Due to challenging efficiency limits facing conventional and unconventional electronic architectures, information processors based on photonics have attracted renewed interest. Research communities have yet to settle on definitive techniques to describe the performance of this class of information processors. Photonic systems are different from electronic ones, so the existing concepts of computer performance measurement cannot necessarily apply. In this manuscript, we attempt to quantify the power use of photonic neural networks with state-of-the-art and future hardware. We derive scaling laws, physical limits, and new platform performance metrics. We find that overall performance is regime-like, which means that energy efficiency characteristics of a photonic processor can be completely described by no less than seven performance numbers. The introduction of these analytical strategies provides a much needed foundation for quantitative roadmapping and commercial value assignment for silicon photonic neural networks.