  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, while retaining competitive accuracies of the
original networks.
