Neurons communicate with downstream systems via sparse and incredibly brief electrical pulses, or spikes. Using these events, they control various targets such as neuromuscular units, neurosecretory systems, and other neurons in connected circuits. This gave rise to the idea of spiking neurons as controllers, in which spikes are the control signal. Using instantaneous events directly as the control inputs, also called `impulse control', is challenging as it does not scale well to larger networks and has low analytical tractability. Therefore, current spiking control usually relies on filtering the spike signal to approximate analog control. This ultimately means spiking neural networks (SNNs) have to output a continuous control signal, necessitating continuous energy input into downstream systems. Here, we circumvent the need for rate-based representations, providing a scalable method for task-specific spiking control with sparse neural activity. In doing so, we take inspiration from both optimal control and neuroscience theory, and define a spiking rule where spikes are only emitted if they bring a dynamical system closer to a target. From this principle, we derive the required connectivity for an SNN, and show that it can successfully control linear systems. We show that for physically constrained systems, predictive control is required, and the control signal ends up exploiting the passive dynamics of the downstream system to reach a target. Finally, we show that the control method scales to both high-dimensional networks and systems. Importantly, in all cases, we maintain a closed-form mathematical derivation of the network connectivity, the network dynamics and the control objective. This work advances the understanding of SNNs as biologically-inspired controllers, providing insight into how real neurons could exert control, and enabling applications in neuromorphic hardware design.

翻译：神经元通过稀疏且极其短暂的电脉冲（即脉冲）与下游系统进行通信。利用这些事件，它们控制着多种目标，如神经肌肉单元、神经分泌系统以及连接回路中的其他神经元。这催生了将脉冲神经元视为控制器的理念，其中脉冲即为控制信号。直接将瞬时事件用作控制输入（也称为“脉冲控制”）具有挑战性，因为它难以扩展到大型网络，且分析可处理性较低。因此，当前的脉冲控制通常依赖于对脉冲信号进行滤波以近似模拟控制。这最终意味着脉冲神经网络（SNNs）必须输出连续的控制信号，从而需要向下游系统持续输入能量。在此，我们绕开了基于速率表征的需求，提出了一种可扩展的方法，用于实现具有稀疏神经活动的任务特异性脉冲控制。为此，我们从最优控制理论和神经科学理论中汲取灵感，定义了一种脉冲规则：仅当脉冲能使动态系统更接近目标时才发放脉冲。基于这一原理，我们推导出SNN所需的连接性，并证明其能够成功控制线性系统。我们表明，对于物理受限的系统，预测控制是必要的，且控制信号最终会利用下游系统的被动动力学来达到目标。最后，我们证明了该控制方法可扩展到高维网络和系统。重要的是，在所有情况下，我们都保持了网络连接性、网络动力学和控制目标的闭式数学推导。这项工作推进了将SNNs视为受生物启发的控制器的理解，为真实神经元如何实施控制提供了见解，并促进了在神经形态硬件设计中的应用。