While deep neural networks are a highly successful model class, their large memory footprint puts considerable strain on energy consumption, communication bandwidth, and storage requirements. Consequently, model size reduction has become an utmost goal in deep learning. Following the classical bits-back argument, we encode the network weights using a random sample, requiring only a number of bits corresponding to the Kullback-Leibler divergence between the sampled variational distribution and the encoding distribution. By imposing a constraint on the Kullback-Leibler divergence, we are able to explicitly control the compression rate, while optimizing the expected loss on the training set. The employed encoding scheme can be shown to be close to the optimal information-theoretical lower bound, with respect to the employed variational family. On benchmarks LeNet-5/MNIST and VGG-16/CIFAR-10, our approach yields the best test performance for a fixed memory budget, and vice versa, it achieves the highest compression rates for a fixed test performance.

This paper proposes an effective coding scheme for neural networks that encodes a random set of weights from a variational distribution.