Layer-Wise Exchange for Subgraph Federated Learning

Abstract

Subgraph pattern detection aims to uncover complex interaction structures, for example those associated with money laundering in financial transaction networks. State-of-the-art graph neural network (GNN) solutions, however, assume centralized access to the entire graph. When the graph is instead distributed across multiple financial institutions, each client computes node representations using only its own subgraph, so client-local GNN computations diverge from those of a centralized model. We formalize this divergence as the structural observability problem, in which subgraph patterns crossing partition boundaries become locally unidentifiable. This divergence manifests as both a forward gap in the node representations and a backward gap in the training-time adjoint signal. To close both gaps, we propose a per-step, layer-wise exchange framework with two complementary components: a forward exchange that synchronizes node representations at every layer of the forward pass, and a backward exchange that synchronizes the corresponding gradient signals at every layer of the backward pass; neither component exposes raw features or labels. Under an extended subgraph assumption and shared model parameters across clients, we prove that the forward exchange recovers the representations a centralized GNN would compute over the full graph (representation equivalence) and the backward exchange makes the per-client parameter gradients sum to the exact centralized gradient (gradient equivalence). Together, forward and backward exchange make federated training equivalent to centralized training. Experiments on synthetic directed multigraphs with cycle, biclique, and scatter-gather patterns show that forward exchange and federated parameter aggregation are complementary rather than interchangeable, and that their combination recovers most of the gap to centralized performance. This recovery depends on per-step freshness, with stale per-epoch exchange leaving a measurable residual. Adding backward exchange yields further improvements, with the largest gains achieved when the cross-client connectivity is densest.