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

TL;DR

This paper presents an exact mathematical framework for a complex-valued neural network exhibiting rich spatiotemporal dynamics, capable of performing various computations and interfacing with biological neurons, advancing bio-hybrid computing.

Contribution

It introduces a fully solvable, complex-valued neural network model with dynamic computation capabilities, bridging theoretical analysis and biological relevance.

Findings

The cv-NN displays chimera states and complex dynamics.

It can implement logic gates and encode memories.

Computations are decodable by biological neurons.

Abstract

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.