🤖 AI Summary
Existing implicit neural layers struggle to disentangle the distinct contributions of input stimuli, local propagation, global context, and solver dynamics to the learned representations. This work proposes SILVA, a unified fixed-point architecture that explicitly decouples stimulus injection, local and global interactions, damping, and readout mechanisms. Through domain-adaptive designs of node, neighborhood, and global summarization modules, SILVA is tailored for diverse tasks spanning images, molecular graphs, citation networks, and long-range graph problems. As the first method to structurally decompose multi-source interactions within implicit layers, SILVA renders internal dynamics trainable, ablatable, and visualizable. Experiments reveal that graph tasks predominantly rely on local interactions, MNIST exhibits limited recursive gains under high capacity, and long-range node classification significantly benefits from explicitly modeled global interactions.
📝 Abstract
Many learning problems require representations that reconcile direct input, nearby structure, and broader context. In implicit neural layers, these influences are usually absorbed into a single fixed-point update, making it hard to identify what enters from the stimulus, what propagates locally, what comes from global context, and what is produced by solver dynamics. Here we introduce SILVA Networks, Structured Implicit Layers and Vector Attractors via Dynamic Interaction Fields. SILVA separates stimulus, local interaction, global interaction, damping, and readout inside one fixed-point architecture. The same template is instantiated for images, molecules, citation networks, and long-range graph benchmarks through domain-specific definitions of nodes, neighborhoods, and global summaries. Experiments and ablations show task-dependent roles for these terms: local interactions are load-bearing in the graph tasks, MNIST gains little from recurrence at the tested capacity, and the clearest global benefit appears in a long-range node-classification benchmark. SILVA therefore provides an implicit representation whose internal interaction dynamics can be trained, ablated, visualized, and diagnosed.