Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2205.03061

A universal training scheme and the resulting universality for machine learning phases

Y. -H. Yseng, F. -J. Jiang, Chenhui Huang

Published May 6, 2022• 0 citations
arXivHTMLPDF

Abstract

An autoencoder (AE) and a generative adversarial networks (GANs) are trained only once on a one-dimensional (1D) lattice of 200 sites. Moreover, the AE contains only one hidden layer consisting of two neurons and both the generator and the discriminator of the GANs are made up of two neurons as well. The training set employed to train both the considered unsupervised neural networks (NN) is composed of two artificial configurations. Remarkably, despite their simple architectures, both the built AE and GANs have precisely determined the critical points of several models, including the three-dimensional (3D) classical $O(3)$ model, the two-dimensional (2D) generalized classical XY model, the 2D two-state Potts model, and the 1D Bose-Hubbard model. The results presented here as well as that shown in {\it Eur. Phys. J. Plus {\bf 136}, 1116 (2021)} suggest that when phase transitions are considered, an elegant universal neural network that is extremely efficient and is applicable to broad physical systems can be constructed with ease. In particular, since a NN trained with two configurations can be applied to many models, it is likely that when machine learning is concerned, the majority of phase transitions belong to a class having two elements, i.e. the Ising class.

DOI
10.48550/arxiv.2205.03061

Related papers

A universal training scheme and the resulting universality for machine learning phases

Yuan-Heng Tseng, Fu-Jiun Jiang, C-Y Huang

Abstract An autoencoder (AE) and a generative adversarial network (GAN) are trained only once on a one-dimensional (1D) lattice of 200 sites. Moreover, the AE contains only one hidden layer consisting of two neurons, and both the generator and the discriminator of the GAN are made up of two neurons as well. The training set employed to train both the considered unsupervised neural networks (NNs) is composed of two artificial configurations. Remarkably, despite their simple architectures, both the built AE and GAN have precisely determined the critical points of several models, including the three-dimensional classical O(3) model, the two-dimensional generalized classical XY model, the two-dimensional two-state Potts model, and the one-dimensional Bose–Hubbard model. In addition, a factor of several thousands in the speed of calculation is gained for the built AE and GAN when they are compared with the conventional unsupervised NN approaches. The results presented here, as well as those shown previously in the literature, suggest that when phase transitions are considered, an elegant universal neural network that is extremely efficient and is applicable to broad physical systems can be constructed with ease. In particular, since an NN trained with two configurations can be applied to many models, it is likely that when machine learning is concerned, the majority of phase transitions belong to a class having two elements, i.e. the Ising class.

Progress of Theoretical and Experimental Physics•Dec 13, 2022•5 citations

A universal neural network for learning phases and criticalities

D.-R. Tan, J.-H. Peng, Y.-H. Tseng +1 more

A universal supervised neural network (NN) relevant to compute the associated criticalities of real experiments studying phase transitions is constructed. The validity of the built NN is examined by applying it to calculate the criticalities of several three-dimensional (3D) models on the cubic lattice, including the classical $O(3)$ model, the 5-state ferromagnetic Potts model, and a dimerized quantum antiferromagnetic Heisenberg model. Particularly, although the considered NN is only trained one time on a one-dimensional (1D) lattice with 120 sites, yet it has successfully determined the related critical points of the studied 3D systems. Moreover, real configurations of states are not used in the testing stage. Instead, the employed configurations for the prediction are constructed on a 1D lattice of 120 sites and are based on the bulk quantities or the microscopic states of the considered models. As a result, our calculations are ultimately efficient in computation and the applications of the built NN is extremely broaden. Considering the fact that the investigated systems vary dramatically from each other, it is amazing that the combination of these two strategies in the training and the testing stages lead to a highly universal supervised neural network for learning phases and criticalities of 3D models. Based on the outcomes presented in this study, it is favorably probable that much simpler but yet elegant machine learning techniques can be constructed for fields of many-body systems other than the critical phenomena.

arXiv:2103.10846•Mar 19, 2021•1 citation

Neural network evidence of a weakly first order phase transition for the two-dimensional 5-state Potts model

Yuan-Heng Tseng, Y.-H. Tseng, Fu-Jiun Jiang

A universal (supervised) neural network (NN), which is only trained once on a one-dimensional lattice of 200 sites, is employed to study the phase transition of the two-dimensional (2D) 5-state ferromagnetic Potts model on the square lattice. In particular, the NN is obtained by using merely two artificially made configurations as the training set. Due to the elegant features of the considered NN, results associated with systems consisting of over 4000000 spins can be obtained with ease, and convincing evidence showing the investigated phase transition is weakly first order is reached. The outcomes demonstrated here can hardly be achieved with the standard NNs that are commonly used in the literature.

arXiv:2111.14063•Nov 28, 2021•0 citations

Machine learning phases of an Abelian gauge theory

Jhao-Hong Peng, Yuan-Heng Tseng, Fu-Jiun Jiang

Abstract The phase transition of the two-dimensional U(1) quantum link model on the triangular lattice is investigated by employing a supervised neural network (NN) consisting of only one input layer, one hidden layer of two neurons, and one output layer. No information on the studied model is used when the NN training is conducted. Instead, two artificially made configurations are considered as the training set. Interestingly, the obtained NN not only estimates the critical point accurately but also uncovers the physics correctly. The results presented here imply that a supervised NN, which has a very simple architecture and is trained without any input from the investigated model, can identify the targeted phase structure with high precision.

arXiv:2212.14655•Progress of Theoretical and Experimental Physics•Jul 1, 2023•6 citations

Berezinskii–Kosterlitz–Thouless Transition – A Universal Neural Network Study with Benchmarks

Y.-H. Tseng, Fu-Jiun Jiang

Using a supervised neural network (NN) trained once on a one-dimensional lattice of 200 sites, we calculate the Berezinskii–Kosterlitz–Thouless phase transitions of the two-dimensional (2D) classical XY and the 2D generalized classical XY models. In particular, both the bulk quantities Binder ratios and the spin states of the studied systems are employed to construct the needed configurations for the NN prediction. By applying semiempirical finite-size scaling to the relevant data, the critical points obtained by the NN approach agree well with the known results established in the literature. This implies that for each of the considered models, the determination of its various phases requires only a little information. The outcomes presented here demonstrate convincingly that the employed universal NN is not only valid for the symmetry breaking related phase transitions, but also works for calculating the critical points of the phase transitions associated with topology. The efficiency of the used NN in the computation is examined by carrying out several detailed benchmark calculations.

Results in Physics•Jan 1, 2021•7 citations

On the generalizability of artificial neural networks in spin models

Hon Man Yau, Nan Su

The applicability of artificial neural networks (ANNs) is typically limited to the models they are trained with and little is known about their generalizability, which is a pressing issue in the practical application of trained ANNs to unseen problems. Here, by using the task of identifying phase transitions in spin models, we establish a systematic generalizability such that simple ANNs trained with the two-dimensional ferromagnetic Ising model can be applied to the ferromagnetic q q -state Potts model in different dimensions for q \geq 2 q ≥ 2 . The same scheme can be applied to the highly nontrivial antiferromagnetic q q -state Potts model. We demonstrate that similar results can be obtained by reducing the exponentially large state space spanned by the training data to one that comprises only three representative configurations artificially constructed through symmetry considerations. We expect our findings to simplify and accelerate the development of machine learning-assisted tasks in spin-model related disciplines in physics and materials science.

arXiv:2006.15021•SciPost Physics Core•Jun 8, 2022•12 citations
An autoencoder (AE) and a generative adversarial networks (GANs) are trained only once on a one-dimensional (1D) lattice of 200 sites. Moreover, the AE contains only one hidden layer consisting of two neurons and both the generator and the discriminator of the GANs are made up of two neurons as well. The training set employed to train both the considered unsupervised neural networks (NN) is composed of two artificial configurations. Remarkably, despite their simple architectures, both the built AE and GANs have precisely determined the critical points of several models, including the three-dimensional (3D) classical O(3)O(3)O(3) model, the two-dimensional (2D) generalized classical XY model, the 2D two-state Potts model, and the 1D Bose-Hubbard model. The results presented here as well as that shown in {\it Eur. Phys. J. Plus {\bf 136}, 1116 (2021)} suggest that when phase transitions are considered, an elegant universal neural network that is extremely efficient and is applicable to broad physical systems can be constructed with ease. In particular, since a NN trained with two configurations can be applied to many models, it is likely that when machine learning is concerned, the majority of phase transitions belong to a class having two elements, i.e. the Ising class.
Abstract An autoencoder (AE) and a generative adversarial network (GAN) are trained only once on a one-dimensional (1D) lattice of 200 sites. Moreover, the AE contains only one hidden layer consisting of two neurons, and both the generator and the discriminator of the GAN are made up of two neurons as well. The training set employed to train both the considered unsupervised neural networks (NNs) is composed of two artificial configurations. Remarkably, despite their simple architectures, both the built AE and GAN have precisely determined the critical points of several models, including the three-dimensional classical O(3) model, the two-dimensional generalized classical XY model, the two-dimensional two-state Potts model, and the one-dimensional Bose–Hubbard model. In addition, a factor of several thousands in the speed of calculation is gained for the built AE and GAN when they are compared with the conventional unsupervised NN approaches. The results presented here, as well as those shown previously in the literature, suggest that when phase transitions are considered, an elegant universal neural network that is extremely efficient and is applicable to broad physical systems can be constructed with ease. In particular, since an NN trained with two configurations can be applied to many models, it is likely that when machine learning is concerned, the majority of phase transitions belong to a class having two elements, i.e. the Ising class.
A universal supervised neural network (NN) relevant to compute the associated criticalities of real experiments studying phase transitions is constructed. The validity of the built NN is examined by applying it to calculate the criticalities of several three-dimensional (3D) models on the cubic lattice, including the classical O(3)O(3)O(3) model, the 5-state ferromagnetic Potts model, and a dimerized quantum antiferromagnetic Heisenberg model. Particularly, although the considered NN is only trained one time on a one-dimensional (1D) lattice with 120 sites, yet it has successfully determined the related critical points of the studied 3D systems. Moreover, real configurations of states are not used in the testing stage. Instead, the employed configurations for the prediction are constructed on a 1D lattice of 120 sites and are based on the bulk quantities or the microscopic states of the considered models. As a result, our calculations are ultimately efficient in computation and the applications of the built NN is extremely broaden. Considering the fact that the investigated systems vary dramatically from each other, it is amazing that the combination of these two strategies in the training and the testing stages lead to a highly universal supervised neural network for learning phases and criticalities of 3D models. Based on the outcomes presented in this study, it is favorably probable that much simpler but yet elegant machine learning techniques can be constructed for fields of many-body systems other than the critical phenomena.
A universal (supervised) neural network (NN), which is only trained once on a one-dimensional lattice of 200 sites, is employed to study the phase transition of the two-dimensional (2D) 5-state ferromagnetic Potts model on the square lattice. In particular, the NN is obtained by using merely two artificially made configurations as the training set. Due to the elegant features of the considered NN, results associated with systems consisting of over 4000000 spins can be obtained with ease, and convincing evidence showing the investigated phase transition is weakly first order is reached. The outcomes demonstrated here can hardly be achieved with the standard NNs that are commonly used in the literature.
Abstract The phase transition of the two-dimensional U(1) quantum link model on the triangular lattice is investigated by employing a supervised neural network (NN) consisting of only one input layer, one hidden layer of two neurons, and one output layer. No information on the studied model is used when the NN training is conducted. Instead, two artificially made configurations are considered as the training set. Interestingly, the obtained NN not only estimates the critical point accurately but also uncovers the physics correctly. The results presented here imply that a supervised NN, which has a very simple architecture and is trained without any input from the investigated model, can identify the targeted phase structure with high precision.
Using a supervised neural network (NN) trained once on a one-dimensional lattice of 200 sites, we calculate the Berezinskii–Kosterlitz–Thouless phase transitions of the two-dimensional (2D) classical XY and the 2D generalized classical XY models. In particular, both the bulk quantities Binder ratios and the spin states of the studied systems are employed to construct the needed configurations for the NN prediction. By applying semiempirical finite-size scaling to the relevant data, the critical points obtained by the NN approach agree well with the known results established in the literature. This implies that for each of the considered models, the determination of its various phases requires only a little information. The outcomes presented here demonstrate convincingly that the employed universal NN is not only valid for the symmetry breaking related phase transitions, but also works for calculating the critical points of the phase transitions associated with topology. The efficiency of the used NN in the computation is examined by carrying out several detailed benchmark calculations.
The applicability of artificial neural networks (ANNs) is typically limited to the models they are trained with and little is known about their generalizability, which is a pressing issue in the practical application of trained ANNs to unseen problems. Here, by using the task of identifying phase transitions in spin models, we establish a systematic generalizability such that simple ANNs trained with the two-dimensional ferromagnetic Ising model can be applied to the ferromagnetic q q -state Potts model in different dimensions for q \geq 2 q ≥ 2 . The same scheme can be applied to the highly nontrivial antiferromagnetic q q -state Potts model. We demonstrate that similar results can be obtained by reducing the exponentially large state space spanned by the training data to one that comprises only three representative configurations artificially constructed through symmetry considerations. We expect our findings to simplify and accelerate the development of machine learning-assisted tasks in spin-model related disciplines in physics and materials science.