Data is the main motivation of all machine learning technic. We deal with data to find correlations and infer properties from this data. In this post, I would like to introduce the notion of a representative dataset. It was firstly proposed in the paper: “Representative datasets for neural networks”, and lately, a deeper approximation was done for the specific case of perceptrons in “Representative Datasets: The Perceptron Case”. As in the previous post, I do not pretend to do a deep explanation of these papers, just an informal taste of them.

In this post, I would like to describe a little bit our first approach to give a constructive solution to the Universal Approximation theorem. This approach is developed in a formal taste in the following preprint: “Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach”.