Xiaowen Dong

Xingchen Wan, Pierre Osselin, Henry Kenlay et al. · oxford

The increasing availability of graph-structured data motivates the task of optimising over functions defined on the node set of graphs. Traditional graph search algorithms can be applied in this case, but they may be sample-inefficient and do not make use of information about the function values; on the other hand, Bayesian optimisation is a class of promising black-box solvers with superior sample efficiency, but it has been scarcely been applied to such novel setups. To fill this gap, we propose a novel Bayesian optimisation framework that optimises over functions defined on generic, large-scale and potentially unknown graphs. Through the learning of suitable kernels on graphs, our framework has the advantage of adapting to the behaviour of the target function. The local modelling approach further guarantees the efficiency of our method. Extensive experiments on both synthetic and real-world graphs demonstrate the effectiveness of the proposed optimisation framework.

Bohan Tang, Siheng Chen, Xiaowen Dong

Hypergraph structure learning, which aims to learn the hypergraph structures from the observed signals to capture the intrinsic high-order relationships among the entities, becomes crucial when a hypergraph topology is not readily available in the datasets. There are two challenges that lie at the heart of this problem: 1) how to handle the huge search space of potential hyperedges, and 2) how to define meaningful criteria to measure the relationship between the signals observed on nodes and the hypergraph structure. In this paper, for the first challenge, we adopt the assumption that the ideal hypergraph structure can be derived from a learnable graph structure that captures the pairwise relations within signals. Further, we propose a hypergraph structure learning framework HGSL with a novel dual smoothness prior that reveals a mapping between the observed node signals and the hypergraph structure, whereby each hyperedge corresponds to a subgraph with both node signal smoothness and edge signal smoothness in the learnable graph structure. Finally, we conduct extensive experiments to evaluate HGSL on both synthetic and real world datasets. Experiments show that HGSL can efficiently infer meaningful hypergraph topologies from observed signals.

Deborah Sulem, Henry Kenlay, Mihai Cucuringu et al.

Dynamic networks are ubiquitous for modelling sequential graph-structured data, e.g., brain connectome, population flows and messages exchanges. In this work, we consider dynamic networks that are temporal sequences of graph snapshots, and aim at detecting abrupt changes in their structure. This task is often termed network change-point detection and has numerous applications, such as fraud detection or physical motion monitoring. Leveraging a graph neural network model, we design a method to perform online network change-point detection that can adapt to the specific network domain and localise changes with no delay. The main novelty of our method is to use a siamese graph neural network architecture for learning a data-driven graph similarity function, which allows to effectively compare the current graph and its recent history. Importantly, our method does not require prior knowledge on the network generative distribution and is agnostic to the type of change-points; moreover, it can be applied to a large variety of networks, that include for instance edge weights and node attributes. We show on synthetic and real data that our method enjoys a number of benefits: it is able to learn an adequate graph similarity function for performing online network change-point detection in diverse types of change-point settings, and requires a shorter data history to detect changes than most existing state-of-the-art baselines.

Enpei Zhang, Shuo Tang, Xiaowen Dong et al.

Multi-agent learning has gained increasing attention to tackle distributed machine learning scenarios under constrictions of data exchanging. However, existing multi-agent learning models usually consider data fusion under fixed and compulsory collaborative relations among agents, which is not as flexible and autonomous as human collaboration. To fill this gap, we propose a distributed multi-agent learning model inspired by human collaboration, in which the agents can autonomously detect suitable collaborators and refer to collaborators' model for better performance. To implement such adaptive collaboration, we use a collaboration graph to indicate the pairwise collaborative relation. The collaboration graph can be obtained by graph learning techniques based on model similarity between different agents. Since model similarity can not be formulated by a fixed graphical optimization, we design a graph learning network by unrolling, which can learn underlying similar features among potential collaborators. By testing on both regression and classification tasks, we validate that our proposed collaboration model can figure out accurate collaborative relationship and greatly improve agents' learning performance.

Emanuele Rossi, Federico Monti, Yan Leng et al.

Strategic interactions between a group of individuals or organisations can be modelled as games played on networks, where a player's payoff depends not only on their actions but also on those of their neighbours. Inferring the network structure from observed game outcomes (equilibrium actions) is an important problem with numerous potential applications in economics and social sciences. Existing methods mostly require the knowledge of the utility function associated with the game, which is often unrealistic to obtain in real-world scenarios. We adopt a transformer-like architecture which correctly accounts for the symmetries of the problem and learns a mapping from the equilibrium actions to the network structure of the game without explicit knowledge of the utility function. We test our method on three different types of network games using both synthetic and real-world data, and demonstrate its effectiveness in network structure inference and superior performance over existing methods.

Felix L. Opolka, Yin-Cong Zhi, Pietro Liò et al.

Graph classification aims to categorise graphs based on their structure and node attributes. In this work, we propose to tackle this task using tools from graph signal processing by deriving spectral features, which we then use to design two variants of Gaussian process models for graph classification. The first variant uses spectral features based on the distribution of energy of a node feature signal over the spectrum of the graph. We show that even such a simple approach, having no learned parameters, can yield competitive performance compared to strong neural network and graph kernel baselines. A second, more sophisticated variant is designed to capture multi-scale and localised patterns in the graph by learning spectral graph wavelet filters, obtaining improved performance on synthetic and real-world data sets. Finally, we show that both models produce well calibrated uncertainty estimates, enabling reliable decision making based on the model predictions.

Pierre Osselin, Henry Kenlay, Xiaowen Dong

Certifying the robustness of a graph-based machine learning model poses a critical challenge for safety. Current robustness certificates for graph classifiers guarantee output invariance with respect to the total number of node pair flips (edge addition or edge deletion), which amounts to an $l_{0}$ ball centred on the adjacency matrix. Although theoretically attractive, this type of isotropic structural noise can be too restrictive in practical scenarios where some node pairs are more critical than others in determining the classifier's output. The certificate, in this case, gives a pessimistic depiction of the robustness of the graph model. To tackle this issue, we develop a randomised smoothing method based on adding an anisotropic noise distribution to the input graph structure. We show that our process generates structural-aware certificates for our classifiers, whereby the magnitude of robustness certificates can vary across different pre-defined structures of the graph. We demonstrate the benefits of these certificates in both synthetic and real-world experiments.

Yin-Cong Zhi, Felix L. Opolka, Yin Cheng Ng et al.

Kernels on graphs have had limited options for node-level problems. To address this, we present a novel, generalized kernel for graphs with node feature data for semi-supervised learning. The kernel is derived from a regularization framework by treating the graph and feature data as two Hilbert spaces. We also show how numerous kernel-based models on graphs are instances of our design. A kernel defined this way has transductive properties, and this leads to improved ability to learn on fewer training points, as well as better handling of highly non-Euclidean data. We demonstrate these advantages using synthetic data where the distribution of the whole graph can inform the pattern of the labels. Finally, by utilizing a flexible polynomial of the graph Laplacian within the kernel, the model also performed effectively in semi-supervised classification on graphs of various levels of homophily.

Shuo Tang, Rui Ye, Chenxin Xu et al.

Decentralized and lifelong-adaptive multi-agent collaborative learning aims to enhance collaboration among multiple agents without a central server, with each agent solving varied tasks over time. To achieve efficient collaboration, agents should: i) autonomously identify beneficial collaborative relationships in a decentralized manner; and ii) adapt to dynamically changing task observations. In this paper, we propose DeLAMA, a decentralized multi-agent lifelong collaborative learning algorithm with dynamic collaboration graphs. To promote autonomous collaboration relationship learning, we propose a decentralized graph structure learning algorithm, eliminating the need for external priors. To facilitate adaptation to dynamic tasks, we design a memory unit to capture the agents' accumulated learning history and knowledge, while preserving finite storage consumption. To further augment the system's expressive capabilities and computational efficiency, we apply algorithm unrolling, leveraging the advantages of both mathematical optimization and neural networks. This allows the agents to `learn to collaborate' through the supervision of training tasks. Our theoretical analysis verifies that inter-agent collaboration is communication efficient under a small number of communication rounds. The experimental results verify its ability to facilitate the discovery of collaboration strategies and adaptation to dynamic learning scenarios, achieving a 98.80% reduction in MSE and a 188.87% improvement in classification accuracy. We expect our work can serve as a foundational technique to facilitate future works towards an intelligent, decentralized, and dynamic multi-agent system. Code is available at https://github.com/ShuoTang123/DeLAMA.

Álvaro Arroyo, Alessio Gravina, Benjamin Gutteridge et al.

Graph Neural Networks (GNNs) are models that leverage the graph structure to transmit information between nodes, typically through the message-passing operation. While widely successful, this approach is well known to suffer from the over-smoothing and over-squashing phenomena, which result in representational collapse as the number of layers increases and insensitivity to the information contained at distant and poorly connected nodes, respectively. In this paper, we present a unified view of these problems through the lens of vanishing gradients, using ideas from linear control theory for our analysis. We propose an interpretation of GNNs as recurrent models and empirically demonstrate that a simple state-space formulation of a GNN effectively alleviates over-smoothing and over-squashing at no extra trainable parameter cost. Further, we show theoretically and empirically that (i) GNNs are by design prone to extreme gradient vanishing even after a few layers; (ii) Over-smoothing is directly related to the mechanism causing vanishing gradients; (iii) Over-squashing is most easily alleviated by a combination of graph rewiring and vanishing gradient mitigation. We believe our work will help bridge the gap between the recurrent and graph neural network literature and will unlock the design of new deep and performant GNNs.

Jacob Bamberger, Federico Barbero, Xiaowen Dong et al.

The dominant paradigm for learning on graph-structured data is message passing. Despite being a strong inductive bias, the local message passing mechanism suffers from pathological issues such as over-smoothing, over-squashing, and limited node-level expressivity. To address these limitations we propose Bundle Neural Networks (BuNN), a new type of GNN that operates via message diffusion over flat vector bundles - structures analogous to connections on Riemannian manifolds that augment the graph by assigning to each node a vector space and an orthogonal map. A BuNN layer evolves the features according to a diffusion-type partial differential equation. When discretized, BuNNs are a special case of Sheaf Neural Networks (SNNs), a recently proposed MPNN capable of mitigating over-smoothing. The continuous nature of message diffusion enables BuNNs to operate on larger scales of the graph and, therefore, to mitigate over-squashing. Finally, we prove that BuNN can approximate any feature transformation over nodes on any (potentially infinite) family of graphs given injective positional encodings, resulting in universal node-level expressivity. We support our theory via synthetic experiments and showcase the strong empirical performance of BuNNs over a range of real-world tasks, achieving state-of-the-art results on several standard benchmarks in transductive and inductive settings.

Mathieu Alain, So Takao, Xiaowen Dong et al.

The problem of classifying graphs is ubiquitous in machine learning. While it is standard to apply graph neural networks or graph kernel methods, Gaussian processes can be employed by transforming spatial features from the graph domain into spectral features in the Euclidean domain, and using them as the input points of classical kernels. However, this approach currently only takes into account features on vertices, whereas some graph datasets also support features on edges. In this work, we present a Gaussian process-based classification algorithm that can leverage one or both vertex and edges features. Furthermore, we take advantage of the Hodge decomposition to better capture the intricate richness of vertex and edge features, which can be beneficial on diverse tasks.

Ning Zhang, Xiaowen Dong, Mihai Cucuringu

Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their extension to directed graphs remains relatively underexplored due to the additional complexity introduced by edge directions. In this paper, we leverage statistical inference on stochastic block models to guide the development of a spectral clustering algorithm for directed graphs. Specifically, we study the maximum likelihood estimation under a widely used directed stochastic block model, and derive a global objective function that aligns with the underlying community structure. We further establish a theoretical upper bound on the misclustering error of its spectral relaxation, and based on this relaxation, introduce a novel, self-adaptive spectral clustering method for directed graphs. Extensive experiments on synthetic and real-world datasets demonstrate significant performance gains over existing baselines.

Enrique Queipo-de-Llano, Álvaro Arroyo, Federico Barbero et al.

Attention sinks and compression valleys have attracted significant attention as two puzzling phenomena in large language models, but have been studied in isolation. In this work, we present a surprising connection between attention sinks and compression valleys, tracing both to the formation of massive activations in the residual stream. We prove theoretically that massive activations necessarily produce representational compression and establish bounds on the resulting entropy reduction. Through experiments across several models (410M-120B parameters), we confirm that when the beginning-of-sequence token develops extreme activation norms in the middle layers, both compression valleys and attention sinks emerge simultaneously. Targeted ablation studies validate our theoretical predictions. This unified view motivates us to propose the Mix-Compress-Refine theory of information flow, as an attempt to explain how LLMs organize their computation in depth by controlling attention and representational compression via massive activations. Specifically, we posit that Transformer-based LLMs process tokens in three distinct phases: (1) broad mixing in the early layers, (2) compressed computation with limited mixing in the middle layers, and (3) selective refinement in the late layers. Our framework helps explain why embedding tasks perform best at intermediate layers, whereas generation tasks benefit from full-depth processing, clarifying differences in task-dependent representations.

Pierre Osselin, Masaki Adachi, Xiaowen Dong et al.

Zeroth-order local optimisation algorithms are essential for solving real-valued black-box optimisation problems. Among these, Natural Evolution Strategies (NES) represent a prominent class, particularly well-suited for scenarios where prior distributions are available. By optimising the objective function in the space of search distributions, NES algorithms naturally integrate prior knowledge during initialisation, making them effective in settings such as semi-supervised learning and user-prior belief frameworks. However, due to their reliance on random sampling and Monte Carlo estimates, NES algorithms can suffer from limited sample efficiency. In this paper, we introduce a novel class of algorithms, termed Probabilistic Natural Evolutionary Strategy Algorithms (ProbNES), which enhance the NES framework with Bayesian quadrature. We show that ProbNES algorithms consistently outperforms their non-probabilistic counterparts as well as global sample efficient methods such as Bayesian Optimisation (BO) or $π$BO across a wide range of tasks, including benchmark test functions, data-driven optimisation tasks, user-informed hyperparameter tuning tasks and locomotion tasks.

Ning Zhang, Henry Kenlay, Li Zhang et al.

Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these models, i.e., their sensitivity to small changes in the graph structure, remains in rather limited settings, hampering the development and deployment of robust and trustworthy models in practice. To fill this gap, we study how perturbations in the graph topology affect GCNN outputs and propose a novel formulation for analyzing model stability. Unlike prior studies that focus only on worst-case perturbations, our distribution-aware formulation characterizes output perturbations across a broad range of input data. This way, our framework enables, for the first time, a probabilistic perspective on the interplay between the statistical properties of the node data and perturbations in the graph topology. We conduct extensive experiments to validate our theoretical findings and demonstrate their benefits over existing baselines, in terms of both representation stability and adversarial attacks on downstream tasks. Our results demonstrate the practical significance of the proposed formulation and highlight the importance of incorporating data distribution into stability analysis.

Benjamin Gutteridge, Xiaowen Dong, Michael Bronstein et al.

Message passing neural networks (MPNNs) have been shown to suffer from the phenomenon of over-squashing that causes poor performance for tasks relying on long-range interactions. This can be largely attributed to message passing only occurring locally, over a node's immediate neighbours. Rewiring approaches attempting to make graphs 'more connected', and supposedly better suited to long-range tasks, often lose the inductive bias provided by distance on the graph since they make distant nodes communicate instantly at every layer. In this paper we propose a framework, applicable to any MPNN architecture, that performs a layer-dependent rewiring to ensure gradual densification of the graph. We also propose a delay mechanism that permits skip connections between nodes depending on the layer and their mutual distance. We validate our approach on several long-range tasks and show that it outperforms graph Transformers and multi-hop MPNNs.

Lucas G. S. Jeub, Giovanni Colavizza, Xiaowen Dong et al.

We propose a decentralised "local2global"' approach to graph representation learning, that one can a-priori use to scale any embedding technique. Our local2global approach proceeds by first dividing the input graph into overlapping subgraphs (or "patches") and training local representations for each patch independently. In a second step, we combine the local representations into a globally consistent representation by estimating the set of rigid motions that best align the local representations using information from the patch overlaps, via group synchronization. A key distinguishing feature of local2global relative to existing work is that patches are trained independently without the need for the often costly parameter synchronization during distributed training. This allows local2global to scale to large-scale industrial applications, where the input graph may not even fit into memory and may be stored in a distributed manner. We apply local2global on data sets of different sizes and show that our approach achieves a good trade-off between scale and accuracy on edge reconstruction and semi-supervised classification. We also consider the downstream task of anomaly detection and show how one can use local2global to highlight anomalies in cybersecurity networks.

Valentin Hofmann, Xiaowen Dong, Janet B. Pierrehumbert et al.

The increasing polarization of online political discourse calls for computational tools that automatically detect and monitor ideological divides in social media. We introduce a minimally supervised method that leverages the network structure of online discussion forums, specifically Reddit, to detect polarized concepts. We model polarization along the dimensions of salience and framing, drawing upon insights from moral psychology. Our architecture combines graph neural networks with structured sparsity learning and results in representations for concepts and subreddits that capture temporal ideological dynamics such as right-wing and left-wing radicalization.