  Deep neural networks (DNN) have shown remarkable success in a variety of
machine learning applications. The capacity of these models (i.e., number of
parameters), endows them with expressive power and allows them to reach the
desired performance. In recent years, there is an increasing interest in
deploying DNNs to resource-constrained devices (i.e., mobile devices) with
limited energy, memory, and computational budget. To address this problem, we
propose Entropy-Constrained Trained Ternarization (EC2T), a general framework
to create sparse and ternary neural networks which are efficient in terms of
storage (e.g., at most two binary-masks and two full-precision values are
required to save a weight matrix) and computation (e.g., MAC operations are
reduced to a few accumulations plus two multiplications). This approach
consists of two steps. First, a super-network is created by scaling the
dimensions of a pre-trained model (i.e., its width and depth). Subsequently,
this super-network is simultaneously pruned (using an entropy constraint) and
quantized (that is, ternary values are assigned layer-wise) in a training
process, resulting in a sparse and ternary network representation. We validate
the proposed approach in CIFAR-10, CIFAR-100, and ImageNet datasets, showing
its effectiveness in image classification tasks.
