dDTW Toolbox

The dDTW Toolbox provides PyTorch losses for differentiable sequence alignment. It implements a unified graph-based dynamic-programming framework for weakly supervised sequence learning problems where target order is known but frame-level timing is not. The toolbox is based on the accompanying paper [1] and a prior article. [2]

References

[1] Johannes Zeitler and Meinard Müller. dDTW: A Unified and Efficient Toolbox for Differentiable Sequence Alignment. Submitted 2026.

[2] Johannes Zeitler and Meinard Müller. A Unified Perspective on CTC and SDTW Using Differentiable DTW. IEEE Transactions on Audio, Speech and Language Processing, 34:936-951, 2026.

In the paper, alignment losses are represented as path-cost aggregation on a weighted directed acyclic graph (DAG). Vertices represent possible correspondences between sequence elements, while step sizes, edge weights, boundary conditions, local costs, and aggregation operators determine the actual objective. Classical DTW [3], Soft-DTW [4], smoothDTW [5], sparseDTW [6], subsequence alignment [7], partial matching [8], and CTC [9] are recovered as particular graph configurations.

User Guide

• Installation
  • Runtime Requirements
  • CUDA Backend
  • Conda CUDA Environments
  • Documentation Requirements
• Quickstart
  • Soft-DTW Loss
  • CTC-Style Loss
  • Precomputed Cost Matrices
  • Variable-Length Batches
  • Backend Choice
• Core Concepts
  • Definition of the Alignment Graph
  • Graph-Based Alignment Cost
  • Summary: Toolbox Mapping
• Built-In Variants
  • Parameter Overview
  • DTW and Differentiable DTW Variants
  • Subsequence (S)DTW
  • Partial Matching
  • CTC
• Architecture
  • Frontend
  • Cost Matrix
  • Backend Dispatch
  • Backend Module Structure

Reference

• API Reference
  • Package Root
  • Core Loss
  • Loss Variants
• Citation

References

[1]

J. Zeitler and M. Müller, “dDTW: A Unified and Efficient Toolbox for Differentiable Sequence Alignment,” submitted, 2026.

[2]

J. Zeitler and M. Müller, “A Unified Perspective on CTC and SDTW Using Differentiable DTW”, IEEE Transactions on Audio, Speech and Language Processing”, 34:936-951, 2026.

[3]

M. Müller, Fundamentals of Music Processing: Using Python and Jupyter Notebooks, 2nd ed. Springer, 2021.

[4]

M. Cuturi and M. Blondel, “Soft-DTW: a Differentiable Loss Function for Time-Series,” in Proceedings of the International Conference on Machine Learning (ICML), Sydney, NSW, Australia, 2017, pp. 894-903.

[5]

I. Hadji, K. G. Derpanis, and A. D. Jepson, “Representation Learning via Global Temporal Alignment and Cycle-Consistency,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Virtual, 2021, pp. 11068-11077.

[6]

A. Mensch and M. Blondel, “Differentiable Dynamic Programming for Structured Prediction and Attention,” in Proceedings of the International Conference on Machine Learning (ICML), Stockholm, Sweden, 2018, pp. 3459-3468.

[7]

J. Zeitler and M. Muller, “Subsequence SDTW: Differentiable Alignment with Flexible Boundary Conditions,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Barcelona, Spain, 2026.

[8]

P. A. Pevzner, Computational Molecular Biology: An Algorithmic Approach. MIT Press, 2000.

[9]

A. Graves, S. Fernandez, F. J. Gomez, and J. Schmidhuber, “Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks,” in Proceedings of the International Conference on Machine Learning (ICML), Pittsburgh, Pennsylvania, USA, 2006, pp. 369-376.