Tensorial Topological Descriptors for Machine Learning Phase Detection

Palumbo (2024) used tensorial Berry connections to describe quasistrings in topological phases, while Käming et al. (2021) applied unsupervised ML to experimental phase transitions. Here, we propose converting Palumbo's tensorial phase-space data into topological descriptors for ML training. Instead of raw wavefunctions (as in Fang et al.'s manifold distance), our model ingests coordinate/momentum-space tensors to classify phases, including fractons and higher-order topological insulators. This diverges from conventional ML approaches by encoding geometric/topological priors into the feature space, improving interpretability. For example, training on extended object currents could identify boundary transitions missed by Shen et al.'s (2024) fermion-focused methods. The framework could also detect unconventional transitions in deformed toric codes (Huxford et al. 2023), where tensorial data captures anyon condensation more sensitively than fidelity alone.

References:

1. Distance between two manifolds, topological phase transitions and scaling laws. ZhaoXiang Fang, Ming Gong, Guangcan Guo, Yongxu Fu, Long Xiong (2024).
2. Gaining insights on anyon condensation and 1-form symmetry breaking across a topological phase transition in a deformed toric code model. Joe Huxford, D. X. Nguyen, Yong Baek Kim (2023). SciPost Physics.
3. Topological phases for extended objects: Semiclassical phase-space approach with tensorial coordinates. G. Palumbo (2024). Physical Review D.
4. New boundary criticality in topological phases. Xiaoyang Shen, Zhengzhi Wu, Shao-Kai Jian (2024).
5. Unsupervised machine learning of topological phase transitions from experimental data. Niklas Käming, Anna Dawid, Korbinian Kottmann, M. Lewenstein, K. Sengstock, A. Dauphin, C. Weitenberg (2021). Machine Learning: Science and Technology.