22 citations · 28 across the 7 of their papers we have counts for
7 papers
A Simple Strategy to Provable Invariance via Orbit Mapping
Kanchana Vaishnavi Gandikota, Jonas Geiping, Zorah Lähner +2
Many applications require robustness, or ideally invariance, of neural networks to certain transformations of input data. Most commonly, this requirement is addressed by training d…
Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations
Adam Czapliński, Andreas Krug, Manfred Lehn +1
We observe that general reducible curves in sufficiently positive linear systems on K3 surfaces are of a form that generalises Kodaira's classification of singular elliptic fibres…
Training or Architecture? How to Incorporate Invariance in Neural Networks
Kanchana Vaishnavi Gandikota, Jonas Geiping, Zorah Lähner +2
Many applications require the robustness, or ideally the invariance, of a neural network to certain transformations of input data. Most commonly, this requirement is addressed by e…
Semi-algebraic properties of Minkowski sums of a twisted cubic segment
Arthur Bik, Adam Czapliński, Markus Wageringel
We find a semi-algebraic description of the Minkowski sum of copies of the bounded twisted cubic for each integer $n\ge…
Uniform matrix product states from an algebraic geometer's point of view
Adam Czapliński, Mateusz Michałek, Tim Seynnaeve
We apply methods from algebraic geometry to study uniform matrix product states. Our main results concern the topology of the locus of tensors expressed as uMPS, their defining equ…
Curve configurations in the projective plane and their characteristic numbers
Adam Czapliński, Piotr Pokora
In this paper we study the concept of characteristic numbers and Chern slopes in the context of curve configurations in the real and complex projective plane. We show that some ext…
A counterexample to the containment over the reals
Adam Czapliński, Agata Główka, Grzegorz Malara +4
The purpose of this note is to give counterexamples to the containment over the real numbers.