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

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