Recognizable Information Bottleneck
This work addresses the challenge of practical generalization guarantees in machine learning for researchers and practitioners, though it is incremental as it builds on existing bounds and methods.
The paper tackles the problem of guaranteeing generalization in Information Bottleneck methods by connecting representation recognizability to a functional conditional mutual information bound, proposing a Recognizable Information Bottleneck (RIB) that regularizes recognizability through density ratio matching. Experiments on multiple datasets show the method effectively regularizes models and estimates generalization gaps.
Information Bottlenecks (IBs) learn representations that generalize to unseen data by information compression. However, existing IBs are practically unable to guarantee generalization in real-world scenarios due to the vacuous generalization bound. The recent PAC-Bayes IB uses information complexity instead of information compression to establish a connection with the mutual information generalization bound. However, it requires the computation of expensive second-order curvature, which hinders its practical application. In this paper, we establish the connection between the recognizability of representations and the recent functional conditional mutual information (f-CMI) generalization bound, which is significantly easier to estimate. On this basis we propose a Recognizable Information Bottleneck (RIB) which regularizes the recognizability of representations through a recognizability critic optimized by density ratio matching under the Bregman divergence. Extensive experiments on several commonly used datasets demonstrate the effectiveness of the proposed method in regularizing the model and estimating the generalization gap.