On sample complexity of neural networks

TL;DR

This paper establishes an almost linear bound on the sample complexity of deep neural networks by analyzing their definability within an o-minimal structure, providing theoretical insights into their learning efficiency.

Contribution

It introduces a novel theoretical framework linking neural network functions to o-minimal structures, deriving nearly linear sample complexity bounds.

Findings

Sample complexity scales almost linearly with the number of weights.

Neural networks can be characterized as definable objects in o-minimal structures.

Theoretical bounds improve understanding of neural network learning efficiency.

Abstract

We consider functions defined by deep neural networks as definable objects in an o-miminal expansion of the real field, and derive an almost linear (in the number of weights) bound on sample complexity of such networks.