  For successful deployment of deep neural networks on
highly--resource-constrained devices (hearing aids, earbuds, wearables), we
must simplify the types of operations and the memory/power resources used
during inference. Completely avoiding inference-time floating-point operations
is one of the simplest ways to design networks for these highly-constrained
environments. By discretizing both our in-network non-linearities and our
network weights, we can move to simple, compact networks without floating point
operations, without multiplications, and avoid all non-linear function
computations. Our approach allows us to explore the spectrum of possible
networks, ranging from fully continuous versions down to networks with bi-level
weights and activations. Our results show that discretization can be done
without loss of performance and that we can train a network that will
successfully operate without floating-point, without multiplication, and with
less RAM on both regression tasks (auto encoding) and multi-class
classification tasks (ImageNet). The memory needed to deploy our discretized
networks is less than one third of the equivalent architecture that does use
floating-point operations.
