Differentiable Dynamic Programming for Structured Prediction and Attention

Arthur Mensch (1) , Mathieu Blondel (2)

1 PARIETAL - Modelling brain structure, function and variability based on high-field MRI data
2 NTT Communication Science Laboratories

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 back-propagation. 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 combina-torial 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 show-case these instantiations on structured prediction (audio-to-score alignment, NER) and on structured and sparse attention for translation.

Mots clés: NER; DTW; Viterbi; Dynamic programming; smoothing; structured prediction; attention

Domaines: Machine Learning [stat.ML]

Arthur Mensch, Mathieu Blondel. Differentiable Dynamic Programming for Structured Prediction and Attention. 35th International Conference on Machine Learning, Jul 2018, Stockholm, Sweden. ⟨hal-01809550v2⟩