Spiking neurons as predictive controllers of linear systems

2025-07-22

AI Summary

This work addresses the high energy consumption and poor scalability in spiking neural control arising from conventional sparse-spike-to-analog signal conversion. We propose a novel predictive control framework for linear systems operating directly in the spike domain, bypassing traditional filtering-based decoding. Leveraging optimal control theory and spike-timing-dependent plasticity (STDP), we derive a closed-form analytical spiking control architecture: an event-driven firing rule is designed, and the network’s connectivity structure and dynamical equations are rigorously formulated. Spikes are generated only when the system state deviates from the target, ensuring biological plausibility, computational optimality, and ultra-low power operation. Experiments demonstrate precise control of high-dimensional networks and multivariable linear systems, achieving substantial energy reduction. Our approach validates the feasibility and scalability of direct spike-domain control.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Intelligent Robots: Behavior Learning & Control
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

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.

Problem

• Develop scalable spiking control for linear systems
• Enable sparse neural activity in predictive control
• Derive closed-form connectivity for SNN controllers

Innovation

• Spiking neurons as predictive controllers
• Task-specific spiking control with sparse activity
• Closed-form derivation of network connectivity