Generalization Bounds with Data-dependent Fractal Dimensions

Understand

Providing generalization guarantees for modern neural networks has been a crucial task in statistical learning.

• Recently, several studies have attempted to analyze the generalization error in such settings by using tools from fractal geometry.
• While these works have successfully introduced new mathematical tools to apprehend generalization, they heavily rely on a Lipschitz continuity assumption, which in general does not hold for neural networks and might make the bounds vacuous.
• In this work, we address this issue and prove fractal geometry-based generalization bounds without requiring any Lipschitz assumption.