# TriSearch: Learning to Optimize Triangulations via Bistellar Flips

arXiv: https://arxiv.org/abs/2605.30220 · HTML: https://mlsanity.com/paper/2605.30220/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 23 of its 48 references that are in the map.
- First posted on arXiv 28 May 2026.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

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

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Reinforcement Learning for Combinatorial Optimization: A Survey](https://mlsanity.com/paper/2003.03600/) (2020)
- [Go-Explore: a New Approach for Hard-Exploration Problems](https://mlsanity.com/paper/1901.10995/) (2019)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [Learning to Perform Local Rewriting for Combinatorial Optimization](https://mlsanity.com/paper/1810.00337/) (2018)
- [Learning Improvement Heuristics for Solving Routing Problems](https://mlsanity.com/paper/1912.05784/) (2019)
- [Simplicial Neural Networks](https://mlsanity.com/paper/2010.03633/) (2020)
- [Exploratory Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1909.04063/) (2019)
- [Learning to Control Local Search for Combinatorial Optimization](https://mlsanity.com/paper/2206.13181/) (2022)
- [What makes math problems hard for reinforcement learning: a case study](https://mlsanity.com/paper/2408.15332/) (2024)
- [Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformers](https://mlsanity.com/paper/2507.03732/) (2025)

## Abstract (arXiv)

We introduce TriSearch, a reinforcement learning framework for optimizing objectives over triangulations of a polytope via bistellar flips. The key idea is a circuit-supported subtriangulation action representation: feasible flips are encoded by their supporting circuit and realized local subtriangulation, enabling a learned policy to rank them using local geometric and combinatorial features. This yields a dimension-agnostic interface and enables efficient traversal of the flip graph without explicit enumeration of the full triangulation space. Instantiated in 3D and 4D, TriSearch generalizes zero-shot from small training instances to larger polytopes with exponentially larger search spaces. It achieves top performance on metric objectives in 3D and, in 4D, discovers more distinct Fine, Regular, Star triangulations of reflexive polytopes, corresponding to Calabi-Yau threefolds, than existing samplers under a fixed budget.