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Machine Learning Line Bundle Cohomology

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arxiv 1906.08730 v1 pith:3QXSZUX2 submitted 2019-06-20 hep-th

Callum R. Brodie , Andrei Constantin , Rehan Deen , Andre Lukas This is my paper
classification hep-th
keywords cohomologybundleformulalearninglinecertaincomplexdescribed
verification ladder T0 review T1 audit T2 compute T3 formal
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We investigate different approaches to machine learning of line bundle cohomology on complex surfaces as well as on Calabi-Yau three-folds. Standard function learning based on simple fully connected networks with logistic sigmoids is reviewed and its main features and shortcomings are discussed. It has been observed recently that line bundle cohomology can be described by dividing the Picard lattice into certain regions in each of which the cohomology dimension is described by a polynomial formula. Based on this structure, we set up a network capable of identifying the regions and their associated polynomials, thereby effectively generating a conjecture for the correct cohomology formula. For complex surfaces, we also set up a network which learns certain rigid divisors which appear in a recently discovered master formula for cohomology dimensions.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Exploring Line Bundle Standard Models with Transformers

    hep-th 2026-06 unverdicted novelty 7.0 of 10

    A Transformer RL agent is trained to generate valid heterotic line bundle sums on CICYs that satisfy gauge embedding, anomaly cancellation, poly-stability, chirality, and no-exotics constraints.

  2. Machine Learning Free Quotients of CICYs

    hep-th 2025-08 conditional novelty 6.0 of 10

    Machine-learning classifiers, especially a multi-head attention model, correctly identify almost all free Z2, Z3, Z4, and Z2xZ2 quotients of CICYs on held-out manifolds, with only three missed Z2xZ2 cases.

  3. Pre-Strings Lectures on Artificial Intelligence

    hep-th 2026-07 accept novelty 5.5 of 10

    Lecture notes define neural-network field theory and survey how it recovers known QFT/string results plus applied AI techniques for string problems.

  4. Exploring Line Bundle Standard Models with Transformers

    hep-th 2026-06 conditional novelty 5.0 of 10

    A Transformer trained by reinforcement learning generates heterotic line-bundle sums that satisfy anomaly-cancellation, stability, and chirality constraints, and its policy transfers usefully across Calabi-Yau geometries.

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