5 papers
About finite differential tropical basis for linear ODE's
Stefano Mereta, Alejandro Vargas
We formulate several open questions regarding the tropicalization of linear ODEs, aiming primarily to develop methods for calculating the radius of convergence of their classical s…
On the fibers and semi-algebraicity of ReLU neuromanifolds
Axel Flinth, Stefano Mereta, Michele Pernice
We study the semi-algebraicity of the neuromanifold of a feedforward ReLU neural network and its symmetries. We prove that is not…
The Fundamental theorem of tropical differential algebra over nontrivially valued fields and the radius of convergence of nonarchimedean differential equations
Francesco Gallinaro, Stefano Mereta
We prove a fundamental theorem for tropical partial differential equations, analogous to the fundamental theorem of tropical geometry in this context. We extend results from Aroca…
Three lectures on tropical algebra
Jeffrey Giansiracusa, Kevin Kuehn, Stefano Mereta +1
This document is a slightly expanded version of a series of talks given by J. Giansiracusa at the workshop `Geometry over semirings' at Universitat Autònoma de Barcelona in July 2…
Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry
Giovanni Luca Marchetti, Vahid Shahverdi, Stefano Mereta +2
In this position paper, we promote the study of function spaces parameterized by machine learning models through the lens of algebraic geometry. To this end, we focus on algebraic…