Recurrent neural networks (RNN) are at the core of modern automatic speech recognition (ASR) systems. In particular, long-short term memory (LSTM) recurrent neural networks have achieved state-of-the-art results in many speech recognition tasks, due to their efficient representation of long and short term dependencies in sequences of inter-dependent features. Nonetheless, internal dependencies within the element composing multidimensional features are weakly considered by traditional real-valued representations. We propose a novel quaternion long-short term memory (QLSTM) recurrent neural network that takes into account both the external relations between the features composing a sequence, and these internal latent structural dependencies with the quaternion algebra. QLSTMs are compared to LSTMs during a memory copy-task and a realistic application of speech recognition on the Wall Street Journal (WSJ) dataset. QLSTM reaches better performances during the two experiments with up to $2.8$ times less learning parameters, leading to a more expressive representation of the information.
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