# Uncovering the Representation of Spiking Neural Networks Trained with Surrogate Gradient

arXiv: https://arxiv.org/abs/2304.13098 · HTML: https://mlsanity.com/paper/2304.13098/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 64 references that are in the map.
- First posted on arXiv 25 Apr 2023.

## Builds on (most cited first, 30 of 40)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Do Vision Transformers See Like Convolutional Neural Networks?](https://mlsanity.com/paper/2108.08810/) (2021)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [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)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [Converting Static Image Datasets to Spiking Neuromorphic Datasets Using Saccades](https://mlsanity.com/paper/1507.07629/) (2015)
- [Going Deeper With Directly-Trained Larger Spiking Neural Networks](https://mlsanity.com/paper/2011.05280/) (2020)
- [Deep Learning in Spiking Neural Networks](https://mlsanity.com/paper/1804.08150/) (2018)
- [Going Deeper in Spiking Neural Networks: VGG and Residual Architectures](https://mlsanity.com/paper/1802.02627/) (2018)
- [Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth](https://mlsanity.com/paper/2010.15327/) (2020)
- [Direct Training for Spiking Neural Networks: Faster, Larger, Better](https://mlsanity.com/paper/1809.05793/) (2018)
- [Convergent Learning: Do different neural networks learn the same representations?](https://mlsanity.com/paper/1511.07543/) (2015)
- [Temporal Efficient Training of Spiking Neural Network via Gradient Re-weighting](https://mlsanity.com/paper/2202.11946/) (2022)
- [Long short-term memory and learning-to-learn in networks of spiking neurons](https://mlsanity.com/paper/1803.09574/) (2018)
- [RMP-SNN: Residual Membrane Potential Neuron for Enabling Deeper High-Accuracy and Low-Latency Spiking Neural Network](https://mlsanity.com/paper/2003.01811/) (2020)
- [Optimal Conversion of Conventional Artificial Neural Networks to Spiking Neural Networks](https://mlsanity.com/paper/2103.00476/) (2021)
- [A Free Lunch From ANN: Towards Efficient, Accurate Spiking Neural Networks Calibration](https://mlsanity.com/paper/2106.06984/) (2021)
- [Temporal Spike Sequence Learning via Backpropagation for Deep Spiking Neural Networks](https://mlsanity.com/paper/2002.10085/) (2020)
- [Defensive Quantization: When Efficiency Meets Robustness](https://mlsanity.com/paper/1904.08444/) (2019)
- [Revisiting Batch Normalization for Training Low-latency Deep Spiking Neural Networks from Scratch](https://mlsanity.com/paper/2010.01729/) (2020)
- [Supervised learning based on temporal coding in spiking neural networks](https://mlsanity.com/paper/1606.08165/) (2016)
- [DIET-SNN: Direct Input Encoding With Leakage and Threshold Optimization in Deep Spiking Neural Networks](https://mlsanity.com/paper/2008.03658/) (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)

## Built on by (most cited first, 11 of 11)

- [Differential Coding for Training-Free ANN-to-SNN Conversion](https://mlsanity.com/paper/2503.00301/) (2025)
- [Advancing Training Efficiency of Deep Spiking Neural Networks through Rate-based Backpropagation](https://mlsanity.com/paper/2410.11488/) (2024)
- [Adversarially Robust Spiking Neural Networks Through Conversion](https://mlsanity.com/paper/2311.09266/) (2023)
- [Efficient ANN-Guided Distillation: Aligning Rate-based Features of Spiking Neural Networks through Hybrid Block-wise Replacement](https://mlsanity.com/paper/2503.16572/) (2025)
- [Topological Representations of Heterogeneous Learning Dynamics of Recurrent Spiking Neural Networks](https://mlsanity.com/paper/2403.12462/) (2024)
- [ReSpike: Residual Frames-based Hybrid Spiking Neural Networks for Efficient Action Recognition](https://mlsanity.com/paper/2409.01564/) (2024)
- [Fast gradient-free activation maximization for neurons in spiking neural networks](https://mlsanity.com/paper/2401.10748/) (2023)
- [Benchmarking Spiking Neural Network Learning Methods with Varying Locality](https://mlsanity.com/paper/2402.01782/) (2024)
- [Network Representation Learning for Biophysical Neural Network Analysis](https://mlsanity.com/paper/2410.11503/) (2024)
- [Random Feature Spiking Neural Networks](https://mlsanity.com/paper/2510.01012/) (2025)
- [Enhanced Self-Distillation Framework for Efficient Spiking Neural Network Training](https://mlsanity.com/paper/2510.06254/) (2025)

## Abstract (arXiv)

Spiking Neural Networks (SNNs) are recognized as the candidate for the next-generation neural networks due to their bio-plausibility and energy efficiency. Recently, researchers have demonstrated that SNNs are able to achieve nearly state-of-the-art performance in image recognition tasks using surrogate gradient training. However, some essential questions exist pertaining to SNNs that are little studied: Do SNNs trained with surrogate gradient learn different representations from traditional Artificial Neural Networks (ANNs)? Does the time dimension in SNNs provide unique representation power? In this paper, we aim to answer these questions by conducting a representation similarity analysis between SNNs and ANNs using Centered Kernel Alignment (CKA). We start by analyzing the spatial dimension of the networks, including both the width and the depth. Furthermore, our analysis of residual connections shows that SNNs learn a periodic pattern, which rectifies the representations in SNNs to be ANN-like. We additionally investigate the effect of the time dimension on SNN representation, finding that deeper layers encourage more dynamics along the time dimension. We also investigate the impact of input data such as event-stream data and adversarial attacks. Our work uncovers a host of new findings of representations in SNNs. We hope this work will inspire future research to fully comprehend the representation power of SNNs. Code is released at https://github.com/Intelligent-Computing-Lab-Yale/SNNCKA.