The Real Tropical Geometry of Neural Networks

arXiv:2403.11871v1 Announce Type: cross
Abstract: We consider a binary classifier defined as the sign of a tropical rational function, that is, as the difference of two convex piecewise linear functions. The parameter space of ReLU neural networks is contained as a semialgebraic set inside the parameter space of tropical rational functions. We initiate the study of two different subdivisions of this parameter space: a subdivision into semialgebraic sets, on which the combinatorial type of the decision boundary is fixed, and …

abstract arxiv binary classifier cs.lg difference function functions geometry inside linear math.co networks neural networks relu set space type