From LIF to QIF: Toward Differentiable Spiking Neurons for Scientific Machine Learning

• URL: http://arxiv.org/abs/2511.06614v1
• Date: Mon, 10 Nov 2025 01:47:17 GMT
• Title: From LIF to QIF: Toward Differentiable Spiking Neurons for Scientific Machine Learning
• Authors: Ruyin Wan, George Em Karniadakis, Panos Stinis,
• Abstract summary: We introduce and evaluate Quadratic Integrate-and-Fire (QIF) neurons as an alternative to the conventional Leaky Integrate-and-Fire (LIF) model.<n>QIF neurons exhibit smooth and differentiable spiking dynamics, enabling gradient-based training and stable optimization.<n>These results position the QIF neuron as a computational bridge between spiking and continuous-valued deep learning.
• Score: 4.745210824486511
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Spiking neural networks (SNNs) offer biologically inspired computation but remain underexplored for continuous regression tasks in scientific machine learning. In this work, we introduce and systematically evaluate Quadratic Integrate-and-Fire (QIF) neurons as an alternative to the conventional Leaky Integrate-and-Fire (LIF) model in both directly trained SNNs and ANN-to-SNN conversion frameworks. The QIF neuron exhibits smooth and differentiable spiking dynamics, enabling gradient-based training and stable optimization within architectures such as multilayer perceptrons (MLPs), Deep Operator Networks (DeepONets), and Physics-Informed Neural Networks (PINNs). Across benchmarks on function approximation, operator learning, and partial differential equation (PDE) solving, QIF-based networks yield smoother, more accurate, and more stable predictions than their LIF counterparts, which suffer from discontinuous time-step responses and jagged activation surfaces. These results position the QIF neuron as a computational bridge between spiking and continuous-valued deep learning, advancing the integration of neuroscience-inspired dynamics into physics-informed and operator-learning frameworks.

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