让脉冲神经网络在异步硬件中实现确定性输出，突破时间随机性限制。
Determinism in the Undetermined: Deterministic Output in Charge-Conserving Continuous-Time Neuromorphic Systems with Temporal Stochasticity
- 通过电荷守恒约束设计连续时间脉冲网络，确保输出仅依赖总输入电荷。
- 在无环网络中输出完全不受脉冲时序影响，实现严格确定性。
- 理论证明其等价于量化神经网络，适合追求高效确定计算的硬件设计者。
异步脉冲神经网络（SNN）在连续时间硬件中实现确定性计算面临根本挑战，源于固有的时间随机性。本文提出统一的连续时间框架，将电荷守恒定律与最小化神经元约束相结合，确保终端状态仅取决于总输入电荷，从而获得对时间随机性不变的唯一累积输出。理论上证明，在无环网络中该映射严格不随脉冲时序变化；而循环连接可能引入时序敏感性。进一步建立了此类电荷守恒SNN与量化人工神经网络之间的精确表示对应关系，无需近似误差地弥合静态深度学习与事件驱动动态之间的鸿沟。这些成果为设计兼具异步处理效率与算法确定性的连续时间类脑系统提供了严格的理论基础。
原文摘要 · Abstract (English)
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.
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