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Abstract Networks throughout physics and biology leverage spatiotemporal dynamics for computation. However, the connection between structure and computation remains unclear. Here, we study a complex-valued neural network (cv-NN) with linear interactions and phase-delays. We report the cv-NN displays sophisticated spatiotemporal dynamics, which we then use, 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 phase-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 as the nonlinear readout. 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. 

Abstract Working memory (WM) is the ability to maintain and manipulate information ‘in mind’. The neural codes underlying WM have been a matter of debate. We simultaneously recorded the activity of hundreds of neurons in the lateral prefrontal cortex of male macaque monkeys during a visuospatial WM task that required navigation in a virtual 3D environment. Here, we demonstrate distinct neuronal activation sequences (NASs) that encode remembered target locations in the virtual environment. This NAS code outperformed the persistent firing code for remembered locations during the virtual reality task, but not during a classical WM task using stationary stimuli and constraining eye movements. Finally, blocking NMDA receptors using low doses of ketamine deteriorated the NAS code and behavioral performance selectively during the WM task. These results reveal the versatility and adaptability of neural codes supporting working memory function in the primate lateral prefrontal cortex.