Learning Representations for Neural Network-Based Classification Using the Information Bottleneck Principle.

Area of Science:

• Machine Learning
• Deep Learning Theory
• Information Theory

Background:

• Deep neural networks (DNNs) are powerful tools for classification.
• The Information Bottleneck (IB) principle offers a theoretical framework for understanding representation learning in DNNs.
• Minimizing the IB functional is proposed as a method for training DNNs for classification.

Purpose of the Study:

• To investigate the theoretical challenges of training DNNs for classification by minimizing the IB functional.
• To identify limitations of the IB functional in capturing desirable properties of learned representations.
• To propose alternative approaches for effective DNN training and representation learning.

Main Methods:

• Theoretical analysis of the IB functional's properties in the context of deterministic and stochastic DNNs.
• Examination of the optimization landscape and gradient-based method applicability.
• Evaluation of the IB functional's invariance properties concerning classification-relevant features like robustness and simplicity.

Main Results:

• For deterministic DNNs, the IB functional is often ill-posed or not amenable to gradient-based optimization.
• The IB functional's invariance under bijections hinders its ability to enforce classification-specific representation properties.
• Stochastic DNNs or alternative cost functions partially resolve these optimization and representation issues.

Conclusions:

• The theoretical limitations of the IB functional suggest that recent successes in IB-based DNN training likely rely on modified approaches.
• The IB framework has inherent limitations for analyzing and training DNNs for classification.
• Designing direct regularizers on latent representations may be a more effective strategy than repairing the IB functional.