Resonance Net: Persistent Structured Dynamics for Post-Input and Multimodal Computation

We introduce Resonance Net, a recurrent architecture in which persistent complex-valued signals evolve on the edges of a sparse directed graph. Motivated by graph-based signal propagation and filtering, the architecture treats each recurrent tick as a native internal computation step over a persistent structured substrate. Each tick pools incoming state, applies learned complex transformations and edge-selective routing, and updates the substrate, allowing computation to continue after external input ends. We evaluate this property on CLRS-style graph problems by holding the encoded instance fixed while varying the number of post-input recurrent ticks. On average, deeper dependencies favor larger computation budgets: at the deepest evaluated settings, 48 post-input ticks improve mean pointer accuracy across five seeds from 69.5% to 83.9% on BFS and from 69.8% to 84.7% on Bellman–Ford. We next evaluate heterogeneous modality-specific interfaces through a shared core. Across five seeds, increasing the core edge budget from 0.5× to 4× raises joint multimodal utility from 0.862 to 0.869, while fixed, permuted, and shared ingress assignments perform similarly. Eight-seed mechanism ablations reveal task- and seed-dependent effects rather than uniformly necessary components: no individual removal produces a consistent cross-seed degradation in the primary dependency-by-tick surface AUC, while edge-selective routing increases the BFS benefit obtained from post-input computation across all eight paired seeds. Together, these results show that persistent structured dynamics can support extended internal computation and heterogeneous task interfaces, while also exhibiting substantial variation across learned recurrent solutions.