# Towards glass-box CNNs

arXiv: https://arxiv.org/abs/2101.10443 · HTML: https://mlsanity.com/paper/2101.10443/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 58 references that are in the map.
- First posted on arXiv 11 Jan 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Skin Lesion Analysis Toward Melanoma Detection 2018: A Challenge Hosted by the International Skin Imaging Collaboration (ISIC)](https://mlsanity.com/paper/1902.03368/) (2019)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Do Deep Nets Really Need to be Deep?](https://mlsanity.com/paper/1312.6184/) (2013)
- [Rotation Equivariant CNNs for Digital Pathology](https://mlsanity.com/paper/1806.03962/) (2018)
- [A Survey on Explainable Artificial Intelligence (XAI): Towards Medical XAI](https://mlsanity.com/paper/1907.07374/) (2019)
- [Understanding Deep Image Representations by Inverting Them](https://mlsanity.com/paper/1412.0035/) (2014)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [On Translation Invariance in CNNs: Convolutional Layers can Exploit Absolute Spatial Location](https://mlsanity.com/paper/2003.07064/) (2020)
- [Understanding Deep Convolutional Networks](https://mlsanity.com/paper/1601.04920/) (2016)
- [Human-Like Autonomous Car-Following Model with Deep Reinforcement Learning](https://mlsanity.com/paper/1901.00569/) (2019)
- [Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learning](https://mlsanity.com/paper/1812.11832/) (2018)
- [Understanding Intra-Class Knowledge Inside CNN](https://mlsanity.com/paper/1507.02379/) (2015)
- [Deep Rotation Equivariant Network](https://mlsanity.com/paper/1705.08623/) (2017)
- [The Plant Pathology 2020 challenge dataset to classify foliar disease of apples](https://mlsanity.com/paper/2004.11958/) (2020)

## Built on by (most cited first, 1 of 1)

- [SWAN: Self-supervised Wavelet Neural Network for Hyperspectral Image Unmixing](https://mlsanity.com/paper/2510.22607/) (2025)

## Abstract (arXiv)

With the substantial performance of neural networks in sensitive fields increases the need for interpretable deep learning models. Major challenge is to uncover the multiscale and distributed representation hidden inside the basket mappings of the deep neural networks. Researchers have been trying to comprehend it through visual analysis of features, mathematical structures, or other data-driven approaches. Here, we work on implementation invariances of CNN-based representations and present an analytical binary prototype that provides useful insights for large scale real-life applications. We begin by unfolding conventional CNN and then repack it with a more transparent representation. Inspired by the attainment of neural networks, we choose to present our findings as a three-layer model. First is a representation layer that encompasses both the class information (group invariant) and symmetric transformations (group equivariant) of input images. Through these transformations, we decrease intra-class distance and increase the inter-class distance. It is then passed through a dimension reduction layer followed by a classifier. The proposed representation is compared with the equivariance of AlexNet (CNN) internal representation for better dissemination of simulation results. We foresee following immediate advantages of this toy version: i) contributes pre-processing of data to increase the feature or class separability in large scale problems, ii) helps designing neural architecture to improve the classification performance in multi-class problems, and iii) helps building interpretable CNN through scalable functional blocks.