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.

翻译：我们研究了一种具有线性时滞相互作用的复值神经网络（cv-NN）。研究发现该复值神经网络展现出复杂的时空动力学行为，包括部分同步的“嵌合体”状态。我们进一步利用这些时空动力学与非线性读出机制相结合执行计算任务。该复值神经网络能够实现基于动力学的逻辑门、编码短期记忆，并通过相互作用与时滞的组合实现安全消息传递。该系统的计算过程可用精确闭式数学表达式完整描述。最后，通过新皮层脑片神经元的直接细胞内记录，我们证明活体生物神经元能够解码复值神经网络的计算结果。这些结果表明复值线性系统既能执行复杂计算又可精确求解。综上，本研究为设计能与其它神经网络无缝对接的高度适应性生物混合计算系统开辟了新途径。