Convolutional Neural Networks Demystified: A Matched Filtering Perspective-Based Tutorial

Abstract

Deep neural networks (DNNs) and especially convolutional neural networks (CNNs) have revolutionized the way we approach the analysis of large quantities of data. However, the largely ad hoc fashion of their development, albeit one reason for their rapid success, has also brought to light the intrinsic limitations of CNNs—in particular, those related to their black box nature. In addition, the ability to “explain” both the way such systems behave and the results they produce is increasingly becoming an imperative in many practical applications. Therefore, it would be particularly useful to establish physically meaningful mechanisms underpinning the operation of CNNs, thus helping to resolve the issue of interpretability of the processing steps and explain their input-output relationship. To this end, we revisit the operation of CNNs from first principles and show that their very backbone—the convolution operation—represents a matched filter which examines the input for the presence of characteristic patterns in data. Our treatment is based on temporal signals, naturally generated by physical sensors, which admit rigorous analysis through systems science. This serves as a vehicle for a unifying account on the overall functionality of CNNs, whereby both the convolution-activation-pooling chain and learning strategies are shown to admit a compact and elegant interpretation under the umbrella of matched filtering. In addition to helping reveal the physical principles underpinning CNNs and providing an intuitive understanding of their operation, the treatment of CNNs from a matched filtering perspective is also shown to offer a platform to support further developments in this area.