Title: Rotation Invariant Quantization for Model Compression. Abstract: Post-training Neural Network (NN) model compression is an attractive approach for deploying large, memory-consuming models on devices with limited memory resources. In this study, we investigate the theoretical limits of the NN model compression rates using the rate-distortion theory. First, we prove that the highest compression is attained by a simple single-letter (scalar) rotation-invariant solution. Then, based on these insights, we suggest a Rotation-Invariant Quantization (RIQ) technique that finds the optimal single-letter solution efficiently, yielding a different rate at each layer, i.e., mixed-precision quantization.  We rigorously evaluate RIQ and demonstrate its capabilities on various models and tasks. For example, RIQ facilitates $\times 19.4$ and $\times 52.9$ compression ratio on pre-trained VGG dense and pruned models, respectively,  with $<0.4\%$ degradation in accuracy.
Code is available in the supplementary material.