June 5, 2024, 4:44 a.m. | Christoph Koutschan, Anton Ponomarchuk, Josef Schicho

cs.LG updates on arXiv.org arxiv.org

arXiv:2406.02421v1 Announce Type: cross
Abstract: Any continuous piecewise-linear function $F\colon \mathbb{R}^{n}\to \mathbb{R}$ can be represented as a linear combination of $\max$ functions of at most $n+1$ affine-linear functions. In our previous paper [``Representing piecewise linear functions by functions with small arity'', AAECC, 2023], we showed that this upper bound of $n+1$ arguments is tight. In the present paper, we extend this result by establishing a correspondence between the function $F$ and the minimal number of arguments that are needed in …

abstract arxiv combination continuous cs.dm cs.lg cs.sc function functions linear max paper small type

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