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 subhomo...
| Authors | Rémi Bourgerie, Šarūnas Girdzijauskas, Viktoria Fodor |
|---|---|
| Primary category | cs.LG |
| Published | 12 August 2026 |
| Last updated at source | 1 October 2026 |
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