Condensing CNNs with Partial Differential Equations

Convolutional neural networks (CNNs) rely on the depth of the architecture to obtain complex features. It results in computationally expensive models for low-resource IoT devices. Convolutional operators are local and restricted in the receptive field, which increases with depth. We explore partial differential equations (PDEs) that offer a global receptive field without the added overhead of maintaining large kernel convolutional filters. We propose a new feature layer, called the Global layer, that enforces PDE constraints on the feature maps, resulting in rich features. These constraints are solved by embedding iterative schemes in the network. The proposed layer can be embedded in any deep CNN to transform it into a shallower network. Thus, resulting in compact and computationally efficient architectures achieving similar performance as the original network. Our experimental evaluation demonstrates that architectures with global layers require 2 - 5 × less computational and storage budget without any significant loss in performance.