# Making Sense of CNNs: Interpreting Deep Representations & Their Invariances with INNs

arXiv: https://arxiv.org/abs/2008.01777 · HTML: https://mlsanity.com/paper/2008.01777/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2020.

## Built on by (most cited first, 10 of 10)

- [High Fidelity Visualization of What Your Self-Supervised Representation Knows About](https://mlsanity.com/paper/2112.09164/) (2021)
- [ControlMat: A Controlled Generative Approach to Material Capture](https://mlsanity.com/paper/2309.01700/) (2023)
- [Stochastic Image-to-Video Synthesis using cINNs](https://mlsanity.com/paper/2105.04551/) (2021)
- [Generative Semantic Segmentation](https://mlsanity.com/paper/2303.11316/) (2023)
- [Diffeomorphic Counterfactuals with Generative Models](https://mlsanity.com/paper/2206.05075/) (2022)
- [Concept-Based Explanations in Computer Vision: Where Are We and Where Could We Go?](https://mlsanity.com/paper/2409.13456/) (2024)
- [Understanding Invariance via Feedforward Inversion of Discriminatively Trained Classifiers](https://mlsanity.com/paper/2103.07470/) (2021)
- [Explaining Deep Convolutional Neural Networks via Latent Visual-Semantic Filter Attention](https://mlsanity.com/paper/2204.04601/) (2022)
- [Knowledge distillation through geometry-aware representational alignment](https://mlsanity.com/paper/2509.25253/) (2025)
- [Show Me What You Don't Know: Efficient Sampling from Invariant Sets for Model Validation](https://mlsanity.com/paper/2603.21782/) (2026)

## Abstract (arXiv)

To tackle increasingly complex tasks, it has become an essential ability of neural networks to learn abstract representations. These task-specific representations and, particularly, the invariances they capture turn neural networks into black box models that lack interpretability. To open such a black box, it is, therefore, crucial to uncover the different semantic concepts a model has learned as well as those that it has learned to be invariant to. We present an approach based on INNs that (i) recovers the task-specific, learned invariances by disentangling the remaining factor of variation in the data and that (ii) invertibly transforms these recovered invariances combined with the model representation into an equally expressive one with accessible semantic concepts. As a consequence, neural network representations become understandable by providing the means to (i) expose their semantic meaning, (ii) semantically modify a representation, and (iii) visualize individual learned semantic concepts and invariances. Our invertible approach significantly extends the abilities to understand black box models by enabling post-hoc interpretations of state-of-the-art networks without compromising their performance. Our implementation is available at https://compvis.github.io/invariances/ .