# Inverting Supervised Representations with Autoregressive Neural Density Models

arXiv: https://arxiv.org/abs/1806.00400 · HTML: https://mlsanity.com/paper/1806.00400/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2018.

## Built on by (most cited first, 12 of 12)

- [To Compress or Not to Compress- Self-Supervised Learning and Information Theory: A Review](https://mlsanity.com/paper/2304.09355/) (2023)
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- [Plug & Play Attacks: Towards Robust and Flexible Model Inversion Attacks](https://mlsanity.com/paper/2201.12179/) (2022)
- [Farewell to Mutual Information: Variational Distillation for Cross-Modal Person Re-Identification](https://mlsanity.com/paper/2104.02862/) (2021)
- [Orchestra: Unsupervised Federated Learning via Globally Consistent Clustering](https://mlsanity.com/paper/2205.11506/) (2022)
- [Understanding Invariance via Feedforward Inversion of Discriminatively Trained Classifiers](https://mlsanity.com/paper/2103.07470/) (2021)
- [Model Inversion Attacks: A Survey of Approaches and Countermeasures](https://mlsanity.com/paper/2411.10023/) (2024)
- [Darker than Black-Box: Face Reconstruction from Similarity Queries](https://mlsanity.com/paper/2106.14290/) (2021)
- [Finding Meaningful Distributions of ML Black-boxes under Forensic Investigation](https://mlsanity.com/paper/2305.05869/) (2023)
- [On the Adversarial Inversion of Deep Biometric Representations](https://mlsanity.com/paper/2304.05561/) (2023)
- [Revealing Unintentional Information Leakage in Low-Dimensional Facial Portrait Representations](https://mlsanity.com/paper/2503.09306/) (2025)
- [From Preimage Search To Source-Grounded Feature Inversion](https://mlsanity.com/paper/2607.12526/) (2026)

## Abstract (arXiv)

We present a method for feature interpretation that makes use of recent advances in autoregressive density estimation models to invert model representations. We train generative inversion models to express a distribution over input features conditioned on intermediate model representations. Insights into the invariances learned by supervised models can be gained by viewing samples from these inversion models. In addition, we can use these inversion models to estimate the mutual information between a model's inputs and its intermediate representations, thus quantifying the amount of information preserved by the network at different stages. Using this method we examine the types of information preserved at different layers of convolutional neural networks, and explore the invariances induced by different architectural choices. Finally we show that the mutual information between inputs and network layers decreases over the course of training, supporting recent work by Shwartz-Ziv and Tishby (2017) on the information bottleneck theory of deep learning.