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

arXiv: https://arxiv.org/abs/2511.06614 · HTML: https://mlsanity.com/paper/2511.06614/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2025.

## Built on by (most cited first, 2 of 2)

- [Quadratic integrate-and-fire neurons exhibit less fragmented loss landscapes and outperform leaky integrate-and-fire neurons in spike-based gradient descent](https://mlsanity.com/paper/2606.03935/) (2026)
- [SPINONet: Scalable Spiking Physics-informed Neural Operator for Computational Mechanics Applications](https://mlsanity.com/paper/2603.21674/) (2026)

## Abstract (arXiv)

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.