AI RESEARCH

A Quotient Homology Theory of Representation in Neural Networks

arXiv CS.LG

ArXi:2502.01360v4 Announce Type: replace 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.