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In this work, we consider the problem of sequence-to-sequence alignment forsignals containing outliers. Assuming the absence of outliers, the standardDynamic Time Warping (DTW) algorithm efficiently computes the optimal alignmentbetween two (generally) variable-length sequences. While DTW is robust totemporal shifts and dilations of the signal, it fails to align sequences in ameaningful way in the presence of outliers that can be arbitrarily interspersedin the sequences. To address this problem, we introduce Drop-DTW, a novelalgorithm that aligns the common signal between the sequences whileautomatically dropping the outlier elements from the matching. The entireprocedure is implemented as a single dynamic program that is efficient andfully differentiable. In our experiments, we show that Drop-DTW is a robustsimilarity measure for sequence retrieval and demonstrate its effectiveness asa training loss on diverse applications. With Drop-DTW, we address temporalstep localization on instructional videos, representation learning from noisyvideos, and cross-modal representation learning for audio-visual retrieval andlocalization. In all applications, we take a weakly- or unsupervised approachand demonstrate state-of-the-art results under these settings.

Drop-DTW: Aligning Common Signal Between Sequences While Dropping Outliers