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

arXiv: https://arxiv.org/abs/2311.16431 · HTML: https://mlsanity.com/paper/2311.16431/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2023.

## Built on by (most cited first, 2 of 2)

- [An explicit operator explains end-to-end computation in the modern neural networks used for sequence and language modeling](https://mlsanity.com/paper/2604.20595/) (2026)
- [Frequency-Based Reservoir computing](https://mlsanity.com/paper/2607.24420/) (2026)

## Abstract (arXiv)

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.