Minimal-dissipation learning for energy-based models

Area of Science:

• Machine Learning
• Statistical Physics
• Computational Science

Background:

• Energy-based models (EBMs) are powerful generative models.
• Training EBMs often involves significant energy dissipation, posing computational challenges.
• Understanding the relationship between estimation bias and thermodynamic work is crucial for efficient training.

Purpose of the Study:

• To establish a precise link between the bias of approximate maximum-likelihood estimation (MLE) in persistent chain EBMs and thermodynamic excess work.
• To investigate the feasibility of training EBMs with minimal energy dissipation within a finite timeframe.
• To introduce and analyze the concept of minimal-dissipation learning.

Main Methods:

• Deriving the exact relationship between MLE bias and thermodynamic excess work for overdamped Langevin dynamics.
• Analyzing the training dynamics of a persistent chain EBM with a Gaussian energy function.
• Developing an optimal learning rate schedule for general potentials.

Main Results:

• The bias of the approximate MLE objective for persistent chain EBMs precisely equals the thermodynamic excess work.
• A Gaussian energy function with constant variance can be trained with minimal excess work by solely adjusting the learning rate.
• This establishes the possibility of finite-time, minimal-dissipation training for persistent chain EBMs and provides a lower bound on computational energy.
• A generalized optimal learning rate schedule induces a natural gradient flow on the MLE objective.

Conclusions:

• Minimal-dissipation learning is a viable strategy for training persistent chain EBMs efficiently.
• The findings offer theoretical insights into the energy costs of computation in machine learning.
• The developed optimal learning rate schedule connects EBM training to natural gradient methods.