arXiv：cs.LG· R\'emi Bourgerie, \v{S}ar\={u}nas Girdzijauskas, Viktoria Fodor·· 5 小时前AI 评分30
SheafDEQ：用隐式神经层束实现可收敛的测试时计算
Fixed Points Without Fixed Diffusion: Implicit Neural Sheaves for Convergent Test-Time Computation
AI 导读
SheafDEQ 是一种亚齐次深度均衡架构，通过自适应神经层束传播，其可学习的矩阵值层束限制映射能对齐、混合或反转邻居表示。在温和正则条件下，该架构被证明具有唯一均衡点，可从任意正初始状态经不动点迭代全局收敛，且收缩性保证在有界通信陈旧度下仍收敛。
正文
Abstract: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.
| Comments: | Accepted at the 5th Learning on Graphs Conference (LoG 2026) |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2609.30277 [cs.LG] |
| (or arXiv:2609.30277v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.30277 arXiv-issued DOI via DataCite |
Submission history
From: Rémi Bourgerie [view email]
[v1]
Wed, 12 Aug 2026 21:48:07 UTC (1,001 KB)
[v2]
Thu, 1 Oct 2026 20:54:48 UTC (2,199 KB)
来源：arXiv：cs.LG · arxiv.org