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

2026-03-16

AI Summary

This work addresses the challenge of achieving deterministic computation in asynchronous neuromorphic systems, where timing stochasticity inherent in continuous-time hardware typically undermines reproducibility. The authors propose a unified continuous-time spiking neural network (SNN) framework grounded in the principle of charge conservation and minimal neuron constraints. They rigorously prove, for the first time, that in acyclic architectures, the network output depends exclusively on the total input charge and is entirely invariant to spike timing, thereby achieving complete immunity to temporal randomness. Furthermore, the framework establishes an exact, approximation-free correspondence between charge-conserving SNNs and quantized artificial neural networks, offering a theoretical foundation for integrating event-driven dynamic systems with static deep learning while preserving algorithmic determinism and enabling efficient asynchronous processing.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Deep Neural Architectures and Foundation Models
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Social Networks and Social Media: Computational social science

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.

Problem

• determinism
• temporal stochasticity
• neuromorphic systems
• spiking neural networks
• charge conservation

Innovation

• charge conservation
• deterministic neuromorphic computing
• temporal stochasticity
• spiking neural networks
• quantized ANNs