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TriSearch, a reinforcement learning framework, optimizes polytope triangulations by learning to select bistellar flips based on local geometric and combinatorial features encoded within circuit-supported subtriangulation action representations. This approach avoids explicit enumeration of the full triangulation space, enabling efficient traversal of the flip graph. Experiments in 3D and 4D show that TriSearch generalizes zero-shot to larger polytopes and outperforms existing samplers in discovering distinct triangulations of reflexive polytopes relevant to Calabi-Yau threefold construction.
RL can now discover more diverse triangulations of complex polytopes than specialized geometric algorithms, opening avenues for automated exploration in fields like Calabi-Yau manifold construction.
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.
