mlsanityData to 7 Oct 2026

Soft-DTW: a Differentiable Loss Function for Time-Series

arXiv 1703.01541 ↗First posted 5 Mar 2017stat.MLcited by 265

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Abstract (arXiv)

We propose in this paper a differentiable learning loss between time series, building upon the celebrated dynamic time warping (DTW) discrepancy. Unlike the Euclidean distance, DTW can compare time series of variable size and is robust to shifts or dilatations across the time dimension. To compute DTW, one typically solves a minimal-cost alignment problem between two time series using dynamic programming. Our work takes advantage of a smoothed formulation of DTW, called soft-DTW, that computes the soft-minimum of all alignment costs. We show in this paper that soft-DTW is a differentiable loss function, and that both its value and gradient can be computed with quadratic time/space complexity (DTW has quadratic time but linear space complexity). We show that this regularization is particularly well suited to average and cluster time series under the DTW geometry, a task for which our proposal significantly outperforms existing baselines. Next, we propose to tune the parameters of a machine that outputs time series by minimizing its fit with ground-truth labels in a soft-DTW sense.

Key facts. Cited by 265 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Mar 2017.

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Citing papers per year: 2021: 28; 2022: 40; 2023: 46; 2024: 38; 2025: 59; 2026: 54.

265 papers.

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  2. 2022Temporal Alignment Networks for Long-term Videocited by 84
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  5. 2021Domain Adaptation for Time Series Forecasting via Attention Sharingcited by 68
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  9. 2023Warpformer: A Multi-scale Modeling Approach for Irregular Clinical Time Seriescited by 54
  10. 2021Learning by Aligning Videos in Timecited by 47
  11. 2023Interpretable and Explainable Logical Policies via Neurally Guided Symbolic Abstractioncited by 45
  12. 2025DBLoss: Decomposition-based Loss Function for Time Series Forecastingcited by 44
38 more
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  5. 2024Multi-granularity Correspondence Learning from Long-term Noisy Videoscited by 34
  6. 2025Patch-wise Structural Loss for Time Series Forecastingcited by 34
  7. 2022Fine-grained Temporal Contrastive Learning for Weakly-supervised Temporal Action Localizationcited by 33
  8. 2023Pre-training for Speech Translation: CTC Meets Optimal Transportcited by 25
  9. 2023Trajectory-Aware Body Interaction Transformer for Multi-Person Pose Forecastingcited by 25
  10. 2022Video-Text Representation Learning via Differentiable Weak Temporal Alignmentcited by 24
  11. 2021Learning Discriminative Prototypes with Dynamic Time Warpingcited by 23
  12. 2021ScanGAN360: A Generative Model of Realistic Scanpaths for 360circ Imagescited by 23
  13. 2022Inductive and Transductive Few-Shot Video Classification via Appearance and Temporal Alignmentscited by 22
  14. 2022Temporal-Viewpoint Transportation Plan for Skeletal Few-shot Action Recognitioncited by 22
  15. 2024Learnable Expansion of Graph Operators for Multi-Modal Feature Fusioncited by 22
  16. 2025Time-o1: Time-Series Forecasting Needs Transformed Label Alignmentcited by 22
  17. 2021Learning with Algorithmic Supervision via Continuous Relaxationscited by 21
  18. 2022Uncertainty-DTW for Time Series and Sequencescited by 21
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  22. 2024Unified Generative and Discriminative Training for Multi-modal Large Language Modelscited by 15
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  25. 2021Learnable Dynamic Temporal Pooling for Time Series Classificationcited by 13
  26. 2022Towards Similarity-Aware Time-Series Classificationcited by 13
  27. 2024SSDM: Scalable Speech Dysfluency Modelingcited by 13
  28. 2025DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignmentcited by 13
  29. 2023Learning Differentiable Logic Programs for Abstract Visual Reasoningcited by 12
  30. 2021Clustering Interval-Censored Time-Series for Disease Phenotypingcited by 11
  31. 2022Context-Aware Sequence Alignment using 4D Skeletal Augmentationcited by 11
  32. 20223D Pose Based Feedback for Physical Exercisescited by 11
  33. 2025Joint Self-Supervised Video Alignment and Action Segmentationcited by 11
  34. 2025Structured Agent Distillation for Large Language Modelcited by 11
  35. 2021Deep Time Series Forecasting with Shape and Temporal Criteriacited by 10
  36. 20213D Skeleton-based Few-shot Action Recognition with JEANIE is not so Na"ivecited by 10
  37. 2024Meet JEANIE: a Similarity Measure for 3D Skeleton Sequences via Temporal-Viewpoint Alignmentcited by 10
  38. 2025FeDaL: Federated Dataset Learning for General Time Series Foundation Modelscited by 10

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