Differentiable Dynamic Programming for Structured Prediction and Attention

Arthur Mensch, Mathieu Blondel
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:3462-3471, 2018.

Abstract

Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, many DP algorithms are non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on structured prediction (audio-to-score alignment, NER) and on structured and sparse attention for translation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-mensch18a, title = {Differentiable Dynamic Programming for Structured Prediction and Attention}, author = {Mensch, Arthur and Blondel, Mathieu}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {3462--3471}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/mensch18a/mensch18a.pdf}, url = {https://proceedings.mlr.press/v80/mensch18a.html}, abstract = {Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, many DP algorithms are non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on structured prediction (audio-to-score alignment, NER) and on structured and sparse attention for translation.} }
Endnote
%0 Conference Paper %T Differentiable Dynamic Programming for Structured Prediction and Attention %A Arthur Mensch %A Mathieu Blondel %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-mensch18a %I PMLR %P 3462--3471 %U https://proceedings.mlr.press/v80/mensch18a.html %V 80 %X Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, many DP algorithms are non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on structured prediction (audio-to-score alignment, NER) and on structured and sparse attention for translation.
APA
Mensch, A. & Blondel, M.. (2018). Differentiable Dynamic Programming for Structured Prediction and Attention. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:3462-3471 Available from https://proceedings.mlr.press/v80/mensch18a.html.

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