# Deep-Learning the Landscape

arXiv: https://arxiv.org/abs/1706.02714 · HTML: https://mlsanity.com/paper/1706.02714/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2017.

## Built on by (most cited first, 21 of 21)

- [Machine Learning Calabi-Yau Hypersurfaces](https://mlsanity.com/paper/2112.06350/) (2021)
- [Rigor with Machine Learning from Field Theory to the Poincar'e Conjecture](https://mlsanity.com/paper/2402.13321/) (2024)
- [Neurons on Amoebae](https://mlsanity.com/paper/2106.03695/) (2021)
- [Deep multi-task mining Calabi-Yau four-folds](https://mlsanity.com/paper/2108.02221/) (2021)
- [Calabi-Yau Metrics, Energy Functionals and Machine-Learning](https://mlsanity.com/paper/2112.10872/) (2021)
- [Cluster Algebras: Network Science and Machine Learning](https://mlsanity.com/paper/2203.13847/) (2022)
- [A Triumvirate of AI Driven Theoretical Discovery](https://mlsanity.com/paper/2405.19973/) (2024)
- [Breeding realistic D-brane models](https://mlsanity.com/paper/2112.08391/) (2021)
- [Machine Learning Algebraic Geometry for Physics](https://mlsanity.com/paper/2204.10334/) (2022)
- [From the String Landscape to the Mathematical Landscape: a Machine-Learning Outlook](https://mlsanity.com/paper/2202.06086/) (2022)
- [Identifying equivalent Calabi--Yau topologies: A discrete challenge from math and physics for machine learning](https://mlsanity.com/paper/2202.07590/) (2022)
- [Learning proofs for the classification of nilpotent semigroups](https://mlsanity.com/paper/2106.03015/) (2021)
- [Machine-Learning Kronecker Coefficients](https://mlsanity.com/paper/2306.04734/) (2023)
- [Machine Learning of the Prime Distribution](https://mlsanity.com/paper/2403.12588/) (2024)
- [Learning 3-Manifold Triangulations](https://mlsanity.com/paper/2405.09610/) (2024)
- [Measuring global properties of neural generative model outputs via generating mathematical objects](https://mlsanity.com/paper/2105.13669/) (2021)
- [Black holes and the loss landscape in machine learning](https://mlsanity.com/paper/2306.14817/) (2023)
- [Calabi-Yau Four/Five/Six-folds as mathbbPnw Hypersurfaces: Machine Learning, Approximation, and Generation](https://mlsanity.com/paper/2311.17146/) (2023)
- [Beyond holography: the entropic quantum gravity foundations of image processing](https://mlsanity.com/paper/2503.14048/) (2025)
- [Testing Transformer Learnability on the Arithmetic Sequence of Rooted Trees](https://mlsanity.com/paper/2512.01870/) (2025)
- [Murmurations: a case study in AI-assisted mathematics](https://mlsanity.com/paper/2603.09680/) (2026)

## Abstract (arXiv)

We propose a paradigm to deep-learn the ever-expanding databases which have emerged in mathematical physics and particle phenomenology, as diverse as the statistics of string vacua or combinatorial and algebraic geometry. As concrete examples, we establish multi-layer neural networks as both classifiers and predictors and train them with a host of available data ranging from Calabi-Yau manifolds and vector bundles, to quiver representations for gauge theories. We find that even a relatively simple neural network can learn many significant quantities to astounding accuracy in a matter of minutes and can also predict hithertofore unencountered results. This paradigm should prove a valuable tool in various investigations in landscapes in physics as well as pure mathematics.