# The SVD of Convolutional Weights: A CNN Interpretability Framework

arXiv: https://arxiv.org/abs/2208.06894 · HTML: https://mlsanity.com/paper/2208.06894/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 14 Aug 2022.

## Builds on (most cited first, 21 of 21)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Understanding Deep Image Representations by Inverting Them](https://mlsanity.com/paper/1412.0035/) (2014)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning](https://mlsanity.com/paper/1810.01075/) (2018)
- [A mathematical theory of semantic development in deep neural networks](https://mlsanity.com/paper/1810.10531/) (2018)
- [Spectral Norm Regularization for Improving the Generalizability of Deep Learning](https://mlsanity.com/paper/1705.10941/) (2017)
- [Predicting trends in the quality of state-of-the-art neural networks without access to training or testing data](https://mlsanity.com/paper/2002.06716/) (2020)
- [Multifaceted Feature Visualization: Uncovering the Different Types of Features Learned By Each Neuron in Deep Neural Networks](https://mlsanity.com/paper/1602.03616/) (2016)
- [The Singular Values of Convolutional Layers](https://mlsanity.com/paper/1805.10408/) (2018)
- [Summit: Scaling Deep Learning Interpretability by Visualizing Activation and Attribution Summarizations](https://mlsanity.com/paper/1904.02323/) (2019)
- [Interpreting CNN Knowledge via an Explanatory Graph](https://mlsanity.com/paper/1708.01785/) (2017)
- [Heavy-Tailed Universality Predicts Trends in Test Accuracies for Very Large Pre-Trained Deep Neural Networks](https://mlsanity.com/paper/1901.08278/) (2019)
- [Understanding Intra-Class Knowledge Inside CNN](https://mlsanity.com/paper/1507.02379/) (2015)
- [Hypernetwork Science via High-Order Hypergraph Walks](https://mlsanity.com/paper/1906.11295/) (2019)
- [Singular Values for ReLU Layers](https://mlsanity.com/paper/1812.02566/) (2018)
- [FD-MobileNet: Improved MobileNet with a Fast Downsampling Strategy](https://mlsanity.com/paper/1802.03750/) (2018)

## Built on by (most cited first, 8 of 8)

- [Talking Heads: Understanding Inter-layer Communication in Transformer Language Models](https://mlsanity.com/paper/2406.09519/) (2024)
- [Approaching Deep Learning through the Spectral Dynamics of Weights](https://mlsanity.com/paper/2408.11804/) (2024)
- [Multi-Layer Confidence Scoring for Detection of Out-of-Distribution Samples, Adversarial Attacks, and In-Distribution Misclassifications](https://mlsanity.com/paper/2512.19472/) (2025)
- [LFA applied to CNNs: Efficient Singular Value Decomposition of Convolutional Mappings by Local Fourier Analysis](https://mlsanity.com/paper/2506.05617/) (2025)
- [Lightweight Cloud Masking Models for On-Board Inference in Hyperspectral Imaging](https://mlsanity.com/paper/2507.08052/) (2025)
- [Make it SING: Analyzing Semantic Invariants in Classifiers](https://mlsanity.com/paper/2603.14610/) (2026)
- [A Convolutional Layer Activation Dimensionality Reduction for Out-of-Distribution and Adversarial Attack Detection Methods](https://mlsanity.com/paper/2608.10203/) (2026)
- [From the Loss Landscape to Diverse Feature Learning in Neural Networks](https://mlsanity.com/paper/2608.28948/) (2026)

## Abstract (arXiv)

Deep neural networks used for image classification often use convolutional filters to extract distinguishing features before passing them to a linear classifier. Most interpretability literature focuses on providing semantic meaning to convolutional filters to explain a model's reasoning process and confirm its use of relevant information from the input domain. Fully connected layers can be studied by decomposing their weight matrices using a singular value decomposition, in effect studying the correlations between the rows in each matrix to discover the dynamics of the map. In this work we define a singular value decomposition for the weight tensor of a convolutional layer, which provides an analogous understanding of the correlations between filters, exposing the dynamics of the convolutional map. We validate our definition using recent results in random matrix theory. By applying the decomposition across the linear layers of an image classification network we suggest a framework against which interpretability methods might be applied using hypergraphs to model class separation. Rather than looking to the activations to explain the network, we use the singular vectors with the greatest corresponding singular values for each linear layer to identify those features most important to the network. We illustrate our approach with examples and introduce the DeepDataProfiler library, the analysis tool used for this study.