# Machine learning phase transitions: Connections to the Fisher information

arXiv: https://arxiv.org/abs/2311.10710 · HTML: https://mlsanity.com/paper/2311.10710/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 74 references that are in the map.
- First posted on arXiv 17 Nov 2023.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Correlator Convolutional Neural Networks: An Interpretable Architecture for Image-like Quantum Matter Data](https://mlsanity.com/paper/2011.03474/) (2020)
- [Machine learning discovery of new phases in programmable quantum simulator snapshots](https://mlsanity.com/paper/2112.10789/) (2021)
- [Empirical non-parametric estimation of the Fisher Information](https://mlsanity.com/paper/1408.1182/) (2014)

## Built on by (most cited first, 7 of 7)

- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [Phase Transitions in the Output Distribution of Large Language Models](https://mlsanity.com/paper/2405.17088/) (2024)
- [Decomposing Behavioral Phase Transitions in LLMs: Order Parameters for Emergent Misalignment](https://mlsanity.com/paper/2508.20015/) (2025)
- [ClassiFIM: An Unsupervised Method To Detect Phase Transitions](https://mlsanity.com/paper/2408.03323/) (2024)
- [Machine learning the Ising transition: A comparison between discriminative and generative approaches](https://mlsanity.com/paper/2411.19370/) (2024)
- [Neural Total Variation Distance Estimators for Changepoint Detection in News Data](https://mlsanity.com/paper/2506.18764/) (2025)
- [TetrisCNN for interpretable detection of phases of matter from experimental quantum simulator data](https://mlsanity.com/paper/2609.20693/) (2026)

## Abstract (arXiv)

Despite the widespread use and success of machine-learning techniques for detecting phase transitions from data, their working principle and fundamental limits remain elusive. Here, we explain the inner workings and identify potential failure modes of these techniques by rooting popular machine-learning indicators of phase transitions in information-theoretic concepts. Using tools from information geometry, we prove that several machine-learning indicators of phase transitions approximate the square root of the system's (quantum) Fisher information from below -- a quantity that is known to indicate phase transitions but is often difficult to compute from data. We numerically demonstrate the quality of these bounds for phase transitions in classical and quantum systems.