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Our model architecture consists of a long-term feature extractor and two branches: the Action Segmentation Branch (ASB) and the Boundary Regression Branch (BRB). The long-term feature extractor provides shared features for the two branches with a wide temporal receptive field. The ASB classifies video frames with action classes, while the BRB regresses the action boundary probabilities. The action boundaries predicted by the BRB refine the output from the ASB, which results in a significant performance improvement. Our contributions are three-fold: (i) We propose a framework for temporal action segmentation, the ASRF, which divides temporal action segmentation into frame-wise action classification and action boundary regression. Our framework refines frame-level hypotheses of action classes using predicted action boundaries. (ii) We propose a loss function for smoothing the transition of action probabilities, and analyze combinations of various loss functions for temporal action segmentation. (iii) Our framework outperforms state-of-the-art methods on three challenging datasets, offering an improvement of up to 13.7% in terms of segmental edit distance and up to 16.1% in terms of segmental F1 score. 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