SILVA Networks reveal interpretable interaction terms for graph AI

SILVA Networks (Structured Implicit Layers and Vector Attractors via Dynamic Interaction Fields) tackle a core problem in implicit neural networks: interpretability. Traditional fixed-point solvers blend input stimulus, local neighborhood effects, global context, and solver dynamics into a single opaque update. Silva's architecture explicitly decomposes these influences into five additive terms—stimulus, local interaction, global interaction, damping, and readout—all within one fixed-point layer. This allows researchers to ablate each component independently and observe exactly how information flows through the network during training and inference.

In experiments spanning image classification (MNIST), molecular property prediction, citation networks, and long-range graph benchmarks, SILVA revealed task-dependent roles for each term. Local interactions proved highly load-bearing, especially in graph tasks, where removing them significantly degraded performance. Conversely, MNIST showed almost no benefit from recurrence at the tested capacity, while the clearest global-context advantage emerged in a long-range node classification benchmark. These findings suggest that SILVA's modular structure can serve as a diagnostic tool: instead of treating deep learning as a black box, researchers can visually and quantitatively map how much each interaction type contributes to a prediction. With 46 pages and 10 figures, the paper positions SILVA as both a practical architecture and a framework for understanding implicit neural dynamics across diverse data domains.