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

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 distribution¹.