  Large-scale deep neural networks are both memory intensive and
computation-intensive, thereby posing stringent requirements on the computing
platforms. Hardware accelerations of deep neural networks have been extensively
investigated in both industry and academia. Specific forms of binary neural
networks (BNNs) and stochastic computing based neural networks (SCNNs) are
particularly appealing to hardware implementations since they can be
implemented almost entirely with binary operations. Despite the obvious
advantages in hardware implementation, these approximate computing techniques
are questioned by researchers in terms of accuracy and universal applicability.
Also it is important to understand the relative pros and cons of SCNNs and BNNs
in theory and in actual hardware implementations. In order to address these
concerns, in this paper we prove that the "ideal" SCNNs and BNNs satisfy the
universal approximation property with probability 1 (due to the stochastic
behavior). The proof is conducted by first proving the property for SCNNs from
the strong law of large numbers, and then using SCNNs as a "bridge" to prove
for BNNs. Based on the universal approximation property, we further prove that
SCNNs and BNNs exhibit the same energy complexity. In other words, they have
the same asymptotic energy consumption with the growing of network size. We
also provide a detailed analysis of the pros and cons of SCNNs and BNNs for
hardware implementations and conclude that SCNNs are more suitable for
hardware.
