Fluctuation-dissipation-type theorem in stochastic linear learning.

Area of Science:

• Theoretical Physics
• Machine Learning
• Statistical Mechanics

Background:

• The fluctuation-dissipation theorem (FDT) connects system fluctuations to dissipation.
• Linear learning dynamics involve updating a matrix based on input-output mapping.
• Stochastic gradient descent introduces randomness, similar to Langevin dynamics.

Purpose of the Study:

• To derive a generalized fluctuation-dissipation theorem (FDT) for stochastic linear learning dynamics.
• To validate the derived FDT in practical machine learning scenarios.

Main Methods:

• Derivation of a generalized FDT based on the principles of statistical mechanics.
• Application and verification of the derived FDT on standard machine learning datasets.
• Utilized stochastic gradient descent as a model for learning dynamics.

Main Results:

• Successfully derived a generalized FDT applicable to stochastic linear learning.
• Empirical validation of the generalized FDT on MNIST, CIFAR-10, and EMNIST datasets.
• Demonstrated the close analogy between stochastic linear learning and Langevin dynamics.

Conclusions:

• The generalized FDT provides a theoretical framework for understanding stochastic learning.
• The findings confirm the applicability of FDT principles beyond traditional physics systems.
• This work bridges concepts from statistical mechanics and machine learning theory.