# Feature extraction of machine learning and phase transition point of Ising model

arXiv: https://arxiv.org/abs/2111.11166 · HTML: https://mlsanity.com/paper/2111.11166/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 25 references that are in the map.
- First posted on arXiv 22 Nov 2021.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Why does deep and cheap learning work so well?](https://mlsanity.com/paper/1608.08225/) (2016)
- [An exact mapping between the Variational Renormalization Group and Deep Learning](https://mlsanity.com/paper/1410.3831/) (2014)
- [Discovering Phase Transitions with Unsupervised Learning](https://mlsanity.com/paper/1606.00318/) (2016)
- [Neural Network Renormalization Group](https://mlsanity.com/paper/1802.02840/) (2018)
- [Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders](https://mlsanity.com/paper/1703.02435/) (2017)
- [Scale-invariant Feature Extraction of Neural Network and Renormalization Group Flow](https://mlsanity.com/paper/1801.07172/) (2018)
- [Thermodynamics and Feature Extraction by Machine Learning](https://mlsanity.com/paper/1810.08179/) (2018)
- [Adding machine learning within Hamiltonians: Renormalization group transformations, symmetry breaking and restoration](https://mlsanity.com/paper/2010.00054/) (2020)
- [Restricted Boltzmann Machine Flows and The Critical Temperature of Ising models](https://mlsanity.com/paper/2006.10176/) (2020)

## Built on by (most cited first, 1 of 1)

- [Exploration of the generative capabilities of Boltzmann machines applied to social systems under the majority rule](https://mlsanity.com/paper/2607.23349/) (2026)

## Abstract (arXiv)

We study the features extracted by the Restricted Boltzmann Machine (RBM) when it is trained with spin configurations of Ising model at various temperatures. Using the trained RBM, we obtain the flow of iterative reconstructions (RBM flow) of the spin configurations and find that in some cases the flow approaches the phase transition point T=Tc in Ising model. Since the extracted features are emphasized in the reconstructed configurations, the configurations at such a fixed point should describe nothing but the extracted features. Then we investigate the dependence of the fixed point on various parameters and conjecture the condition where the fixed point of the RBM flow is at the phase transition point. We also provide supporting evidence for the conjecture by analyzing the weight matrix of the trained RBM.