On the ambiguity in classification

Arif Dönmez
Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations, PMLR 197:158-170, 2023.

Abstract

We develop a theoretical framework for geometric deep learning that incorporates ambiguous data in learning tasks. This framework uncovers deep connections between noncommutative geometry and learning tasks. Namely, it turns out that learning tasks naturally arise from groupoids, and vice versa. We also find that learning tasks are closely linked to the geometry of its groupoid $*$-algebras. This point of view allows us to answer the question of what actually constitutes a classification problem and link unsupervised learning tasks to random walks on the second groupoid cohomology of its groupoid.

Cite this Paper

BibTeX
@InProceedings{pmlr-v197-donmez23a, title = {On the ambiguity in classification}, author = {D\"{o}nmez, Arif}, booktitle = {Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations}, pages = {158--170}, year = {2023}, editor = {Sanborn, Sophia and Shewmake, Christian and Azeglio, Simone and Di Bernardo, Arianna and Miolane, Nina}, volume = {197}, series = {Proceedings of Machine Learning Research}, month = {03 Dec}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v197/donmez23a/donmez23a.pdf}, url = {https://proceedings.mlr.press/v197/donmez23a.html}, abstract = {We develop a theoretical framework for geometric deep learning that incorporates ambiguous data in learning tasks. This framework uncovers deep connections between noncommutative geometry and learning tasks. Namely, it turns out that learning tasks naturally arise from groupoids, and vice versa. We also find that learning tasks are closely linked to the geometry of its groupoid $*$-algebras. This point of view allows us to answer the question of what actually constitutes a classification problem and link unsupervised learning tasks to random walks on the second groupoid cohomology of its groupoid.} }
Endnote
%0 Conference Paper %T On the ambiguity in classification %A Arif Dönmez %B Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations %C Proceedings of Machine Learning Research %D 2023 %E Sophia Sanborn %E Christian Shewmake %E Simone Azeglio %E Arianna Di Bernardo %E Nina Miolane %F pmlr-v197-donmez23a %I PMLR %P 158--170 %U https://proceedings.mlr.press/v197/donmez23a.html %V 197 %X We develop a theoretical framework for geometric deep learning that incorporates ambiguous data in learning tasks. This framework uncovers deep connections between noncommutative geometry and learning tasks. Namely, it turns out that learning tasks naturally arise from groupoids, and vice versa. We also find that learning tasks are closely linked to the geometry of its groupoid $*$-algebras. This point of view allows us to answer the question of what actually constitutes a classification problem and link unsupervised learning tasks to random walks on the second groupoid cohomology of its groupoid.
APA
Dönmez, A.. (2023). On the ambiguity in classification. Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations, in Proceedings of Machine Learning Research 197:158-170 Available from https://proceedings.mlr.press/v197/donmez23a.html.

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