Determinism in the Undetermined: Deterministic Output in Charge-Conserving Continuous-Time Neuromorphic Systems with Temporal Stochasticity

TL;DR

This paper introduces a continuous-time framework for charge-conserving spiking neural networks that guarantees deterministic outputs despite inherent temporal stochasticity, bridging neuromorphic hardware and deep learning.

Contribution

It develops a unified charge-conserving model for SNNs, proves invariance to spike timing in acyclic networks, and establishes a correspondence with quantized neural networks.

Findings

Terminal state depends only on input charge

Invariance to spike timing in acyclic networks

Exact mapping to quantized neural networks

Abstract

Achieving deterministic computation results in asynchronous neuromorphic systems remains a fundamental challenge due to the inherent temporal stochasticity of continuous-time hardware. To address this, we develop a unified continuous-time framework for spiking neural networks (SNNs) that couples the Law of Charge Conservation with minimal neuron-level constraints. This integration ensures that the terminal state depends solely on the aggregate input charge, providing a unique cumulated output invariant to temporal stochasticity. We prove that this mapping is strictly invariant to spike timing in acyclic networks, whereas recurrent connectivity can introduce temporal sensitivity. Furthermore, we establish an exact representational correspondence between these charge-conserving SNNs and quantized artificial neural networks, bridging the gap between static deep learning and event-driven dynamics without approximation errors. These results establish a rigorous theoretical basis for designing continuous-time neuromorphic systems that harness the efficiency of asynchronous processing while maintaining algorithmic determinism.