A rare 3D human pose in a motion sequence may reflect either a genuine movement or an estimation error, making correction difficult when reference databases contain few comparable examples. We investigate whether local geometric structure can support the recovery and generation of rare configura- tions, using motion-capture sequences from AMASS, which unifies datasets through a common parametric human-body model, together with video-based pose estimates. We develop the cylindrical manifold attention transformer (CMAT), which extends local manifold fitting through geometry- and task- dependent neighborhood weights. For motion correction, Self-Action CMAT draws on comparable windows within a sequence, adjusts their contributions for neighborhood imbalance and temporal dependence, and integrates local geometry with robust temporal regularization. Experiments on perturbed and estimated motions show reductions in position and acceleration errors, with component analyses examining how weighting and temporal processing con- tribute to recovery. The controlled correction comparisons are exploratory and conditional on the selected motion-amplitude bound. For generation, Rarity-preserving CMAT explores locally supported configurations subject to independently calibrated rarity and separation from stored observations. Under common screening criteria, it achieves a higher yield of eligible rare poses than the evaluated generation baselines.

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