# Neurons on Amoebae

arXiv: https://arxiv.org/abs/2106.03695 · HTML: https://mlsanity.com/paper/2106.03695/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 55 references that are in the map.
- First posted on arXiv 7 Jun 2021.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Tropical Geometry of Deep Neural Networks](https://mlsanity.com/paper/1805.07091/) (2018)
- [A Tropical Approach to Neural Networks with Piecewise Linear Activations](https://mlsanity.com/paper/1805.08749/) (2018)
- [Machine-Learning Mathematical Structures](https://mlsanity.com/paper/2101.06317/) (2021)
- [Deep-Learning the Landscape](https://mlsanity.com/paper/1706.02714/) (2017)
- [The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning](https://mlsanity.com/paper/1812.02893/) (2018)
- [Quiver Mutations, Seiberg Duality and Machine Learning](https://mlsanity.com/paper/2006.10783/) (2020)
- [Learning Algebraic Structures: Preliminary Investigations](https://mlsanity.com/paper/1905.02263/) (2019)
- [Graph Laplacians, Riemannian Manifolds and their Machine-Learning](https://mlsanity.com/paper/2006.16619/) (2020)
- [Machine-Learning Dessins d'Enfants: Explorations via Modular and Seiberg-Witten Curves](https://mlsanity.com/paper/2004.05218/) (2020)

## Built on by (most cited first, 11 of 11)

- [Machine Learning Calabi-Yau Hypersurfaces](https://mlsanity.com/paper/2112.06350/) (2021)
- [Cluster Algebras: Network Science and Machine Learning](https://mlsanity.com/paper/2203.13847/) (2022)
- [Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality](https://mlsanity.com/paper/2309.05702/) (2023)
- [Machine Learning Clifford invariants of ADE Coxeter elements](https://mlsanity.com/paper/2310.00041/) (2023)
- [Machine Learning Regularization for the Minimum Volume Formula of Toric Calabi-Yau 3-folds](https://mlsanity.com/paper/2310.19276/) (2023)
- [Machine Learning Algebraic Geometry for Physics](https://mlsanity.com/paper/2204.10334/) (2022)
- [Lessons on Datasets and Paradigms in Machine Learning for Symbolic Computation: A Case Study on CAD](https://mlsanity.com/paper/2401.13343/) (2024)
- [Learning 3-Manifold Triangulations](https://mlsanity.com/paper/2405.09610/) (2024)
- [Algebraic Representations for Faster Predictions in Convolutional Neural Networks](https://mlsanity.com/paper/2408.07815/) (2024)
- [Machine Learning Mutation-Acyclicity of Quivers](https://mlsanity.com/paper/2411.04209/) (2024)
- [Calabi-Yau Four/Five/Six-folds as mathbbPnw Hypersurfaces: Machine Learning, Approximation, and Generation](https://mlsanity.com/paper/2311.17146/) (2023)

## Abstract (arXiv)

We apply methods of machine-learning, such as neural networks, manifold learning and image processing, in order to study 2-dimensional amoebae in algebraic geometry and string theory. With the help of embedding manifold projection, we recover complicated conditions obtained from so-called lopsidedness. For certain cases it could even reach ~99% accuracy, in particular for the lopsided amoeba of F0 with positive coefficients which we place primary focus. Using weights and biases, we also find good approximations to determine the genus for an amoeba at lower computational cost. In general, the models could easily predict the genus with over 90% accuracies. With similar techniques, we also investigate the membership problem, and image processing of the amoebae directly.