| Abstract: |
| The Kolmogorov Superposition Theorem (KST, 1957), offers a mathematically elegant framework for expressing any high-dimensional continuous function as a superposition of one-dimensional continuous functions. This foundational result has recently gained renewed interest, particularly in neural networks. However, a major challenge remains: the one-dimensional functions resulted from all constructions are highly non-smooth. In this talk, we present a novel approximate version of KST involving $C^2$ inner functions and piecewise $C^2$ outer functions and show its applications in neural network approximations. |
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