  We consider network sparsification as an $L_0$-norm regularized binary
optimization problem, where each unit of a neural network (e.g., weight,
neuron, or channel, etc.) is attached with a stochastic binary gate, whose
parameters are jointly optimized with original network parameters. The
Augment-Reinforce-Merge (ARM), a recently proposed unbiased gradient estimator,
is investigated for this binary optimization problem. Compared to the hard
concrete gradient estimator from Louizos et al., ARM demonstrates superior
performance of pruning network architectures while retaining almost the same
accuracies of baseline methods. Similar to the hard concrete estimator, ARM
also enables conditional computation during model training but with improved
effectiveness due to the exact binary stochasticity. Thanks to the flexibility
of ARM, many smooth or non-smooth parametric functions, such as scaled sigmoid
or hard sigmoid, can be used to parameterize this binary optimization problem
and the unbiasness of the ARM estimator is retained, while the hard concrete
estimator has to rely on the hard sigmoid function to achieve conditional
computation and thus accelerated training. Extensive experiments on multiple
public datasets demonstrate state-of-the-art pruning rates with almost the same
accuracies of baseline methods. The resulting algorithm $L_0$-ARM sparsifies
the Wide-ResNet models on CIFAR-10 and CIFAR-100 while the hard concrete
estimator cannot. The code is public available at
https://github.com/leo-yangli/l0-arm.
