arXiv:2602.12300 · v2

Fast and General Automatic Differentiation for Finite-State Methods

首次提交 2026-02-11 18:36

版本更新 2026-11-06 18:03

雷达观测 2026-11-09 11:19

摘要

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.