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Gradient descent learning in and out of equilibrium
N Caticha1, E Araújo de Oliveira
1Instituto de Física, Universidade de São Paulo, CP 66318 São Paulo, SP, CEP05389-970 Brazil.
Summary
This study explores online learning dynamics, comparing them to offline learning. The closest online algorithm minimizes information loss by using an effective potential, distinct from the original offline potential.
Area of Science:
- Machine Learning
- Statistical Physics
Background:
- Investigates the relationship between off-thermal equilibrium online learning and equilibrated offline learning.
- Utilizes Opper's approach for analyzing online Bayesian algorithms in potential-based or maximum likelihood learning scenarios.
Purpose of the Study:
- To identify the online learning algorithm that most accurately approximates offline learning.
- To minimize Kullback-Leibler information loss between online and offline learning processes.
Main Methods:
- Applies Opper's method for studying online Bayesian algorithms.
- Analyzes the Kullback-Leibler information loss to find the closest online approximation.
- Examines potential gradient descent learning dynamics.
Main Results:
- The optimal online algorithm updates weights using the gradient of an effective potential.
- This effective potential differs from the potential used in the parent offline algorithm.
- Potential annealing origins are discussed through analyzed examples.
Conclusions:
- Establishes a clear connection between online and offline learning through an effective potential.
- Highlights the importance of the effective potential in approximating offline learning dynamics.
- Provides insights into potential annealing in machine learning algorithms.
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