  Recurrent neural networks (RNNs) are powerful architectures to model
sequential data, due to their capability to learn short and long-term
dependencies between the basic elements of a sequence. Nonetheless, popular
tasks such as speech or images recognition, involve multi-dimensional input
features that are characterized by strong internal dependencies between the
dimensions of the input vector. We propose a novel quaternion recurrent neural
network (QRNN), alongside with a quaternion long-short term memory neural
network (QLSTM), that take into account both the external relations and these
internal structural dependencies with the quaternion algebra. Similarly to
capsules, quaternions allow the QRNN to code internal dependencies by composing
and processing multidimensional features as single entities, while the
recurrent operation reveals correlations between the elements composing the
sequence. We show that both QRNN and QLSTM achieve better performances than RNN
and LSTM in a realistic application of automatic speech recognition. Finally,
we show that QRNN and QLSTM reduce by a maximum factor of 3.3x the number of
free parameters needed, compared to real-valued RNNs and LSTMs to reach better
results, leading to a more compact representation of the relevant information.
