2024/06/04 by Koutschan, Christoph, Ponomarchuk, Anton, Schicho, Josef
#Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Symbolic Computation (cs.SC)
paper · doi:10.48550/arxiv.2406.02421
Any continuous piecewise-linear function F\colon ℝn→ 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 any such decomposition. We show that the tessellation of the input space ℝn induced by the function F has a direct connection to the number of arguments in the max functions.