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

arXiv: https://arxiv.org/abs/2603.15987 · HTML: https://mlsanity.com/paper/2603.15987/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 31 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 6 of 6)

- [Event-based Vision: A Survey](https://mlsanity.com/paper/1904.08405/) (2019)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Deep Learning in Spiking Neural Networks](https://mlsanity.com/paper/1804.08150/) (2018)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Going Deeper in Spiking Neural Networks: VGG and Residual Architectures](https://mlsanity.com/paper/1802.02627/) (2018)
- [Supervised learning based on temporal coding in spiking neural networks](https://mlsanity.com/paper/1606.08165/) (2016)

## Abstract (arXiv)

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.