  The enormous size of modern deep neural networks makes it challenging to
deploy those models in memory and communication limited scenarios. Thus,
compressing a trained model without a significant loss in performance has
become an increasingly important task. Tremendous advances has been made
recently, where the main technical building blocks are parameter pruning,
parameter sharing (quantization), and low-rank factorization. In this paper, we
propose principled approaches to improve upon the common heuristics used in
those building blocks, namely pruning and quantization.
  We first study the fundamental limit for model compression via the rate
distortion theory. We bring the rate distortion function from data compression
to model compression to quantify this fundamental limit. We prove a lower bound
for the rate distortion function and prove its achievability for linear models.
Although this achievable compression scheme is intractable in practice, this
analysis motivates a novel model compression framework. This framework provides
a new objective function in model compression, which can be applied together
with other classes of model compressor such as pruning or quantization.
Theoretically, we prove that the proposed scheme is optimal for compressing
one-hidden-layer ReLU neural networks. Empirically, we show that the proposed
scheme improves upon the baseline in the compression-accuracy tradeoff.
