SILVA Networks Offer Structured Implicit Learning for Diverse Data

Many machine learning tasks require representations that can effectively integrate direct input, local structural information, and broader contextual cues. Traditional implicit neural layers often blend these influences into a single fixed-point update, making it difficult to discern the contribution of each factor. This paper introduces SILVA Networks (Structured Implicit Layers and Vector Attractors via Dynamic Interaction Fields), a new architecture designed to address this challenge. SILVA Networks explicitly disentangle the roles of stimulus, local interaction, global interaction, damping, and readout within a unified fixed-point framework. This modular design allows the same architectural template to be adapted for diverse data modalities, such as images, molecular structures, and citation networks, by simply defining domain-specific nodes, neighborhoods, and global summaries. Experimental evaluations and ablation studies demonstrate that different interaction terms play task-dependent roles, with local interactions being crucial for graph tasks and global benefits appearing in long-range node classification.