REALIGN: Regularized Procedure Alignment with Matching Video Embeddings via Partial Gromov-Wasserstein Optimal Transport

Learning from procedural videos remains a core challenge in self-supervised representation learning, as real-world instructional data often contains background segments, repeated actions, and steps presented out of order. Such variability violates the strong monotonicity assumptions underlying many alignment methods. Prior state-of-the-art approaches, such as OPEL, leverage Kantorovich Optimal Transport (KOT) to build frame-to-frame correspondences, but rely solely on feature similarity and fail to capture the higher-order temporal structure of a task. In this paper, we introduce REALIGN, a self-supervised framework for procedure learning based on Regularized Fused Partial Gromov-Wasserstein Optimal Transport (R-FPGWOT). In contrast to KOT, our formulation jointly models visual correspondences and temporal relations under a partial alignment scheme, enabling robust handling of irrelevant frames, repeated actions, and non-monotonic step orders common in instructional videos. To stabilize training, we integrate FPGWOT distances with inter-sequence contrastive learning, avoiding the need for multiple regularizers and preventing collapse to degenerate solutions. Across egocentric (EgoProceL) and third-person (ProceL, CrossTask) benchmarks, REALIGN achieves up to 18.9% average F1-score improvements and over 30% temporal IoU gains, while producing more interpretable transport maps that preserve key-step orderings and filter out noise.