Neural networks can represent functions to solve complex tasks that are difficult -- if not impossible -- to write instructions for by hand, such as understanding language and recognizing objects. Conveniently, we've seen that task performance increases as we use larger networks. However, the increase in computational costs also increases dollars and time required to train and use models. Practitioners are plagued with networks that are too large to store in on-device memory, or too slow for real-world utility. Progress made in network sparsification has presented post-hoc (after training) methods that allow us to remove parameters in a neural network and then fine tune the leftover parameters to achieve a similar task performance.

Neural plasticity is an important functionality of human brain, in which number of neurons and synapses can shrink or expand in response to stimuli throughout the span of life. We model this dynamic learning process as an $L_0$-norm regularized binary optimization problem, in which each unit of a neural network (e.g., weight, neuron or channel, etc.) is attached with a stochastic binary gate, whose parameters determine the level of activity of a unit in the network. At the beginning, only a small portion of binary gates (therefore the corresponding neurons) are activated, while the remaining neurons are in a hibernation mode. As the learning proceeds, some neurons might be activated or deactivated if doing so can be justified by the cost-benefit tradeoff measured by the $L_0$-norm regularized objective. As the training gets mature, the probability of transition between activation and deactivation will diminish until a final hardening stage. We demonstrate that all of these learning dynamics can be modulated by a single parameter $k$ seamlessly. Our neural plasticity network (NPN) can prune or expand a network depending on the initial capacity of network provided by the user; it also unifies dropout (when $k=0$), traditional training of DNNs (when $k=\infty$) and interpolates between these two. To the best of our knowledge, this is the first learning framework that unifies network sparsification and network expansion in an end-to-end training pipeline. Extensive experiments on synthetic dataset and multiple image classification benchmarks demonstrate the superior performance of NPN. We show that both network sparsification and network expansion can yield compact models of similar architectures and of similar predictive accuracies that are close to or sometimes even higher than baseline networks. We plan to release our code to facilitate the research in this area.

While variational dropout approaches have been shown to be effective for network sparsification, they are still suboptimal in the sense that they set the dropout rate for each neuron without consideration of the input data. With such input-independent dropout, each neuron is evolved to be generic across inputs, which makes it difficult to sparsify networks without accuracy loss. To overcome this limitation, we propose adaptive variational dropout whose probabilities are drawn from sparsity-inducing beta-Bernoulli prior. It allows each neuron to be evolved either to be generic or specific for certain inputs, or dropped altogether. Such input-adaptive sparsity- inducing dropout allows the resulting network to tolerate larger degree of sparsity without losing its expressive power by removing redundancies among features. We validate our dependent variational beta-Bernoulli dropout on multiple public datasets, on which it obtains significantly more compact networks than baseline methods, with consistent accuracy improvements over the base networks.