# Graph-Based Similarity of Neural Network Representations

arXiv: https://arxiv.org/abs/2111.11165 · HTML: https://mlsanity.com/paper/2111.11165/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 82 references that are in the map.
- First posted on arXiv 22 Nov 2021.

## Builds on (most cited first, 30 of 52)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Do Vision Transformers See Like Convolutional Neural Networks?](https://mlsanity.com/paper/2108.08810/) (2021)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Threat of Adversarial Attacks on Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/1801.00553/) (2018)
- [Understanding Deep Image Representations by Inverting Them](https://mlsanity.com/paper/1412.0035/) (2014)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [Opportunities and Challenges in Explainable Artificial Intelligence (XAI): A Survey](https://mlsanity.com/paper/2006.11371/) (2020)

## Built on by (most cited first, 7 of 7)

- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [A Generic Layer Pruning Method for Signal Modulation Recognition Deep Learning Models](https://mlsanity.com/paper/2406.07929/) (2024)
- [How to Determine the Most Powerful Pre-trained Language Model without Brute Force Fine-tuning? An Empirical Survey](https://mlsanity.com/paper/2312.04775/) (2023)
- [Investigating the Effects of Fairness Interventions Using Pointwise Representational Similarity](https://mlsanity.com/paper/2305.19294/) (2023)
- [Normalized Space Alignment: A Versatile Metric for Representation Analysis](https://mlsanity.com/paper/2411.04512/) (2024)
- [Multi-Modal Machine Learning Framework for Predicting Early Recurrence of Brain Tumors Using MRI and Clinical Biomarkers](https://mlsanity.com/paper/2509.01161/) (2025)
- [A Multimodal Deep Learning Framework for Early Diagnosis of Liver Cancer via Optimized BiLSTM-AM-VMD Architecture](https://mlsanity.com/paper/2509.01164/) (2025)

## Abstract (arXiv)

Understanding the black-box representations in Deep Neural Networks (DNN) is an essential problem in deep learning. In this work, we propose Graph-Based Similarity (GBS) to measure the similarity of layer features. Contrary to previous works that compute the similarity directly on the feature maps, GBS measures the correlation based on the graph constructed with hidden layer outputs. By treating each input sample as a node and the corresponding layer output similarity as edges, we construct the graph of DNN representations for each layer. The similarity between graphs of layers identifies the correspondences between representations of models trained in different datasets and initializations. We demonstrate and prove the invariance property of GBS, including invariance to orthogonal transformation and invariance to isotropic scaling, and compare GBS with CKA. GBS shows state-of-the-art performance in reflecting the similarity and provides insights on explaining the adversarial sample behavior on the hidden layer space.