Stimulus-Voltage-Based Prediction of Action Potential Onset Timing: Classical vs. Quantum-Inspired Approaches

TL;DR

The paper tackles the problem of accurately predicting action potential onset timing $t$, which is crucial for neural coding of rapid danger signals. It introduces two approaches beyond the classical LIF: a Stimulus-Accelerated LIF (SA-LIF) and a Quantum-Inspired LIF (QI-LIF) that treats onset as a probabilistic event modeled by a Gaussian $G(t; t_0, \sigma)$, with a stimulus-dependent time constant $\tau_{eff}$. Analytic derivations yield $t_{LIF} = -\tau_m \ln\left(1 - \frac{V_{th}}{V_\infty}\right)$ for the classical case and $t_{QLIF} = -\frac{\tau_m}{1 + \alpha S} \ln\left(1 - \frac{V_{th}(1 + \alpha S)}{I_{inj} R_m}\right)$ for the SA-LIF, while the QI-LIF expresses timing uncertainty via the Gaussian and allows superposition across inputs. Empirical-style benchmarking on synthetic data shows SA-LIF struggles with large errors (including over 1000% at low stimuli), whereas the QI-LIF achieves substantially lower relative errors (mostly <30%) by incorporating timing variability and rapid depolarization under strong stimuli. Overall, the work demonstrates a promising quantum-inspired framework for more accurate neural timing predictions with potential ramifications for neuromorphic hardware and quantum-inspired neural computation.

Abstract

Accurate modeling of neuronal action potential (AP) onset timing is crucial for understanding neural coding of danger signals. Traditional leaky integrate-and-fire (LIF) models, while widely used, exhibit high relative error in predicting AP onset latency, especially under strong or rapidly changing stimuli. Inspired by recent experimental findings and quantum theory, we present a quantum-inspired leaky integrate-and-fire (QI-LIF) model that treats AP onset as a probabilistic event, represented by a Gaussian wave packet in time. This approach captures the biological variability and uncertainty inherent in neuronal firing. We systematically compare the relative error of AP onset predictions between the classical LIF and QI-LIF models using synthetic data from hippocampal and sensory neurons subjected to varying stimulus amplitudes. Our results demonstrate that the QI-LIF model significantly reduces prediction error, particularly for high-intensity stimuli, aligning closely with observed biological responses. This work highlights the potential of quantum-inspired computational frameworks in advancing the accuracy of neural modeling and has implications for quantum engineering approaches to brain-inspired computing.

Figures (2)

• Figure 1: AP onset time for LIF vs. QI-LIF models compared to experimental data.
• Figure 2: Predicted AP onset times for the experimental (saturating), SA-LIF, and QI models as a function of spike count. The QI model tracks the experimental curve much more closely across the entire range.