arXiv subjects

Rémi Bourgerie

Publications and source records attributed to Rémi Bourgerie.

5 recordsLinked to original sources

arXiv2026

Fixed Points Without Fixed Diffusion: Implicit Neural Sheaves for Convergent Test-Time Computation

Implicit Graph Neural Networks (IGNNs) define node representations as fixed points of graph neural operators, enabling effectively infinite-depth propagation, iteration-independent parameterization, and flexible test-time computation. Yet these benefits depend on the equilibrium being unique and reached by fixed-point iteration. Existing constructions often impose constraints on recurrent updates to obtain these guarantees, limiting the transformations available at equilibrium. This raises a central question: can IGNNs gain expressiveness through richer, edge-dependent transformations while retaining the inherent strengths of their equilibrium formulation? We introduce SheafDEQ, a subhomogeneous deep-equilibrium architecture with adaptive neural-sheaf propagation. Its learned, matrix-valued sheaf restriction maps can align, mix, or reverse neighbouring representations. Under mild regularity conditions, we prove that SheafDEQ admits a unique equilibrium reached globally by fixed-point iteration from any positive initial state. Contractivity further guarantees convergence under bounded communication staleness. We evaluate SheafDEQ on distributed-inference tasks requiring repeated nonlocal aggregation and on community detection whose rewiring increasingly favours cross-community interactions. SheafDEQ improves over implicit baselines on Sums, MNIST Terrain, and Coordinates, and on community detection as connectivity becomes increasingly heterophilic. SheafDEQ remains competitive with recurrent models without equilibrium guarantees. Continued-iteration diagnostics show decreasing residuals and retained test accuracy through 100 iterations, unlike the finite-horizon control, while delayed-update experiments show low sensitivity to bounded communication staleness.

cs.LG↗

arXiv2026

Do Sheaf Neural Networks Use Holonomy? A Measure--Intervene--Control Study

Geometric architectures are often motivated by internal mechanisms, but accuracy alone does not show whether predictions use them. In Sheaf Neural Networks (SNNs), edge transports form a connection whose cycle products define holonomy. We ask whether training changes triangle holonomy, whether predictions rely on the learned connection, and whether holonomy drives triangle counting. We use basis-independent loop readouts with identity interventions and shortcut controls. On high-homophily GraphUniverse graphs, triangle counting increases the mean SO(2) triangle rotation in Neural Sheaf Propagation (NSP) from 0.010 to 0.388 radians, while community detection ends at 0.029 radians. With more data, learned SO(2)--NSP outperforms Identity NSP, and replacing its transports after training increases error further. However, ridge regression is more accurate, diagonal maps improve without continuous rotation, and fixed-degree models develop rotation without improved counting. Thus, NSP can learn and rely on a nontrivial connection, but our experiments do not show that triangle holonomy drives its predictions.

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arXiv2026

From Euclidean to Graph-Structured Data: A Survey of Collaborative Learning

The conventional approach to machine learning, that is, collecting data, training models, and performing inference in a single location, faces fundamental limitations, including scalability and privacy, that restrict its applicability. To address these challenges, recent research has explored collaborative learning approaches, including federated learning and decentralized learning, where individual agents perform training and inference locally, with limited collaboration. Most collaborative learning research focuses on Euclidean data with regular, grid-like structure (e.g., images, text). However, these approaches fail to capture the relational patterns in many real-world applications, best represented by graphs. Learning on graphs relies on message-passing mechanisms to propagate information between connected nodes, making it conceptually well-suited for collaborative environments where agents must exchange information. Yet, the opportunities and challenges of learning on graph-structured data in collaborative settings remain largely underexplored. This survey provides a comprehensive investigation of collaborative learning from Euclidean to graph-structured data, aiming to consolidate this emerging field. We begin by reviewing its foundational principles for Euclidean data, organizing them along three core dimensions: learning effectiveness, efficiency, and privacy preservation. We then extend the discussion to graph-structured data, introducing a taxonomy of graph distribution scenarios, characterizing associated statistical heterogeneities, and developing standardized problem formulations and algorithmic frameworks. Finally, we systematically identify open challenges and promising research directions.

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arXiv2026

Deep Neural Sheaf Diffusion

Deep Graph Neural Networks (GNNs) are essential for capturing complex dependencies in graph-structured data. However, scaling GNNs to depth remains challenging, as stacking layers leads to representation collapse and diminishing sensitivity due to repeated aggregation. While Neural Sheaf Diffusion (NSD) provides strong theoretical guarantees against such collapse, these guarantees do not translate to practice: as depth increases, the disagreement signal of the sheaf Laplacian vanishes, limiting the contribution of deeper layers. We identify mechanisms that hinder NSD effectiveness at depth and propose \emph{Deep Neural Sheaf Diffusion} (DNSD), which replaces the sheaf Laplacian with a sheaf adjacency operator to maintain informative signals across layers. This is complemented by normalization, odd nonlinearities, and gating. To provide a principled explanation of the expected performance improvement, we contrast sheaf diffusion to graph attention mechanisms, highlighting that DNSD replaces scalar attention scores with matrix-valued edge functions and normalizes node representations rather than attention scores. We demonstrate empirically that DNSD effectively utilizes deep aggregation in graph tasks, outperforming GNN and NSD baselines with up to 30pp accuracy on synthetic long-range datasets, and consistently outperforming them on real-world benchmarks. These results position sheaf-based architectures as a promising building block for graph foundation models by supporting effective deep architectures.

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arXiv2026

Is One Token All It Takes? Graph Pooling Tokens for LLM-based GraphQA

The integration of Graph Neural Networks (GNNs) with Large Language Models (LLMs) has emerged as a promising paradigm for Graph Question Answering (GraphQA). However, effective methods for encoding complex structural information into the LLM's latent space remain an open challenge. Current state-of-the-art architectures, such as G-Retriever, typically rely on standard GNNs and aggressive mean pooling to compress entire graph substructures into a single token, creating a severe information bottleneck. This work mitigates this bottleneck by investigating two orthogonal strategies: (1) increasing the bandwidth of the graph-to-LLM interface via multi-token pooling, and (2) enhancing the semantic quality of the graph encoder via global attention mechanisms. We evaluate a suite of hierarchical pruning and clustering-based pooling operators including Top-k, SAGPool, DiffPool, MinCutPool, and Virtual Node Pooling (VNPool) to project graph data into multiple learnable tokens. Empirically, we demonstrate that while pooling introduces significant instability during soft prompt tuning, the application of Low-Rank Adaptation (LoRA) effectively stabilizes specific hierarchical projections (notably VNPool and pruning methods), though dense clustering operators remain challenging. This stabilization allows compressed representations to rival full-graph baselines (achieving ~73% Hit@1 on WebQSP). Conceptually, we demonstrate that a Graph Transformer with VNPool implementation functions structurally as a single-layer Perceiver IO encoder. Finally, we adapt the FandE (Features and Edges) Score to the generative GraphQA domain. Our analysis reveals that the GraphQA benchmark suffers from representational saturation, where target answers are often highly correlated with isolated node features. The implementation is available at https://github.com/Agrover112/G-Retriever/tree/all_good/

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