Training Normalizing Flows with the Information Bottleneck for Competitive Generative Classification

TL;DR

This paper introduces IB-INNs, a novel approach that applies the Information Bottleneck to train invertible neural networks for generative classification, balancing generative quality and classification accuracy.

Contribution

It develops the theory of IB-INNs, enabling controlled information loss in invertible networks to improve generative classifiers without sacrificing their generative capabilities.

Findings

Improved uncertainty quantification and out-of-distribution detection.

Trade-off parameter controls balance between generative ability and classification accuracy.

Empirical results show favorable uncertainty estimates compared to traditional classifiers.

Abstract

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.