A Critical Analysis of the Theoretical Framework of the Extreme Learning Machine

TL;DR

This paper critically examines the theoretical foundations of the Extreme Learning Machine (ELM), revealing gaps in its mathematical justification, providing counterexamples, and proposing alternative theoretical explanations for its effectiveness.

Contribution

It refutes existing proofs of ELM's foundational principles, introduces counterexamples, and offers revised theoretical statements to better justify ELM's efficiency.

Findings

Refutes two main proofs of ELM's theoretical basis

Constructs a dataset as a counterexample to ELM learning algorithm

Proposes alternative theoretical justifications for ELM's effectiveness

Abstract

Despite the number of successful applications of the Extreme Learning Machine (ELM), we show that its underlying foundational principles do not have a rigorous mathematical justification. Specifically, we refute the proofs of two main statements, and we also create a dataset that provides a counterexample to the ELM learning algorithm and explain its design, which leads to many such counterexamples. Finally, we provide alternative statements of the foundations, which justify the efficiency of ELM in some theoretical cases.