# Discretized Quadratic Integrate-and-Fire Neuron Model for Deep Spiking Neural Networks

arXiv: https://arxiv.org/abs/2510.05168 · HTML: https://mlsanity.com/paper/2510.05168/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Builds on (most cited first, 13 of 13)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Spatio-Temporal Backpropagation for Training High-performance Spiking Neural Networks](https://mlsanity.com/paper/1706.02609/) (2017)
- [Incorporating Learnable Membrane Time Constant to Enhance Learning of Spiking Neural Networks](https://mlsanity.com/paper/2007.05785/) (2020)
- [Going Deeper With Directly-Trained Larger Spiking Neural Networks](https://mlsanity.com/paper/2011.05280/) (2020)
- [Temporal Efficient Training of Spiking Neural Network via Gradient Re-weighting](https://mlsanity.com/paper/2202.11946/) (2022)
- [Deep Directly-Trained Spiking Neural Networks for Object Detection](https://mlsanity.com/paper/2307.11411/) (2023)
- [GLIF: A Unified Gated Leaky Integrate-and-Fire Neuron for Spiking Neural Networks](https://mlsanity.com/paper/2210.13768/) (2022)
- [Event-Based Backpropagation can compute Exact Gradients for Spiking Neural Networks](https://mlsanity.com/paper/2009.08378/) (2020)
- [Ternary Spike: Learning Ternary Spikes for Spiking Neural Networks](https://mlsanity.com/paper/2312.06372/) (2023)
- [Membrane Potential Batch Normalization for Spiking Neural Networks](https://mlsanity.com/paper/2308.08359/) (2023)
- [Take A Shortcut Back: Mitigating the Gradient Vanishing for Training Spiking Neural Networks](https://mlsanity.com/paper/2401.04486/) (2024)
- [Ultra-low-power Image Classification on Neuromorphic Hardware](https://mlsanity.com/paper/2309.16795/) (2023)
- [Izhikevich-Inspired Optoelectronic Neurons with Excitatory and Inhibitory Inputs for Energy-Efficient Photonic Spiking Neural Networks](https://mlsanity.com/paper/2105.02809/) (2021)

## Abstract (arXiv)

Spiking Neural Networks (SNNs) have emerged as energy-efficient alternatives to traditional artificial neural networks, leveraging asynchronous and biologically inspired neuron dynamics. Among existing neuron models, the Leaky Integrate-and-Fire (LIF) neuron has become widely adopted in deep SNNs due to its simplicity and computational efficiency. However, this efficiency comes at the expense of expressiveness, as LIF dynamics are constrained to linear decay at each timestep. In contrast, more complex models, such as the Quadratic Integrate-and-Fire (QIF) neuron, exhibit richer, nonlinear dynamics but have seen limited adoption due to their training instability. On that note, we propose the first discretization of the QIF neuron model tailored for high-performance deep spiking neural networks and provide an in-depth analysis of its dynamics. To ensure training stability, we derive an analytical formulation for surrogate gradient windows directly from our discretizations' parameter set, minimizing gradient mismatch. We evaluate our method on CIFAR-10, CIFAR-100, ImageNet, and CIFAR-10 DVS, demonstrating its ability to outperform state-of-the-art LIF-based methods. These results establish our discretization of the QIF neuron as a compelling alternative to LIF neurons for deep SNNs, combining richer dynamics with practical scalability.