REMAP: Regularized Matching and Partial Alignment of Video Embeddings

Real-world instructional videos are long, noisy, and often contain extended background segments, repeated actions, and execution variability that do not correspond to meaningful procedural steps. We propose **REMAP**, an unsupervised framework for procedure learning based on *Regularized Fused Partial Gromov-Wasserstein Optimal Transport*. REMAP relaxes balanced transport constraints, allowing non-informative or redundant frames to remain unmatched through partial transport. The formulation jointly models semantic similarity and temporal structure, while incorporating Laplacian-based smoothness and structural regularization to prevent degenerate alignments and reduce background interference. We evaluate REMAP on large-scale egocentric and third-person benchmarks. The method consistently outperforms state-of-the-art approaches, achieving up to **11.6\% (+4.45pp)** F1 and **19.6\% (+4.73pp)** IoU improvements on EgoProceL, and an average **41\% (+17.15pp)** F1 gain on ProceL and CrossTask. These results highlight the importance of partial alignment in handling real-world procedural variability and demonstrate that REMAP provides a robust and scalable approach for instructional video understanding.