GPU-Accelerated Forward-Backward Algorithm with Application to Lattice-Free MMI

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Lucas Ondel, Léa-Marie Lam-Yee-Mui, Martin Kocour, Caio Filippo Corro, Lukás Burget

Published: 2022, Last Modified: 26 Jan 2026ICASSP 2022EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: We propose to express the forward-backward algorithm in terms of operations between sparse matrices in a specific semiring. This new perspective naturally leads to a GPU-friendly algorithm which is easy to implement in Julia or any programming languages with native support of semiring algebra. We use this new implementation to train a TDNN with the LF-MMI objective function and we compare the training time of our system with PyChain—a recently introduced C++/CUDA implementation of the LF-MMI loss. Our implementation is about two times faster while not having to use any approximation such as the "leaky-HMM".