# Training Normalizing Flows with the Information Bottleneck for Competitive Generative Classification

arXiv: https://arxiv.org/abs/2001.06448 · HTML: https://mlsanity.com/paper/2001.06448/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2020.

## Built on by (most cited first, 3 of 3)

- [Conditional Invertible Neural Networks for Diverse Image-to-Image Translation](https://mlsanity.com/paper/2105.02104/) (2021)
- [Bounding generalization error with input compression: An empirical study with infinite-width networks](https://mlsanity.com/paper/2207.09408/) (2022)
- [Maximum Likelihood on the Joint (Data, Condition) Distribution for Solving Ill-Posed Problems with Conditional Flow Models](https://mlsanity.com/paper/2208.11782/) (2022)

## Abstract (arXiv)

The Information Bottleneck (IB) objective uses information theory to formulate a task-performance versus robustness trade-off. It has been successfully applied in the standard discriminative classification setting. We pose the question whether the IB can also be used to train generative likelihood models such as normalizing flows. Since normalizing flows use invertible network architectures (INNs), they are information-preserving by construction. This seems contradictory to the idea of a bottleneck. In this work, firstly, we develop the theory and methodology of IB-INNs, a class of conditional normalizing flows where INNs are trained using the IB objective: Introducing a small amount of em controlled information loss allows for an asymptotically exact formulation of the IB, while keeping the INN's generative capabilities intact. Secondly, we investigate the properties of these models experimentally, specifically used as generative classifiers. This model class offers advantages such as improved uncertainty quantification and out-of-distribution detection, but traditional generative classifier solutions suffer considerably in classification accuracy. We find the trade-off parameter in the IB controls a mix of generative capabilities and accuracy close to standard classifiers. Empirically, our uncertainty estimates in this mixed regime compare favourably to conventional generative and discriminative classifiers.