A tight upper bound on the generalization error of feedforward neural networks

Area of Science:

• Machine Learning
• Neural Networks
• Statistical Learning Theory

Background:

• Feedforward neural networks are widely used but their generalization error is complex to bound.
• Understanding generalization error is crucial for reliable model performance.
• Existing bounds may not be tight or easily applicable.

Purpose of the Study:

• To derive a tight upper bound on the generalization error for a specific class of neural networks.
• To analyze the components contributing to the generalization error.
• To provide practical tools for calculating error sensitivity.

Main Methods:

• Utilizing concepts from differential calculus and statistical learning theory.
• Analyzing the properties of 2-times continuously differentiable feedforward neural networks and loss functions.
• Developing analytical expressions for the generalization error bound.

Main Results:

• A tight upper bound on generalization error was established.
• The bound decomposes into two key terms: empirical error estimation and input sensitivity.
• Explicit formulas for calculating the input sensitivity term were derived.

Conclusions:

• The derived bound offers improved theoretical understanding of neural network generalization.
• The explicit formulas facilitate practical assessment of model robustness to input variations.
• This work contributes to the theoretical foundations of deep learning generalization.