Deep modeling: Circuit characterization using theory based models in a data driven framework

Analog computational circuits have been demonstrated to provide substantial improvements in power and speed relative to digital circuits, especially for applications requiring extreme parallelism but only modest precision. Deep machine learning is one such area and stands to benefit greatly from analog and mixed-signal implementations. However, even at modest precisions, offsets and non-linearity can degrade system performance. Furthermore, in all but the simplest systems, it is impossible to directly measure the intermediate outputs of all sub-circuits. The result is that circuit designers are unable to accurately evaluate the non-idealities of computational circuits in-situ and are therefore unable to fully utilize measurement results to improve future designs. In this paper we present a technique to use deep learning frameworks to model physical systems. Recently developed libraries like TensorFlow make it possible to use back propagation to learn parameters in the context of modeling circuit behavior. Offsets and scaling errors can be discovered even for sub-circuits that are deeply embedded in a computational system and not directly observable. The learned parameters can be used to refine simulation methods or to identify appropriate compensation strategies. We demonstrate the framework using a mixed-signal convolution operator as an example circuit.