Grokking as an entanglement transition in tensor network machine learning
Abstract
Grokking is a intriguing phenomenon in machine learning where a neural network, after many training iterations with negligible improvement in generalization, suddenly achieves high accuracy on unseen data. By working in the quantum-inspired machine learning framework based on tensor networks, we numerically prove that grokking phenomenon can be related to an entanglement dynamical transition in the underlying quantum many-body systems, consisting in a one-dimensional lattice with each site hosting a qubit. Two datasets are considered as use case scenarios, namely fashion MNIST and gene expression communities of hepatocellular carcinoma. In both cases, we train Matrix Product State (MPS) to perform binary classification tasks, and we analyse the learning dynamics. We exploit measurement of qubits magnetization and correlation functions in the MPS network as a tool to identify meaningful and relevant gene subcommunities, verified by means of enrichment procedures.
Cite
@article{arxiv.2503.10483,
title = {Grokking as an entanglement transition in tensor network machine learning},
author = {Domenico Pomarico and Alfonso Monaco and Giuseppe Magnifico and Antonio Lacalamita and Ester Pantaleo and Loredana Bellantuono and Sabina Tangaro and Tommaso Maggipinto and Marianna La Rocca and Ernesto Picardi and Nicola Amoroso and Graziano Pesole and Sebastiano Stramaglia and Roberto Bellotti},
journal= {arXiv preprint arXiv:2503.10483},
year = {2025}
}