Learning Partial Sequence Alignments through Shared Group Structure

Related sequences often observe different portions of a shared underlying process. Aligning them requires identifying both overlapping regions and correspondences within those regions. Yet individually plausible pairwise matches can be mutually incompatible when considered across a group. We introduce a supervised groupwise partial alignment framework that makes collective correspondence compatibility an explicit learning objective. The framework processes sequence groups jointly to estimate overlap boundaries and monotone alignments, organizing their directed soft correspondences into a common relation. Relations expressible as inner products of shared representations have a positive-semidefinite Gram structure. We therefore penalize the directed group relation’s distance to the symmetric positive-semidefinite cone as a soft compatibility constraint. Experiments on CMU ARCTIC speech and simulated stratigraphic sequences with relative-geological-time ground truth show lower mean alignment error and more accurate overlap estimation than the evaluated classical, differentiable, and learned baselines. Ablations show that the group objective further improves direct and composed correspondence accuracy in both domains. These results support learning partial correspondences according to both their pairwise accuracy and their compatibility with the other alignments in the group.