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arXiv · 2602.12300

Fast and General Automatic Differentiation for Finite-State Methods

Lucas Ondel Yang·Tina Raissi·Martin Kocour·Pablo Riera·Caio Corro
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Abstract

We propose a new method, that we coined the ``morphism-trick'', to integrate custom implementations of vector-Jacobian products in automatic differentiation softwares, applicable to a wide range of semiring-based computations. Our approach leads to efficient and semiring-agnostic implementations of the backward pass of dynamic programming algorithms. For the particular case of finite-state methods, we introduce an algorithm that computes and differentiates the $\oplus$-sum of all paths' weight of a finite-state automaton. Results show that, with minimal effort from the user, our novel library allows computing the gradient of a function w.r.t. to the weights of a finite state automaton orders of magnitude faster than state-of-the-art automatic differentiation systems. Implementations are made available via an open-source library distributed under a permissive license.

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Lucas Ondel Yang, Tina Raissi, Martin Kocour, Pablo Riera, Caio Corro. 2026-02-11. Fast and General Automatic Differentiation for Finite-State Methods. https://arxiv.org/abs/2602.12300

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