Statistical Predictions in String Theory and Deep Generative Models

Halverson, Jeffrey B.; Long, Cody

doi:10.1002/prop.202000005

Cited by 28 publications

(15 citation statements)

References 64 publications

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“…Finally, the immense size of discrete data sets in string theory, such as those encountered here, suggests the use of data science techniques — see [4–25] as well as the reviews [26] and [27]. In the final part of this work, we develop machine learning algorithms to predict the topological data of Calabi‐Yau threefolds.…”

Section: Introductionmentioning

confidence: 99%

Bounding the Kreuzer‐Skarke Landscape

Demirtaş

McAllister

Rios-Tascon

2020

Fortschritte der Physik

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We study Calabi-Yau threefolds with large Hodge numbers by constructing and counting triangulations of reflexive polytopes. By counting points in the associated secondary polytopes, we show that the number of fine, regular, star triangulations of polytopes in the Kreuzer-Skarke list is bounded above by (14,111 494) ≈ 10 928. Adapting a result of Anclin on triangulations of lattice polygons, we obtain a bound on the number of triangulations of each 2-face of each polytope in the list. In this way we prove that the number of topologically inequivalent Calabi-Yau hypersurfaces arising from the Kreuzer-Skarke list is bounded above by 10 428. We introduce efficient algorithms for constructing representative ensembles of Calabi-Yau hypersurfaces, including the extremal case h 1,1 = 491, and we study the distributions of topological and physical data therein. Finally, we demonstrate that neural networks can accurately predict these data once the triangulation is encoded in terms of the secondary polytope.

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Section: Introductionmentioning

confidence: 99%

Bounding the Kreuzer‐Skarke Landscape

Demirtaş

McAllister

Rios-Tascon

2020

Fortschritte der Physik

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“…Such structures appear in string theory fairly often, and more sophisticated machine learning (beyond simple feed-forward network architecture) has also been applied fruitfully to the study of the string landscape. For a small sample, see[45,[50][51][52][53], and also see the review[54] for more complete references in this area.…”

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confidence: 99%

Disentangling a deep learned volume formula

Craven

Jejjala

Kar

2021

J. High Energ. Phys.

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We present a simple phenomenological formula which approximates the hyperbolic volume of a knot using only a single evaluation of its Jones polynomial at a root of unity. The average error is just 2.86% on the first 1.7 million knots, which represents a large improvement over previous formulas of this kind. To find the approximation formula, we use layer-wise relevance propagation to reverse engineer a black box neural network which achieves a similar average error for the same approximation task when trained on 10% of the total dataset. The particular roots of unity which appear in our analysis cannot be written as e2πi/(k+2) with integer k; therefore, the relevant Jones polynomial evaluations are not given by unknot-normalized expectation values of Wilson loop operators in conventional SU(2) Chern-Simons theory with level k. Instead, they correspond to an analytic continuation of such expectation values to fractional level. We briefly review the continuation procedure and comment on the presence of certain Lefschetz thimbles, to which our approximation formula is sensitive, in the analytically continued Chern-Simons integration cycle.

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“…Artificial neural networks (ANNs) are algorithms inspired in the biological learning process. The use of machine learning techniques to solve classification problems has attracted more attention in the last years [33,37,39,[50][51][52][53]. The machine learning techniques allows to search in large amount of data for specific patterns and thus, it provides an exhaustive check in a short time.…”

Section: Appendix A: Artificial Neural Networkmentioning

confidence: 99%

Testing swampland conjectures with machine learning

et al. 2020

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We consider Type IIB compactifications on an isotropic torus $$T^6$$T6 threaded by geometric and non geometric fluxes. For this particular setup we apply supervised machine learning techniques, namely an artificial neural network coupled to a genetic algorithm, in order to obtain more than sixty thousand flux configurations yielding to a scalar potential with at least one critical point. We observe that both stable AdS vacua with large moduli masses and small vacuum energy as well as unstable dS vacua with small tachyonic mass and large energy are absent, in accordance to the refined de Sitter conjecture. Moreover, by considering a hierarchy among fluxes, we observe that perturbative solutions with small values for the vacuum energy and moduli masses are favored, as well as scenarios in which the lightest modulus mass is much smaller than the corresponding AdS vacuum scale. Finally we apply some results on random matrix theory to conclude that the most probable mass spectrum derived from this string setup is that satisfying the Refined de Sitter and AdS scale conjectures.

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Statistical Predictions in String Theory and Deep Generative Models

Cited by 28 publications

References 64 publications

Bounding the Kreuzer‐Skarke Landscape

Bounding the Kreuzer‐Skarke Landscape

Disentangling a deep learned volume formula

Testing swampland conjectures with machine learning

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