Learning the mapping $\mathbf{x}\mapsto \sum_{i=1}^d x_i^2$: the cost of finding the needle in a haystack

24 Feb 2020 Jiefu Zhang Leonardo Zepeda-Núñez Yuan YAO Lin Lin

The task of using machine learning to approximate the mapping $\mathbf{x}\mapsto\sum_{i=1}^d x_i^2$ with $x_i\in[-1,1]$ seems to be a trivial one. Given the knowledge of the separable structure of the function, one can design a sparse network to represent the function very accurately, or even exactly... (read more)

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