## 6 Conclusions  
We present Hybrid Reduced-CTC to align actions in instructional videos. The main contribution is a hybrid convolutional transformer LSTM to capture long-term temporal dynamics within and between actions, as well as the modified dynamic programming to recursively sum together every possible alignment and reduce the decoding search space by weighting the priority of qualified paths by their visual consistency with existing labels. Our results were found to be competitive in terms of accuracy on four publicly available datasets of different size and difficulty. Based on the confirmed effectiveness of CTC in frame- and transcript-level localization, we plan to further explore its impact on the stability of convergence, due to the observation that that CTC empirically tends to become more difficult to converge than non-CTC models as the length of the input video increases, which suggests more effective under-sampling techniques may be needed to adapt CTC with longer time span. Conceptualization, L.W. and X.W. ; methodology, L.W. ; software, L.W. ; validation, L.W., A.H., and X.W. ; formal analysis, L.W. ; investigation, L.W. ; resources, L.W. ; data curation, L.W. ; writing--original draft preparation, L.W. ; writing--review and editing, A.H.; visualization, L.W. ; supervision, A.H.; project administration, A.H.; funding acquisition, X.W., Y.X., and A.H. All authors have read and agreed to the published version of the manuscript. This research was funded by Fundamental Research Funds for the Central Universities grant numbers WK2150110007 and WK2150110012, and the National Natural Science Foundation of China grant numbers 61772490, 61472382, 61472381, and 61572454. Not applicable. YouTube Instructional is publicly available at [[https://www.di.ens.fr/willow/research/instructionvideos](https://www.di.ens.fr/willow/research/instructionvideos)]([https://www.di.ens.fr/willow/research/instructionvideos](https://www.di.ens.fr/willow/research/instructionvideos)), YouCook2 is publicly available at [[http://youcool2.eecs.umich.edu](http://youcool2.eecs.umich.edu)]([http://youcool2.eecs.umich.edu](http://youcool2.eecs.umich.edu)), Breakfast is publicly available at [[https://serre-lab.clps.brown.edu/resource/breakfast-actions-dataset](https://serre-lab.clps.brown.edu/resource/breakfast-actions-dataset)]([https://serre-lab.clps.brown.edu/resource/breakfast-actions-dataset](https://serre-lab.clps.brown.edu/resource/breakfast-actions-dataset)), and 50 Salads is publicly available at [[http://cvip.computing.dundee.ac.uk/datasets/foodpreparation/50](http://cvip.computing.dundee.ac.uk/datasets/foodpreparation/50) salads]([http://cvip.computing.dundee.ac.uk/datasets/foodpreparation/50](http://cvip.computing.dundee.ac.uk/datasets/foodpreparation/50) salads). We would like to thank the unknown reviewers for their effort and time spent on this work. Hardware platform (a workstation with GeForce GTX Titan Z GPU and 6 GB RAM) and software distribution license (Matlab Deep Learning Toolbox) were provided by the Super Computing Center and Network Information Center of University of Science and Technology of China, respectively. The 50 Salads dataset is distributed by the Computer Vision Image Processing (CVIP) group at the University of Dundee, Scotland, UK; YouTube Instructions dataset is distributed by the Willow project team at the Computer Science Department of the Ecole Normale Superieure (DI ENS), Paris, France. The Breakfast Actions Dataset is distributed by the Serre Lab at Brown University. YouCook2 is distributed by University of Michigan. Figure 8: Frame and alignment accuracy on randomly selected testing videos from Breakfast (**Top**) and YouTube Instructions (**Bottom**), respectively. (Note: there is a background class () in YouTube Instructions, usually present in between neighboring steps, whose fraction varied from 46% to 83% across different tasks, whereas Breakfast is tightly trimmed). Conflicts of Interest: The authors declare no conflicts of interest.