  Traditional Recurrent Neural Networks assume vectorized data as inputs.
However many data from modern science and technology come in certain structures
such as tensorial time series data. To apply the recurrent neural networks for
this type of data, a vectorisation process is necessary, while such a
vectorisation leads to the loss of the precise information of the spatial or
longitudinal dimensions. In addition, such a vectorized data is not an optimum
solution for learning the representation of the longitudinal data. In this
paper, we propose a new variant of tensorial neural networks which directly
take tensorial time series data as inputs. We call this new variant as
Tensorial Recurrent Neural Network (TRNN). The proposed TRNN is based on tensor
Tucker decomposition.
