Formal Analysis of the Sigmoid Function and Formal Proof of the Universal Approximation Theorem

This article presents a formal analysis of the sigmoid function and a formal proof of the Universal Approximation Theorem. This suggests a focus on mathematical rigor and theoretical foundations within the field of AI, specifically concerning neural networks. The use of 'formal' indicates a reliance on precise mathematical language and proof techniques, potentially making the work highly technical and aimed at a specialized audience.