Statistical mechanics of lossy compression using multilayer perceptrons

Area of Science:

• Information Theory
• Statistical Mechanics
• Machine Learning

Background:

• Lossy compression aims to reduce data size while minimizing information loss.
• Multilayer perceptrons are a type of artificial neural network used in machine learning.
• Statistical mechanics provides tools to analyze systems with many degrees of freedom.

Purpose of the Study:

• To apply statistical mechanics principles to analyze lossy compression using multilayer perceptrons.
• To investigate the performance of treelike committee machines and parity machines for compressing Boolean messages.
• To derive theoretical limits for compression performance.

Main Methods:

• Utilizing treelike committee machines (committee trees) and treelike parity machines (parity trees).
• Employing monotonic transfer functions within these neural network architectures.
• Applying concepts from statistical mechanics to analyze the compression process.

Main Results:

• For committee trees, increasing hidden units (K) reduces achievable distortion but does not reach the theoretical Shannon bound.
• For parity trees with K>=2 hidden units, the rate distortion function is derived.
• The derived rate distortion function for parity trees is obtained at infinite code length.

Conclusions:

• Multilayer perceptrons, analyzed via statistical mechanics, offer insights into lossy compression limits.
• Committee trees show performance improvements with scale but have inherent limitations compared to theoretical bounds.
• Parity trees provide a framework for deriving the fundamental rate distortion function in this context.