Temporal Evolution of Generalization during Learning in Linear Networks

Area of Science:

• Machine Learning
• Neural Networks
• Optimization

Background:

• Gradient descent is a common training method for neural networks.
• Understanding generalization is crucial for effective model training.
• Linear networks provide a simplified model for studying complex phenomena.

Purpose of the Study:

• To analytically investigate generalization in feedforward linear networks.
• To understand the influence of initial conditions and noise on network training.
• To identify optimal stopping times for gradient descent training.

Main Methods:

• Analytical derivation of validation function behavior.
• Utilizing the Least Mean Squares (LMS) error function on validation patterns.
• Studying feedforward linear networks with n inputs and n outputs.

Main Results:

• Validation function behavior is critically dependent on initial weights and noise characteristics.
• Small initial weights can lead to a unique minimum, indicating an optimal stopping time.
• Complex behaviors like multiple local minima and plateau effects can occur.

Conclusions:

• Optimal training duration for linear networks can be bounded under specific conditions.
• Network generalization is sensitive to initialization and data noise.
• Further research can explore extensions to more complex network architectures.