7 papers
Fast Isotopy Computation for T-Curves
Zoe Geiselmann, Michael Joswig, Lars Kastner +5
A T-curve of degree is given by a regular unimodular triangulation of together with a sign distribution on its lattice points. By Viro's Patchworking Theorem, thi…
Limits of combinatorial patchworking
Zoe Geiselmann, Michael Joswig, Lars Kastner +5
It is shown that there are real plane algebraic curves of degree eight that cannot be realized as T-curves, i.e., via combinatorial patchworking. In fact, this holds for several re…
Neural Sum-of-Squares: Certifying the Nonnegativity of Polynomials with Transformers
Nico Pelleriti, Christoph Spiegel, Shiwei Liu +3
Certifying nonnegativity of polynomials is a well-known NP-hard problem with direct applications spanning non-convex optimization, control, robotics, and beyond. A sufficient condi…
Neural Discovery in Mathematics: Do Machines Dream of Colored Planes?
Konrad Mundinger, Max Zimmer, Aldo Kiem +2
We demonstrate how neural networks can drive mathematical discovery through a case study of the Hadwiger-Nelson problem, a long-standing open problem at the intersection of discret…
Extending the Continuum of Six-Colorings
Konrad Mundinger, Sebastian Pokutta, Christoph Spiegel +1
We present two novel six-colorings of the Euclidean plane that avoid monochromatic pairs of points at unit distance in five colors and monochromatic pairs at another specified dist…
The Four-Color Ramsey Multiplicity of Triangles
Aldo Kiem, Sebastian Pokutta, Christoph Spiegel
We study a generalization of a famous result of Goodman and establish that asymptotically at least a fraction of all triangles needs to be monochromatic in any four-colorin…
PERP: Rethinking the Prune-Retrain Paradigm in the Era of LLMs
Max Zimmer, Megi Andoni, Christoph Spiegel +1
Neural Networks can be effectively compressed through pruning, significantly reducing storage and compute demands while maintaining predictive performance. Simple yet effective met…