$Π-$nets: Deep Polynomial Neural Networks

Deep Convolutional Neural Networks (DCNNs) is currently the method of choice\nboth for generative, as well as for discriminative learning in computer vision\nand machine learning. The success of DCNNs can be attributed to the careful\nselection of their building blocks (e.g., residual blocks, rectifiers,\nsophisticated normalization schemes, to mention but a few). In this paper, we\npropose $\\Pi$-Nets, a new class of DCNNs. $\\Pi$-Nets are polynomial neural\nnetworks, i.e., the output is a high-order polynomial of the input. $\\Pi$-Nets\ncan be implemented using special kind of skip connections and their parameters\ncan be represented via high-order tensors. We empirically demonstrate that\n$\\Pi$-Nets have better representation power than standard DCNNs and they even\nproduce good results without the use of non-linear activation functions in a\nlarge battery of tasks and signals, i.e., images, graphs, and audio. When used\nin conjunction with activation functions, $\\Pi$-Nets produce state-of-the-art\nresults in challenging tasks, such as image generation. Lastly, our framework\nelucidates why recent generative models, such as StyleGAN, improve upon their\npredecessors, e.g., ProGAN.\n