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

• URL: http://arxiv.org/abs/2311.16431v1
• Date: Tue, 28 Nov 2023 02:23:30 GMT
• Title: An exact mathematical description of computation with transient spatiotemporal dynamics in a complex-valued neural network
• Authors: Roberto C. Budzinski, Alexandra N. Busch, Samuel Mestern, Erwan Martin, Luisa H. B. Liboni, Federico W. Pasini, J\'an Min\'a\v{c}, Todd Coleman, Wataru Inoue, Lyle E. Muller
• Abstract summary: We study a complex-valued neural network (-NN) with linear time-delayed interactions. cv-NN displays sophisticated dynamics, including partially synchronized chimera adaptable'' states. We demonstrate that computations in cv-NN computation are decodable by living biological neurons.
• Score: 33.7054351451505
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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