Differentiable Dynamic Programming for Structured Prediction and Attention
Résumé
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.
Domaines
Machine Learning [stat.ML]Origine | Fichiers produits par l'(les) auteur(s) |
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