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Paper details minimal arity for piecewise-linear function representation

A new paper on arXiv by Anton Ponomarchuk explores the representation of continuous piecewise-linear functions. The research establishes a connection between the function's tessellation of the input space and the minimal number of arguments required in its decomposition using max functions. This work builds upon previous findings that demonstrated the tightness of the upper bound for such decompositions. AI

RANK_REASON The cluster contains a research paper published on arXiv. [lever_c_demoted from research: ic=1 ai=0.4]

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Paper details minimal arity for piecewise-linear function representation

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  1. arXiv cs.LG TIER_1 English(EN) · Christoph Koutschan, Anton Ponomarchuk, Josef Schicho ·

    Representing Piecewise-Linear Functions by Functions with Minimal Arity

    arXiv:2406.02421v2 Announce Type: replace-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…