mlsanityData to 7 Oct 2026

Differentiable Divergences Between Time Series

arXiv 2010.08354 ↗First posted 16 Oct 2020cs.LG stat.MLcited by 26

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Abstract (arXiv)

Computing the discrepancy between time series of variable sizes is notoriously challenging. While dynamic time warping (DTW) is popularly used for this purpose, it is not differentiable everywhere and is known to lead to bad local optima when used as a "loss". Soft-DTW addresses these issues, but it is not a positive definite divergence: due to the bias introduced by entropic regularization, it can be negative and it is not minimized when the time series are equal. We propose in this paper a new divergence, dubbed soft-DTW divergence, which aims to correct these issues. We study its properties; in particular, under conditions on the ground cost, we show that it is a valid divergence: it is non-negative and minimized if and only if the two time series are equal. We also propose a new "sharp" variant by further removing entropic bias. We showcase our divergences on time series averaging and demonstrate significant accuracy improvements compared to both DTW and soft-DTW on 84 time series classification datasets.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). First posted on arXiv 16 Oct 2020.

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Citing papers per year: 2021: 4; 2022: 7; 2023: 5; 2024: 2; 2025: 2; 2026: 6.

26 papers.

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  1. 2021ScanGAN360: A Generative Model of Realistic Scanpaths for 360circ Imagescited by 23
  2. 2021Learning with Algorithmic Supervision via Continuous Relaxationscited by 21
  3. 2022Uncertainty-DTW for Time Series and Sequencescited by 21
  4. 2022Learning Temporal Point Processes for Efficient Retrieval of Continuous Time Event Sequencescited by 14
  5. 2021Deep Time Series Forecasting with Shape and Temporal Criteriacited by 10
  6. 2022Closed-Form Diffeomorphic Transformations for Time Series Alignmentcited by 7
  7. 2022A Convolutional-Attentional Neural Framework for Structure-Aware Performance-Score Synchronizationcited by 5
  8. 2023Deep Declarative Dynamic Time Warping for End-to-End Learning of Alignment Pathscited by 5
  9. 2024SCORE: Self-supervised Correspondence Fine-tuning for Improved Content Representationscited by 3
  10. 2025Diffeomorphic Temporal Alignment Nets for Time-series Joint Alignment and Averagingcited by 3
  11. 2021An Empirical Study of Graph-Based Approaches for Semi-Supervised Time Series Classificationcited by 2
  12. 2023OTW: Optimal Transport Warping for Time Seriescited by 2
14 more
  1. 2024LASER: Learning by Aligning Self-supervised Representations of Speech for Improving Content-related Taskscited by 2
  2. 2022Time Series Forecasting Models Copy the Past: How to Mitigatecited by 1
  3. 2023Retrieving Continuous Time Event Sequences using Neural Temporal Point Processes with Learnable Hashingcited by 1
  4. 2023Revisiting the Entropy Semiring for Neural Speech Recognitioncited by 1
  5. 2025Measuring Time-Series Dataset Similarity using Wasserstein Distancecited by 1
  6. 2022Measuring dissimilarity with diffeomorphism invariancecited by 0
  7. 2022Efficient Forecasting of Large Scale Hierarchical Time Series via Multilevel Clusteringcited by 0
  8. 2023DPP-TTS: Diversifying prosodic features of speech via determinantal point processescited by 0
  9. 2026STAER: Temporal Aligned Rehearsal for Continual Spiking Neural Networkcited by 0
  10. 2026Position-invariant Fine-tuning of Speech Enhancement Models with Self-supervised Speech Representationscited by 0
  11. 2026SoftDTW-CUDA-Torch: Memory-Efficient GPU-Accelerated Soft Dynamic Time Warping for PyTorchcited by 0
  12. 2026Deep Time-Series Forecasting in 10 Years: A Surveycited by 0
  13. 2026Soft-MSM: Differentiable Context-Aware Elastic Alignment for Time Seriescited by 0
  14. 2026Distill Locally, Schedule Globally: Flow Maps for Few-Step Text-to-Speechcited by 0