This paper considers two challenging trends affecting low-power sensing systems: (1) the applications of interest increasingly involve embedded signals that are very complex to analyze; and (2) the platforms themselves face elevating constraints in terms of energy and possibly cost. Motivated by the complexities of analyzing the application signals, we emphasize the benefits of data-driven approaches. Most notably, these approaches are based on machine learning, as opposed to traditional DSP. We consider how the algorithms lend themselves to specialized signal-analysis platforms. Hardware specialization is well regarded as an approach to address issues of computational efficiency, performance, and capacity, thus playing a key role in leveraging Moore's Law. However, we describe how hardware specialization of machine-learning kernels, this time with an explicit focus on error resilience, can also play a powerful role in enabling system-wide fault tolerance, thereby aiding Moore's Law on another dimension.