  The significant computational costs of deploying neural networks in
large-scale or resource constrained environments, such as data centers and
mobile devices, has spurred interest in model compression, which can achieve a
reduction in both arithmetic operations and storage memory. Several techniques
have been proposed for reducing or compressing the parameters for feed-forward
and convolutional neural networks, but less is understood about the effect of
parameter compression on recurrent neural networks (RNN). In particular, the
extent to which the recurrent parameters can be compressed and the impact on
short-term memory performance, is not well understood. In this paper, we study
the effect of complexity reduction, through singular value decomposition rank
reduction, on RNN and minimal gated recurrent unit (MGRU) networks for several
tasks. We show that considerable rank reduction is possible when compressing
recurrent weights, even without fine tuning. Furthermore, we propose a
perturbation model for the effect of general perturbations, such as a
compression, on the recurrent parameters of RNNs. The model is tested against a
noiseless memorization experiment that elucidates the short-term memory
performance. In this way, we demonstrate that the effect of compression of
recurrent parameters is dependent on the degree of temporal coherence present
in the data and task. This work can guide on-the-fly RNN compression for novel
environments or tasks, and provides insight for applying RNN compression in
low-power devices, such as hearing aids.
