arXiv:2502.01360v4 Announce Type: replace Abstract: Previous research has proven that the set of maps implemented by neural networks with a ReLU activation function is identical to the set of piecewise linear continuous maps. Furthermore, such networks induce a hyperplane arrangement splitting the input domain of the network into convex polyhedra $G_J$ over which a network $\Phi$ operates in an affine manner. In this work, we leverage these properties to define an equivalence relation $\sim_\Phi$ on top of an input dataset, which defines a quotient space that can be split into two sets related
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