Machine learning in the string landscape

Carifio, Jonathan; Halverson, Jeffrey B.; Krioukov, Dmitri; Nelson, Brent D.

doi:10.1007/jhep09(2017)157

Cited by 161 publications

(126 citation statements)

References 40 publications

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“…It might also be interesting to apply machine learning techniques to investigate the quantum entanglement structure of links studied in [25,26]. Recently, [27][28][29][30] have pioneered investigations of the string landscape with machine learning techniques. Exploring the mathematics landscape in a similar spirit, we expect that the strategy we employ of analyzing correlations between properties of basic objects can suggest new relationships of an approximate form.…”

Section: Discussionmentioning

confidence: 99%

Deep learning the hyperbolic volume of a knot

2019

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An important conjecture in knot theory relates the large-N , double scaling limit of the colored Jones polynomial J K,N (q) of a knot K to the hyperbolic volume of the knot complement, Vol(K). A less studied question is whether Vol(K) can be recovered directly from the original Jones polynomial (N = 2). In this report we use a deep neural network to approximate Vol(K) from the Jones polynomial. Our network is robust and correctly predicts the volume with 97.6% accuracy when training on 10% of the data. This points to the existence of a more direct connection between the hyperbolic volume and the Jones polynomial.B.6) The network can be straightforwardly implemented in Mathematica 11.3.0.0 [19] with the command 2 KnotNet = NetChain[{DotPlusLayer[100], ElementwiseLayer[LogisticSigmoid], DotPlusLayer[100], ElementwiseLayer[LogisticSigmoid], SummationLayer[]}, "Input" -> {18}];2 In Mathematica 12.0.0.0, the DotPlusLayer command is replaced by LinearLayer.

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Section: Discussionmentioning

confidence: 99%

Deep learning the hyperbolic volume of a knot

2019

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“…In [12] it was shown that genetic algorithms can be utilized to optimize neural network architectures for prediction in physical problems. In [13] it was shown that simpler supervised learning techniques that do not utilize neural networks can lead to rigorous theorems by conjecture generation, such as a theorem regarding the prevalence of E 6 gauge sectors in the ensemble [3] of 10 755 F-theory geometries. Supervised learning was also utilized [11] to predict a central charges in 4d N = 1 SCFTs via volume minimization in gravity duals with toric descriptions.…”

Section: Contentsmentioning

confidence: 99%

Branes with brains: exploring string vacua with deep reinforcement learning

Halverson

Nelson

Ruehle

2019

J. High Energ. Phys.

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We propose deep reinforcement learning as a model-free method for exploring the landscape of string vacua. As a concrete application, we utilize an artificial intelligence agent known as an asynchronous advantage actor-critic to explore type IIA compactifications with intersecting D6-branes. As different string background configurations are explored by changing D6-brane configurations, the agent receives rewards and punishments related to string consistency conditions and proximity to Standard Model vacua. These are in turn utilized to update the agent's policy and value neural networks to improve its behavior. By reinforcement learning, the agent's performance in both tasks is significantly improved, and for some tasks it finds a factor of O(200) more solutions than a random walker. In one case, we demonstrate that the agent learns a human-derived strategy for finding consistent string models. In another case, where no human-derived strategy exists, the agent learns a genuinely new strategy that achieves the same goal twice as efficiently per unit time. Our results demonstrate that the agent learns to solve various string theory consistency conditions simultaneously, which are phrased in terms of non-linear, coupled Diophantine equations.

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“…Given these accurate predictions of n FRST , it is interesting to study the interpretability of the predictions made by the neural network. Sometimes refered to as intelligible artificial intelligence, interpretability is a major current goal of machine learning research, and it is one of the reasons for developing the EQL architecture; see [33] for the related idea of conjecture generation, by which interpretable numerical decisions may be turned into rigorous results. In the EQL context, the idea is to mimic what happens in natural sciences such as physics, where a physical phenomenon is often described in terms of an interpretable function that allows for understanding and generalization.…”

Section: Motivationmentioning

confidence: 99%

Estimating Calabi-Yau hypersurface and triangulation counts with equation learners

Altman

Carifio

Halverson

et al. 2019

J. High Energ. Phys.

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We provide the first estimate of the number of fine, regular, star triangulations of the four-dimensional reflexive polytopes, as classified by Kreuzer and Skarke (KS). This provides an upper bound on the number of Calabi-Yau threefold hypersurfaces in toric varieties. The estimate is performed with deep learning, specifically the novel equation learner (EQL) architecture. We demonstrate that EQL networks accurately predict numbers of triangulations far beyond the h 1,1 training region, allowing for reliable extrapolation. We estimate that number of triangulations in the KS dataset is 10 10,505 , dominated by the polytope with the highest h 1,1 value.

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Machine learning in the string landscape

Cited by 161 publications

References 40 publications

Deep learning the hyperbolic volume of a knot

Deep learning the hyperbolic volume of a knot

Branes with brains: exploring string vacua with deep reinforcement learning

Estimating Calabi-Yau hypersurface and triangulation counts with equation learners

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