Shallow Neural Network can Perfectly Classify an Object following Separable Probability Distribution

TL;DR

This paper demonstrates that shallow sigmoid neural networks can perfectly classify data sampled from a separable probability distribution, even under more relaxed conditions than traditional linear separability, leveraging sigmoid saturation.

Contribution

It constructs shallow neural networks that achieve perfect classification for datasets from separable probability distributions under relaxed conditions, enhancing understanding of neural network generalization.

Findings

Achieves 100% accuracy on separable probability distribution datasets.

Uses sigmoid saturation to exploit small margins near decision boundaries.

Generalizes beyond traditional linear separability conditions.

Abstract

Guiding the design of neural networks is of great importance to save enormous resources consumed on empirical decisions of architectural parameters. This paper constructs shallow sigmoid-type neural networks that achieve 100% accuracy in classification for datasets following a linear separability condition. The separability condition in this work is more relaxed than the widely used linear separability. Moreover, the constructed neural network guarantees perfect classification for any datasets sampled from a separable probability distribution. This generalization capability comes from the saturation of sigmoid function that exploits small margins near the boundaries of intervals formed by the separable probability distribution.