Title: BioRNN: Bio-Inspired Synergistic Integration of Neuromodulation and Wave Propagation in Recurrent Networks
Primary area: applications to neuroscience & cognitive science
Keywords: Bio-inspired neural networks, Wave propagation, Oscillatory dynamics, Spatiotemporal dynamics, Frequency-selective processing

Abstract: Training recurrent networks that directly implement physical wave equations has been hindered by numerical instability and incompatibility with gradient-based optimization. We introduce BioRNN, a recurrent architecture that embeds two-dimensional wave propagation dynamics on a neural grid and achieves stable training via a mixed finite-difference scheme with learnable damping. Inspired by neuromodulation in biological systems, BioRNN incorporates a lightweight frequency-modulation stage that transforms inputs into oscillatory patterns, enabling the recurrent layer to exploit resonance and frequency selectivity. This combination allows BioRNN to model spatiotemporal dependencies through constructive interference while retaining theoretical guarantees of stability during backpropagation. On sequential visual (sMNIST, noisy CIFAR-10) and auditory (ESC-50) benchmarks, BioRNN achieves competitive performance across domains, with pronounced gains on frequency-rich auditory tasks and comparable accuracy on vision. This work demonstrates that integrating biologically inspired neuromodulation with physically grounded wave dynamics yields recurrent models that are both biologically grounded and reliably trainable within modern deep learning.