Insights on the different convergences in Extreme Learning Machine

Neural Networks (NN) are a powerful tool in approximation theory because of the existence of Universal Approximation (UA) results. In the last decades, a significant attention has been given to Extreme Learning Machines (ELMs), typically employed for the training of single layer NNs, and for which a UA result can also be proven. In a generic NN, the design of the optimal approximator can be recast as a non-convex optimization problem that turns out to be particularly demanding from the computational viewpoint. However, under the adoption of ELM, the optimization task reduces to a - possibly rectangular - linear problem. In this work, we detail how to design a sequence of ELM networks trained via a target dataset. Different convergence procedures are proposed and tested for some reference datasets constructed to be equivalent to approximation problems.