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.

翻译：尽管极限学习机（ELM）已取得诸多成功应用，本文指出其基础原理缺乏严格的数学论证。具体而言，我们反驳了两个核心命题的证明，并构建了一个数据集作为ELM学习算法的反例，同时阐释了该数据集的设计原理——该设计可衍生出大量类似反例。最后，我们提出了修正后的基础理论表述，这些表述在特定理论场景下为ELM的有效性提供了依据。