  The paper proposes a numerically stable recursive algorithm for the exact
computation of the linear-chain conditional random field gradient. It operates
as a forward algorithm over the log-domain expectation semiring and has the
purpose of enhancing memory efficiency when applied to long observation
sequences. Unlike the traditional algorithm based on the forward-backward
recursions, the memory complexity of our algorithm does not depend on the
sequence length. The experiments on real data show that it can be useful for
the problems which deal with long sequences.
