Learning Optimal Representations with the Decodable Information Bottleneck
This addresses the challenge of improving generalization in machine learning for practitioners by providing a decoder-aware framework, though it appears incremental as it builds on the Information Bottleneck.
The paper tackles the problem of finding optimal representations for supervised learning by proposing the Decodable Information Bottleneck (DIB), which focuses on generalization rather than compression, resulting in representations that optimize expected test performance and can be used to enforce a small generalization gap and predict neural network generalization ability.
We address the question of characterizing and finding optimal representations for supervised learning. Traditionally, this question has been tackled using the Information Bottleneck, which compresses the inputs while retaining information about the targets, in a decoder-agnostic fashion. In machine learning, however, our goal is not compression but rather generalization, which is intimately linked to the predictive family or decoder of interest (e.g. linear classifier). We propose the Decodable Information Bottleneck (DIB) that considers information retention and compression from the perspective of the desired predictive family. As a result, DIB gives rise to representations that are optimal in terms of expected test performance and can be estimated with guarantees. Empirically, we show that the framework can be used to enforce a small generalization gap on downstream classifiers and to predict the generalization ability of neural networks.