Learning Representations for Neural Network-Based Classification Using the Information Bottleneck Principle
This is a theoretical critique that challenges the applicability of the information bottleneck framework in deep learning, highlighting limitations for researchers and practitioners in neural network optimization.
The paper identifies fundamental issues with using the information bottleneck principle to train deep neural networks for classification, showing that the optimization problem is ill-posed or non-differentiable for deterministic networks and fails to capture desirable properties like robustness, and suggests that reported successes rely on workarounds such as stochastic networks or alternative cost functions.
In this theory paper, we investigate training deep neural networks (DNNs) for classification via minimizing the information bottleneck (IB) functional. We show that the resulting optimization problem suffers from two severe issues: First, for deterministic DNNs, either the IB functional is infinite for almost all values of network parameters, making the optimization problem ill-posed, or it is piecewise constant, hence not admitting gradient-based optimization methods. Second, the invariance of the IB functional under bijections prevents it from capturing properties of the learned representation that are desirable for classification, such as robustness and simplicity. We argue that these issues are partly resolved for stochastic DNNs, DNNs that include a (hard or soft) decision rule, or by replacing the IB functional with related, but more well-behaved cost functions. We conclude that recent successes reported about training DNNs using the IB framework must be attributed to such solutions. As a side effect, our results indicate limitations of the IB framework for the analysis of DNNs. We also note that rather than trying to repair the inherent problems in the IB functional, a better approach may be to design regularizers on latent representation enforcing the desired properties directly.