Machines and Mathematical Mutations: Using GNNs to Characterize Quiver Mutation Classes

no code implementations • 12 Nov 2024 • Jesse He, Helen Jenne, Herman Chau, Davis Brown, Mark Raugas, Sara Billey, Henry Kvinge

In this work, we use graph neural networks to investigate quiver mutation -- an operation that transforms one quiver (or directed multigraph) into another -- which is central to the theory of cluster algebras with deep connections to geometry, topology, and physics.

Using Skew to Assess the Quality of GAN-generated Image Features

no code implementations • 31 Oct 2023 • Lorenzo Luzi, Helen Jenne, Ryan Murray, Carlos Ortiz Marrero

The rapid advancement of Generative Adversarial Networks (GANs) necessitates the need to robustly evaluate these models.

ICML 2023 Topological Deep Learning Challenge : Design and Results

1 code implementation • 26 Sep 2023 • Mathilde Papillon, Mustafa Hajij, Helen Jenne, Johan Mathe, Audun Myers, Theodore Papamarkou, Tolga Birdal, Tamal Dey, Tim Doster, Tegan Emerson, Gurusankar Gopalakrishnan, Devendra Govil, Aldo Guzmán-Sáenz, Henry Kvinge, Neal Livesay, Soham Mukherjee, Shreyas N. Samaga, Karthikeyan Natesan Ramamurthy, Maneel Reddy Karri, Paul Rosen, Sophia Sanborn, Robin Walters, Jens Agerberg, Sadrodin Barikbin, Claudio Battiloro, Gleb Bazhenov, Guillermo Bernardez, Aiden Brent, Sergio Escalera, Simone Fiorellino, Dmitrii Gavrilev, Mohammed Hassanin, Paul Häusner, Odin Hoff Gardaa, Abdelwahed Khamis, Manuel Lecha, German Magai, Tatiana Malygina, Rubén Ballester, Kalyan Nadimpalli, Alexander Nikitin, Abraham Rabinowitz, Alessandro Salatiello, Simone Scardapane, Luca Scofano, Suraj Singh, Jens Sjölund, Pavel Snopov, Indro Spinelli, Lev Telyatnikov, Lucia Testa, Maosheng Yang, Yixiao Yue, Olga Zaghen, Ali Zia, Nina Miolane

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning.

Deep Learning

The combinatorial PT-DT correspondence

no code implementations • 15 Dec 2020 • Helen Jenne, Gautam Webb, Benjamin Young

We resolve an open conjecture from algebraic geometry, which states that two generating functions for plane partition-like objects (the "box-counting" formulae for the Calabi-Yau topological vertices in Donaldson-Thomas theory and Pandharipande-Thomas theory) are equal up to a factor of MacMahon's generating function for plane partitions.

Combinatorics 05A15, 05E14