In this paper, we study training of automatic speech recognition system in a weakly supervised setting where the order of words in transcript labels of the audio training data is not known. We train a word-level acoustic model which aggregates the distribution of all output frames using LogSumExp operation and uses a cross-entropy loss to match with the ground-truth words distribution. Using the pseudo-labels generated from this model on the training set, we then train a letter-based acoustic model using Connectionist Temporal Classification loss. Our system achieves 2.3%/4.6% on test-clean/test-other subsets of LibriSpeech, which closely matches with the supervised baseline's performance.
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