A Limitation of Gradient Descent Learning.

Area of Science:

• Machine Learning
• Artificial Intelligence
• Optimization

Background:

• Gradient descent is a fundamental algorithm for training neural networks.
• Persistent weight noise is a common issue in neural network training.
• The relationship between the ideal performance measure and the actual learning objective under noisy conditions is not fully understood.

Purpose of the Study:

• To reveal a limitation of gradient descent learning when applied to neural networks with persistent weight noise.
• To differentiate the actual learning objective from the desired performance measure in the presence of weight noise.
• To analyze the impact of different types of persistent weight noise (additive vs. multiplicative) on the attained model.

Main Methods:

• Theoretical analysis of the learning objective function L(w) under persistent weight noise.
• Comparison of L(w) with the desired performance measure J(w) = E[V(~w)|w].
• Simulation studies on a regression problem and MNIST handwritten digit recognition.

Main Results:

• Additive persistent weight noise results in L(w) = J(w), meaning the attained model matches the desired model.
• Multiplicative persistent weight noise results in L(w) ≠ J(w), indicating the attained model deviates from the desired model.
• Analysis of attained model properties and learning curves under both noise conditions.

Conclusions:

• The type of persistent weight noise significantly affects the success of gradient descent in training neural networks.
• A misconception exists that gradient descent always optimizes the desired performance measure, which is not true for multiplicative weight noise.
• Understanding these distinctions is crucial for developing robust neural network training algorithms.