Shaped by What's Missing

Abstract

Understanding how animals transition between behavioral modes is central to neuro-ethology, yet existing tools describe these transitions only at macro resolution. AR-HMM-based segmenters such as Keypoint-MoSeq [Weinreb et al., 2024] summarize transitions in a matrix over discrete syllables after coarsening each trajectory into states; deep autoencoder-based segmenters (VAME, [Luxem et al., 2022]) and topological tools such as Mapper [Singh et al., 2007] also coarsen first, then read transitions off the coarsened object. In every case the resolution of any transition claim inherits from that coarsening. We take the opposite route and recover transition structure directly from the raw trajectory, at the fidelity of individual frames. Using discrete Morse theory on density-weighted point clouds, we extract two topological primitives (DM-primitives) on the behavioral manifold: DM-paths ($H_0$), the low-density corridors the trajectory follows between dense behavioral regions, segmented at the branch points where the behavior subtly changes, and DM-cycles ($H_1$), which encode asymmetric forward and return motor programs whose entry and exit arms occupy spatially distinct routes. Discrete Morse theory motivates why behavioral transitions should leave these primitives in the skeleton, grounding their presence in the geometry of the density landscape rather than in a heuristic. On a rat behavior dataset across three representations (egocentric keypoints, joint configurations, learned intentions), unsupervised Wasserstein clustering of the primitives (DM-WKC) recovers transitions that the AR-HMM, deep-autoencoder, and Mapper baselines miss, at a fidelity coarsening-based methods structurally cannot reach. DM-primitives provide a complementary feature space whose transition information the existing camps leave on the table.