful PE for Transformers and GNNs in a robust experimental setting. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2023. ( edit, beta )

ICLR Conference 2023 Conference Paper

Long-Tailed Learning Requires Feature Learning

• Thomas Laurent 0001
• James von Brecht
• Xavier Bresson

We propose a simple data model inspired from natural data such as text or images, and use it to study the importance of learning features in order to achieve good generalization. Our data model follows a long-tailed distribution in the sense that some rare and uncommon subcategories have few representatives in the training set. In this context we provide evidence that a learner succeeds if and only if it identifies the correct features, and moreover derive non-asymptotic generalization error bounds that precisely quantify the penalty that one must pay for not learning features.

ICLR Conference 2022 Conference Paper

Graph Neural Networks with Learnable Structural and Positional Representations

• Vijay Prakash Dwivedi
• Anh Tuan Luu
• Thomas Laurent 0001
• Yoshua Bengio
• Xavier Bresson

Graph neural networks (GNNs) have become the standard learning architectures for graphs. GNNs have been applied to numerous domains ranging from quantum chemistry, recommender systems to knowledge graphs and natural language processing. A major issue with arbitrary graphs is the absence of canonical positional information of nodes, which decreases the representation power of GNNs to distinguish e.g. isomorphic nodes and other graph symmetries. An approach to tackle this issue is to introduce Positional Encoding (PE) of nodes, and inject it into the input layer, like in Transformers. Possible graph PE are Laplacian eigenvectors. In this work, we propose to decouple structural and positional representations to make easy for the network to learn these two essential properties. We introduce a novel generic architecture which we call \texttt{LSPE} (Learnable Structural and Positional Encodings). We investigate several sparse and fully-connected (Transformer-like) GNNs, and observe a performance increase for molecular datasets, from $1.79\%$ up to $64.14\%$ when considering learnable PE for both GNN classes.

NeurIPS Conference 2017 Conference Paper

Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks

• Federico Monti
• Michael Bronstein
• Xavier Bresson

Matrix completion models are among the most common formulations of recommender systems. Recent works have showed a boost of performance of these techniques when introducing the pairwise relationships between users/items in the form of graphs, and imposing smoothness priors on these graphs. However, such techniques do not fully exploit the local stationary structures on user/item graphs, and the number of parameters to learn is linear w. r. t. the number of users and items. We propose a novel approach to overcome these limitations by using geometric deep learning on graphs. Our matrix completion architecture combines a novel multi-graph convolutional neural network that can learn meaningful statistical graph-structured patterns from users and items, and a recurrent neural network that applies a learnable diffusion on the score matrix. Our neural network system is computationally attractive as it requires a constant number of parameters independent of the matrix size. We apply our method on several standard datasets, showing that it outperforms state-of-the-art matrix completion techniques.

YNIMG Journal 2017 Journal Article

Transient networks of spatio-temporal connectivity map communication pathways in brain functional systems

• Alessandra Griffa
• Benjamin Ricaud
• Kirell Benzi
• Xavier Bresson
• Alessandro Daducci
• Pierre Vandergheynst
• Jean-Philippe Thiran
• Patric Hagmann

The study of brain dynamics enables us to characterize the time-varying functional connectivity among distinct neural groups. However, current methods suffer from the absence of structural connectivity information. We propose to integrate infra-slow neural oscillations and anatomical-connectivity maps, as derived from functional and diffusion MRI, in a multilayer-graph framework that captures transient networks of spatio-temporal connectivity. These networks group anatomically wired and temporary synchronized brain regions and encode the propagation of functional activity on the structural connectome. In a group of 71 healthy subjects, we find that these transient networks demonstrate power-law spatial and temporal size, globally organize into well-known functional systems and describe wave-like trajectories of activation across anatomically connected regions. Within the transient networks, activity propagates through polysynaptic paths that include selective ensembles of structural connections and differ from the structural shortest paths. In the light of the communication-through-coherence principle, the identified spatio-temporal networks could encode communication channels' selection and neural assemblies, which deserves further attention. This work contributes to the understanding of brain structure-function relationships by considering the time-varying nature of resting-state interactions on the axonal scaffold, and it offers a convenient framework to study large-scale communication mechanisms and functional dynamics.

JMLR Journal 2016 Journal Article

Consistency of Cheeger and Ratio Graph Cuts

• Nicolás García Trillos
• Dejan Slepčev
• James von Brecht
• Thomas Laurent
• Xavier Bresson

This paper establishes the consistency of a family of graph-cut- based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on minimizing objective functionals defined on proximity graphs of the given sample. Our focus is on functionals based on graph cuts like the Cheeger and ratio cuts. We show that minimizers of these cuts converge as the sample size increases to a minimizer of a corresponding continuum cut (which partitions the ground truth measure). Moreover, we obtain sharp conditions on how the connectivity radius can be scaled with respect to the number of sample points for the consistency to hold. We provide results for two-way and for multiway cuts. Furthermore we provide numerical experiments that illustrate the results and explore the optimality of scaling in dimension two. [abs] [ pdf ][ bib ] &copy JMLR 2016. ( edit, beta )

NeurIPS Conference 2016 Conference Paper

Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

• Michaël Defferrard
• Xavier Bresson
• Pierre Vandergheynst

In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words’ embedding, represented by graphs. We present a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs. Importantly, the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs, while being universal to any graph structure. Experiments on MNIST and 20NEWS demonstrate the ability of this novel deep learning system to learn local, stationary, and compositional features on graphs.

NeurIPS Conference 2016 Conference Paper

The Product Cut

• Thomas Laurent
• James von Brecht
• Xavier Bresson
• Arthur Szlam

We introduce a theoretical and algorithmic framework for multi-way graph partitioning that relies on a multiplicative cut-based objective. We refer to this objective as the Product Cut. We provide a detailed investigation of the mathematical properties of this objective and an effective algorithm for its optimization. The proposed model has strong mathematical underpinnings, and the corresponding algorithm achieves state-of-the-art performance on benchmark data sets.

YNIMG Journal 2015 Journal Article

An efficient total variation algorithm for super-resolution in fetal brain MRI with adaptive regularization

• Sébastien Tourbier
• Xavier Bresson
• Patric Hagmann
• Jean-Philippe Thiran
• Reto Meuli
• Meritxell Bach Cuadra

Although fetal anatomy can be adequately viewed in new multi-slice MR images, many critical limitations remain for quantitative data analysis. To this end, several research groups have recently developed advanced image processing methods, often denoted by super-resolution (SR) techniques, to reconstruct from a set of clinical low-resolution (LR) images, a high-resolution (HR) motion-free volume. It is usually modeled as an inverse problem where the regularization term plays a central role in the reconstruction quality. Literature has been quite attracted by Total Variation energies because of their ability in edge preserving but only standard explicit steepest gradient techniques have been applied for optimization. In a preliminary work, it has been shown that novel fast convex optimization techniques could be successfully applied to design an efficient Total Variation optimization algorithm for the super-resolution problem. In this work, two major contributions are presented. Firstly, we will briefly review the Bayesian and Variational dual formulations of current state-of-the-art methods dedicated to fetal MRI reconstruction. Secondly, we present an extensive quantitative evaluation of our SR algorithm previously introduced on both simulated fetal and real clinical data (with both normal and pathological subjects). Specifically, we study the robustness of regularization terms in front of residual registration errors and we also present a novel strategy for automatically select the weight of the regularization as regards the data fidelity term. Our results show that our TV implementation is highly robust in front of motion artifacts and that it offers the best trade-off between speed and accuracy for fetal MRI recovery as in comparison with state-of-the art methods.

NeurIPS Conference 2013 Conference Paper

Multiclass Total Variation Clustering

• Xavier Bresson
• Thomas Laurent
• David Uminsky
• James von Brecht

Ideas from the image processing literature have recently motivated a new set of clustering algorithms that rely on the concept of total variation. While these algorithms perform well for bi-partitioning tasks, their recursive extensions yield unimpressive results for multiclass clustering tasks. This paper presents a general framework for multiclass total variation clustering that does not rely on recursion. The results greatly outperform previous total variation algorithms and compare well with state-of-the-art NMF approaches.

NeurIPS Conference 2012 Conference Paper

Convergence and Energy Landscape for Cheeger Cut Clustering

• Xavier Bresson
• Thomas Laurent
• David Uminsky
• James Brecht

Unsupervised clustering of scattered, noisy and high-dimensional data points is an important and difficult problem. Continuous relaxations of balanced cut problems yield excellent clustering results. This paper provides rigorous convergence results for two algorithms that solve the relaxed Cheeger Cut minimization. The first algorithm is a new steepest descent algorithm and the second one is a slight modification of the Inverse Power Method algorithm \cite{pro: HeinBuhler10OneSpec}. While the steepest descent algorithm has better theoretical convergence properties, in practice both algorithm perform equally. We also completely characterize the local minima of the relaxed problem in terms of the original balanced cut problem, and relate this characterization to the convergence of the algorithms.

ICML Conference 2010 Conference Paper

Total Variation, Cheeger Cuts

• Arthur Szlam
• Xavier Bresson