# Probabilistic Modeling: Proving the Lottery Ticket Hypothesis in Spiking Neural Network

arXiv: https://arxiv.org/abs/2305.12148 · HTML: https://mlsanity.com/paper/2305.12148/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 51 references that are in the map.
- First posted on arXiv 20 May 2023.

## Builds on (most cited first, 30 of 33)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [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)
- [The Lottery Ticket Hypothesis for Pre-trained BERT Networks](https://mlsanity.com/paper/2007.12223/) (2020)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)
- [Dynamic Network Surgery for Efficient DNNs](https://mlsanity.com/paper/1608.04493/) (2016)
- [Deconstructing Lottery Tickets: Zeros, Signs, and the Supermask](https://mlsanity.com/paper/1905.01067/) (2019)
- [Proving the Lottery Ticket Hypothesis: Pruning is All You Need](https://mlsanity.com/paper/2002.00585/) (2020)
- [Long short-term memory and learning-to-learn in networks of spiking neurons](https://mlsanity.com/paper/1803.09574/) (2018)
- [Drawing Early-Bird Tickets: Towards More Efficient Training of Deep Networks](https://mlsanity.com/paper/1909.11957/) (2019)
- [Attention Spiking Neural Networks](https://mlsanity.com/paper/2209.13929/) (2022)
- [Temporal-wise Attention Spiking Neural Networks for Event Streams Classification](https://mlsanity.com/paper/2107.11711/) (2021)
- [Optimal Lottery Tickets via SubsetSum: Logarithmic Over-Parameterization is Sufficient](https://mlsanity.com/paper/2006.07990/) (2020)
- [Pruning from Scratch](https://mlsanity.com/paper/1909.12579/) (2019)
- [Logarithmic Pruning is All You Need](https://mlsanity.com/paper/2006.12156/) (2020)
- [HIRE-SNN: Harnessing the Inherent Robustness of Energy-Efficient Deep Spiking Neural Networks by Training with Crafted Input Noise](https://mlsanity.com/paper/2110.11417/) (2021)
- [GLIF: A Unified Gated Leaky Integrate-and-Fire Neuron for Spiking Neural Networks](https://mlsanity.com/paper/2210.13768/) (2022)
- [STDP Based Pruning of Connections and Weight Quantization in Spiking Neural Networks for Energy Efficient Recognition](https://mlsanity.com/paper/1710.04734/) (2017)
- [Comprehensive SNN Compression Using ADMM Optimization and Activity Regularization](https://mlsanity.com/paper/1911.00822/) (2019)
- [Pruning of Deep Spiking Neural Networks through Gradient Rewiring](https://mlsanity.com/paper/2105.04916/) (2021)
- [The Lottery Ticket Hypothesis for Object Recognition](https://mlsanity.com/paper/2012.04643/) (2020)
- [A Long Short-Term Memory for AI Applications in Spike-based Neuromorphic Hardware](https://mlsanity.com/paper/2107.03992/) (2021)
- [Exploring Lottery Ticket Hypothesis in Spiking Neural Networks](https://mlsanity.com/paper/2207.01382/) (2022)
- [Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines](https://mlsanity.com/paper/1511.04484/) (2015)
- [Network Plasticity as Bayesian Inference](https://mlsanity.com/paper/1504.05143/) (2015)

## Built on by (most cited first, 3 of 3)

- [Spike-driven Transformer](https://mlsanity.com/paper/2307.01694/) (2023)
- [Gaining the Sparse Rewards by Exploring Lottery Tickets in Spiking Neural Network](https://mlsanity.com/paper/2309.13302/) (2023)
- [Artificial Structure Function Search: Preserving Artificial Functional Connectivity for Structured Pruning](https://mlsanity.com/paper/2609.24401/) (2026)

## Abstract (arXiv)

The Lottery Ticket Hypothesis (LTH) states that a randomly-initialized large neural network contains a small sub-network (i.e., winning tickets) which, when trained in isolation, can achieve comparable performance to the large network. LTH opens up a new path for network pruning. Existing proofs of LTH in Artificial Neural Networks (ANNs) are based on continuous activation functions, such as ReLU, which satisfying the Lipschitz condition. However, these theoretical methods are not applicable in Spiking Neural Networks (SNNs) due to the discontinuous of spiking function. We argue that it is possible to extend the scope of LTH by eliminating Lipschitz condition. Specifically, we propose a novel probabilistic modeling approach for spiking neurons with complicated spatio-temporal dynamics. Then we theoretically and experimentally prove that LTH holds in SNNs. According to our theorem, we conclude that pruning directly in accordance with the weight size in existing SNNs is clearly not optimal. We further design a new criterion for pruning based on our theory, which achieves better pruning results than baseline.