Sequence-to-sequence models, such as attention-based models in automatic speech recognition (ASR), are typically trained to optimize the cross-entropy criterion which corresponds to improving the log-likelihood of the data. However, system performance is usually measured in terms of word error rate (WER), not log-likelihood. Traditional ASR systems benefit from discriminative sequence training which optimizes criteria such as the state-level minimum Bayes risk (sMBR) which are more closely related to WER. In the present work, we explore techniques to train attention-based models to directly minimize expected word error rate. We consider two loss functions which approximate the expected number of word errors: either by sampling from the model, or by using N-best lists of decoded hypotheses, which we find to be more effective than the sampling-based method. In experimental evaluations, we find that the proposed training procedure improves performance by up to 8.2% relative to the baseline system. This allows us to train grapheme-based, uni-directional attention-based models which match the performance of a traditional, state-of-the-art, discriminative sequence-trained system on a mobile voice-search task.
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