  Recently, a new recurrent neural network (RNN) named the Legendre Memory Unit
(LMU) was proposed and shown to achieve state-of-the-art performance on several
benchmark datasets. Here we leverage the linear time-invariant (LTI) memory
component of the LMU to construct a simplified variant that can be parallelized
during training (and yet executed as an RNN during inference), thus overcoming
a well known limitation of training RNNs on GPUs. We show that this
reformulation that aids parallelizing, which can be applied generally to any
deep network whose recurrent components are linear, makes training up to 200
times faster. Second, to validate its utility, we compare its performance
against the original LMU and a variety of published LSTM and transformer
networks on seven benchmarks, ranging from psMNIST to sentiment analysis to
machine translation. We demonstrate that our models exhibit superior
performance on all datasets, often using fewer parameters. For instance, our
LMU sets a new state-of-the-art result on psMNIST, and uses half the parameters
while outperforming DistilBERT and LSTM models on IMDB sentiment analysis.
