Model compression as constrained optimization, with application to neural nets. Part V: combining compressions

TL;DR

This paper introduces a constrained optimization framework for combining different neural network compression techniques, demonstrating that hybrid approaches can outperform individual methods depending on the model architecture.

Contribution

It formulates a novel optimization approach for combining compression methods and provides algorithms to learn optimal combinations, showing improved neural network compression results.

Findings

Combining compression methods yields better models than single techniques.

Different neural network architectures benefit from different compression combinations.

Hybrid compression can achieve significant size reduction without accuracy loss.

Abstract

Model compression is generally performed by using quantization, low-rank approximation or pruning, for which various algorithms have been researched in recent years. One fundamental question is: what types of compression work better for a given model? Or even better: can we improve by combining compressions in a suitable way? We formulate this generally as a problem of optimizing the loss but where the weights are constrained to equal an additive combination of separately compressed parts; and we give an algorithm to learn the corresponding parts' parameters. Experimentally with deep neural nets, we observe that 1) we can find significantly better models in the error-compression space, indicating that different compression types have complementary benefits, and 2) the best type of combination depends exquisitely on the type of neural net. For example, we can compress ResNets and AlexNet using only 1 bit per weight without error degradation at the cost of adding a few floating point weights. However, VGG nets can be better compressed by combining low-rank with a few floating point weights.