We study self-supervised procedure learning, which discovers key steps and their order from a set of unlabeled videos. Previous methods typically learn frame-to-frame correspondences between videos before determining key steps and their order. However, their performance often suffers from order variations, background/redundant frames, and repeated actions. To overcome these challenges, we propose a self-supervised framework, which utilizes a fused Gromov-Wasserstein optimal transport with a structural prior for frame-to-frame mapping. However, optimizing only for the above temporal alignment may lead to degenerate solutions, where all frames are mapped to a small cluster in the embedding space and thus every video is assigned to just one key step. To address that issue, we integrate a contrastive regularization, which maps different frames to various points, avoiding trivial solutions. Finally, extensive experiments on egocentric and third-person benchmarks demonstrate our superior performance over prior works, including OPEL which relies on a classical Kantorovich optimal transport with an optimality prior.

We introduce a novel approach for simultaneous self-supervised video alignment and action segmentation based on a unified optimal transport framework. In particular, we first tackle self-supervised video alignment by developing a fused Gromov-Wasserstein optimal transport formulation with a structural prior, which trains efficiently on GPUs and needs only a few iterations for solving the optimal transport problem. Our single-task method achieves the state-of-the-art performance on multiple video alignment benchmarks and outperforms VAVA, which relies on a traditional Kantorovich optimal transport formulation with an optimality prior. Furthermore, we extend our approach by proposing a unified optimal transport framework for joint self-supervised video alignment and action segmentation, which requires training and storing a single model and saves both time and memory consumption as compared to two different single-task models. Extensive evaluations on several video alignment and action segmentation datasets demonstrate that our multi-task method achieves comparable video alignment yet superior action segmentation results over previous methods in video alignment and action segmentation respectively. Finally, to the best of our knowledge, this is the first work to unify video alignment and action segmentation into a single model. Our code is available on our research website: https://retrocausal.ai/research/.