The 9 October preprint studies “representational topological expressivity,” which concerns the topology of a network’s output rather than the topology of classification decision boundaries. The author proves constructive upper bounds for ReLU architectures capable of representing spaces such as spheres and wedge sums of spheres. The first page lists Kosio Beshkov’s affiliation as the Department of Physics at the University of Oslo in Norway.

The paper gives bounds on architecture width and layer dimensions for networks that can express, for example, a space homotopy-equivalent to a d-sphere; it also conjectures a tighter bound for spaces homeomorphic to a sphere. This is a mathematical result about which topological representations an architecture can construct, not evidence of improved model performance on particular datasets. The paper is an arXiv preprint. Its framework extends expressivity analysis beyond classification toward tasks including regression and representation learning.