Paper ID: 2311.16431

An exact mathematical description of computation with transient spatiotemporal dynamics in a complex-valued neural network

Roberto C. Budzinski, Alexandra N. Busch, Samuel Mestern, Erwan Martin, Luisa H. B. Liboni, Federico W. Pasini, Ján Mináč, Todd Coleman, Wataru Inoue, Lyle E. Muller

We study a complex-valued neural network (cv-NN) with linear, time-delayed interactions. We report the cv-NN displays sophisticated spatiotemporal dynamics, including partially synchronized ``chimera'' states. We then use these spatiotemporal dynamics, in combination with a nonlinear readout, for computation. The cv-NN can instantiate dynamics-based logic gates, encode short-term memories, and mediate secure message passing through a combination of interactions and time delays. The computations in this system can be fully described in an exact, closed-form mathematical expression. Finally, using direct intracellular recordings of neurons in slices from neocortex, we demonstrate that computations in the cv-NN are decodable by living biological neurons. These results demonstrate that complex-valued linear systems can perform sophisticated computations, while also being exactly solvable. Taken together, these results open future avenues for design of highly adaptable, bio-hybrid computing systems that can interface seamlessly with other neural networks.

Submitted: Nov 28, 2023