# Phylogenetic Inference

CRISPR lineage recorders can trace the ancestry of hundreds of thousands of cells, but likelihood-based tree building searches over tree topologies and becomes impractical at that scale. HERACLES places each cell as a point in hyperbolic space, scores the CRISPR editing likelihood of sampled cell quartets, and optimizes those coordinates by gradient descent before a single neighbour-joining pass yields the full tree. On simulated benchmarks its reconstruction error is lower than LAML, Startle-NNI and distance-based methods, and it handles 150,000 cells in about four hours on one GPU.

CRISPR lineage recorders can trace the ancestry of hundreds of thousands of cells, but likelihood-based tree building searches over tree topologies and becomes impractical at that scale. HERACLES places each cell as a point in hyperbolic space, scores the CRISPR editing likelihood of sampled cell quartets, and optimizes those coordinates by gradient descent before a single neighbour-joining pass yields the full tree. On simulated benchmarks its reconstruction error is lower than LAML, Startle-NNI and distance-based methods, and it handles 150,000 cells in about four hours on one GPU.