Why is topology hard to learn?

Fuente: arXiv
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Bibliographic Details
Main Authors: Oriekhov, D. O., Bergkamp, Stan, Jin, Guliuxin, Luna, Juan Daniel Torres, Zouggari, Badr, van der Meer, Sibren, Yazidi, Naoual El, Greplova, Eliska
Format: Preprint
Published: 2025
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author Oriekhov, D. O.
Bergkamp, Stan
Jin, Guliuxin
Luna, Juan Daniel Torres
Zouggari, Badr
van der Meer, Sibren
Yazidi, Naoual El
Greplova, Eliska
author_facet Oriekhov, D. O.
Bergkamp, Stan
Jin, Guliuxin
Luna, Juan Daniel Torres
Zouggari, Badr
van der Meer, Sibren
Yazidi, Naoual El
Greplova, Eliska
contents Much attention has been devoted to the use of machine learning to approximate physical concepts. Yet, due to challenges in interpretability of machine learning techniques, the question of what physics machine learning models are able to learn remains open. Here we bridge the concept a physical quantity and its machine learning approximation in the context of the original application of neural networks in physics: topological phase classification. We construct a hybrid tensor-neural network object that exactly expresses real space topological invariant and rigorously assess its trainability and generalization. Specifically, we benchmark the accuracy and trainability of a tensor-neural network to multiple types of neural networks, thus exemplifying the differences in trainability and representational power. Our work highlights the challenges in learning topological invariants and constitutes a stepping stone towards more accurate and better generalizable machine learning representations in condensed matter physics.
format Preprint
id arxiv_https___arxiv_org_abs_2509_26261
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Why is topology hard to learn?
Oriekhov, D. O.
Bergkamp, Stan
Jin, Guliuxin
Luna, Juan Daniel Torres
Zouggari, Badr
van der Meer, Sibren
Yazidi, Naoual El
Greplova, Eliska
Mesoscale and Nanoscale Physics
Disordered Systems and Neural Networks
Machine Learning
Much attention has been devoted to the use of machine learning to approximate physical concepts. Yet, due to challenges in interpretability of machine learning techniques, the question of what physics machine learning models are able to learn remains open. Here we bridge the concept a physical quantity and its machine learning approximation in the context of the original application of neural networks in physics: topological phase classification. We construct a hybrid tensor-neural network object that exactly expresses real space topological invariant and rigorously assess its trainability and generalization. Specifically, we benchmark the accuracy and trainability of a tensor-neural network to multiple types of neural networks, thus exemplifying the differences in trainability and representational power. Our work highlights the challenges in learning topological invariants and constitutes a stepping stone towards more accurate and better generalizable machine learning representations in condensed matter physics.
title Why is topology hard to learn?
topic Mesoscale and Nanoscale Physics
Disordered Systems and Neural Networks
Machine Learning
url https://arxiv.org/abs/2509.26261