4 papers
Minimal-Norm Univariate Two-Layer ReLU Classification: Exact Solutions and Global Optimality with Skip Connections
Karolina Drabik, Ben Lewis, Antoni Puch +4
We study minimal-norm interpolation and -regularized logistic-loss minimization for binary classification by univariate two-layer ReLU networks. We give complete geometric…
Reachability in VASS Extended with Integer Counters
Clotilde Bizière, Wojciech Czerwiński, Roland Guttenberg +5
We consider a variant of VASS extended with integer counters, denoted VASS+Z. These are automata equipped with N and Z counters; the N-counters are required to remain nonnegative a…
Pumping-Like Results for Copyless Cost Register Automata and Polynomially Ambiguous Weighted Automata
Filip Mazowiecki, Antoni Puch, Daniel Smertnig
In this work we consider two rich subclasses of weighted automata over fields: polynomially ambiguous weighted automata and copyless cost register automata. Primarily we are intere…
Factoring through monomial representations: arithmetic characterizations and ambiguity of weighted automata
Antoni Puch, Daniel Smertnig
We characterize group representations that factor through monomial representations, respectively, block-triangular representations with monomial diagonal blocks, by arithmetic prop…