# Learning 3-Manifold Triangulations

arXiv: https://arxiv.org/abs/2405.09610 · HTML: https://mlsanity.com/paper/2405.09610/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 87 references that are in the map.
- First posted on arXiv 15 May 2024.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [Deep-Learning the Landscape](https://mlsanity.com/paper/1706.02714/) (2017)
- [Quiver Mutations, Seiberg Duality and Machine Learning](https://mlsanity.com/paper/2006.10783/) (2020)
- [Machine Learning Calabi-Yau Hypersurfaces](https://mlsanity.com/paper/2112.06350/) (2021)
- [Bayesian Renormalization](https://mlsanity.com/paper/2305.10491/) (2023)
- [Disentangling a Deep Learned Volume Formula](https://mlsanity.com/paper/2012.03955/) (2020)
- [Learning knot invariants across dimensions](https://mlsanity.com/paper/2112.00016/) (2021)
- [Searching for ribbons with machine learning](https://mlsanity.com/paper/2304.09304/) (2023)
- [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)
- [Group invariant machine learning by fundamental domain projections](https://mlsanity.com/paper/2202.02164/) (2022)
- [Machine-Learning Dessins d'Enfants: Explorations via Modular and Seiberg-Witten Curves](https://mlsanity.com/paper/2004.05218/) (2020)
- [A duality connecting neural network and cosmological dynamics](https://mlsanity.com/paper/2202.11104/) (2022)
- [Cluster Algebras: Network Science and Machine Learning](https://mlsanity.com/paper/2203.13847/) (2022)
- [Metric Flows with Neural Networks](https://mlsanity.com/paper/2310.19870/) (2023)
- [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)
- [Graph Neural Networks and 3-Dimensional Topology](https://mlsanity.com/paper/2305.05966/) (2023)
- [Constructing and Machine Learning Calabi-Yau Five-folds](https://mlsanity.com/paper/2310.15966/) (2023)

## Built on by (most cited first, 1 of 1)

- [Learning the Graphical Nature of Symmetries](https://mlsanity.com/paper/2607.12026/) (2026)

## Abstract (arXiv)

Real 3-manifold triangulations can be uniquely represented by isomorphism signatures. Databases of these isomorphism signatures are generated for a variety of 3-manifolds and knot complements, using SnapPy and Regina, then these language-like inputs are used to train various machine learning architectures to differentiate the manifolds, as well as their Dehn surgeries, via their triangulations. Gradient saliency analysis then extracts key parts of this language-like encoding scheme from the trained models. The isomorphism signature databases are taken from the 3-manifolds' Pachner graphs, which are also generated in bulk for some selected manifolds of focus and for the subset of the SnapPy orientable cusped census with <8 initial tetrahedra. These Pachner graphs are further analysed through the lens of network science to identify new structure in the triangulation representation; in particular for the hyperbolic case, a relation between the length of the shortest geodesic (systole) and the size of the Pachner graph's ball is observed.