Paper:
Compression-aware Training of Deep Networks
In recent years, great progress has been made in a variety of application domains thanks to the development of increasingly deeper neural networks. Unfortunately, the huge number of units of these networks makes them expensive both computationally and memory-wise. To overcome this, exploiting the fact that deep networks are over-parametrized, several compression strategies have been proposed. These methods, however, typically start from a network that has been trained in a standard manner, without considering such a future compression. In this paper, we propose to explicitly account for compression in the training process. To this end, we introduce a regularizer that encourages the parameter matrix of each layer to have low rank during training. We show that accounting for compression during training allows us to learn much more compact, yet at least as effective, models than state-of-the-art compression techniques.
low rank in the training loss, and rely on a stochastic proximal gradient descent strategy to optimize the network parameters. In essence, and by contrast with methods that aim to learn uncorrelated units to prevent overfitting [5,54,40], we seek to learn correlated ones, which can then easily be pruned in a second phase. Our compression-aware training scheme therefore yields networks that are well adapted to the following post-processing stage. As a consequence, we achieve higher compression rates than the above-mentioned techniques at virtually no loss in prediction accuracy.
Our approach constitutes one of the very few attempts at explicitly training a compact network from scratch. In this context, the work of [4] has proposed to learn correlated units by making use of additional noise outputs. This strategy, however, is only guaranteed to have the desired effect for simple networks and has only been demonstrated on relatively shallow architectures. In the contemporary work [51], units are coordinated via a regularizer acting on all pairs of filters within a layer. While effective, exploiting all pairs can quickly become cumbersome in the presence of large numbers of units. Recently, group sparsity has also been employed to obtain compact networks [2,50]. Such a regularizer, however, acts on individual units, without explicitly aiming to model their redundancies. Here, we show that accounting for interactions between the units within a layer allows us to obtain more compact networks. Furthermore, using such a group sparsity prior in conjunction with our compression-aware strategy lets us achieve even higher compression rates.
We demonstrate the benefits of our approach on several deep architectures, including the 8-layers DecomposeMe network of [1] and the 50-layers ResNet of [23]. Our experiments on ImageNet and ICDAR show that we can achieve compression rates of more than 90%, thus hugely reducing the number of required operations at inference time.

Review:
The authors present a regularization term that encourages weight matrices to be low rank during network training, effectively increasing the compression of the network, and making it possible to explicitly reduce the rank during post-processing, reducing the number of operations required for inference. Overall the paper seems like a good and well written paper on an interesting topic. I have some caveats however: firstly the authors do not mention variational inference, which also explicitly compresses the network (in the literal sense of reducing the number of bits in its description length) and can be used to prune away many weights after training - see 'Practical Variational Inference for Neural Networks' for details. More generally, almost any regularizer provides a form of implicit 'compression-aware training' (that's why they work - simpler models generalize better) and can often be used to prune networks post-hoc. For example a network trained with l1 or l2 regularization will generally end up with many weights very close to 0, which can be removed without greatly altering network performance. I think it's important to clarify this, especially since the authors use an l2 term in addition to their own regularizer during training. They also don't compare seem to compare how well previous low rank post processing works with and without their regulariser, or with other regularisers used in previous work. All of these caveats could be answered by providing more baseline results in the experimental section, demonstrating that training with this particular regulariser does indeed lead to a better accuracy / compression tradeoff than other approaches.
In general I found the results a little hard to interpret, so may be missing something: the graph I wanted to see was a set of curves for accuracy vs compression ratio (either in terms of number of parameters or number of MACs) rather than accuracy against the strength of the regularisation term.  On this graph it should be possible to explicitly compare your approach vs previous regularisers / compressors.