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SUMMARY:Learning Euler characteristics wit AI and the EuLearn 3D database 
 [MPIM]
DTSTART:20260615T080000Z
DTEND:20260615T090000Z
DTSTAMP:20260618T164000Z
UID:indico-event-1404@math-events.uni-bonn.de
DESCRIPTION:Speakers: Pablo Suarez-Serrato (UNAM\, Mexico\; UCLA\, Santa B
 arbara/MPIM)\n\nOberseminar Representation Theory\nWe present EuLearn\, th
 e first surface datasets equitably representing a diversity of topological
  types. We designed our embedded surfaces of uniformly varying genera rely
 ing on random knots\, thus allowing our surfaces to knot with themselves. 
 EuLearn contributes new topological datasets of meshes\, point clouds\, an
 d scalar fields in 3D. We aim to facilitate the training of machine learni
 ng systems that can discern topological features. We experimented with spe
 cific emblematic 3D neural network architectures\, finding that their vani
 lla implementations perform poorly on genus classification. To enhance per
 formance\, we developed a novel\, non-Euclidean\, statistical sampling met
 hod adapted to graph and manifold data. We also introduce adjacency-inform
 ed adaptations of PointNet and Transformer architectures that rely on our 
 non-Euclidean sampling strategy. Our results demonstrate that incorporatin
 g topological information into deep learning workflows significantly impro
 ves performance on these otherwise challenging EuLearn datasets. Paper: ht
 tps://iopscience.iop.org/article/10.1088/2632-2153/ae622e . Datasets: htt
 ps://huggingface.co/datasets/appliedgeometry/EuLearn .\n\nhttps://math-eve
 nts.uni-bonn.de/event/1404/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1404/
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