$Π-$nets: Deep Polynomial Neural Networks
This addresses the need for more powerful neural network architectures in computer vision and machine learning, offering a novel approach that improves performance in generative and discriminative tasks.
The paper tackles the problem of enhancing the representation power of deep convolutional neural networks by proposing $\\Pi$-Nets, which are polynomial neural networks that output high-order polynomials of the input, and empirically shows they outperform standard DCNNs and achieve state-of-the-art results in tasks like image generation.
Deep Convolutional Neural Networks (DCNNs) is currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful selection of their building blocks (e.g., residual blocks, rectifiers, sophisticated normalization schemes, to mention but a few). In this paper, we propose $Π$-Nets, a new class of DCNNs. $Π$-Nets are polynomial neural networks, i.e., the output is a high-order polynomial of the input. $Π$-Nets can be implemented using special kind of skip connections and their parameters can be represented via high-order tensors. We empirically demonstrate that $Π$-Nets have better representation power than standard DCNNs and they even produce good results without the use of non-linear activation functions in a large battery of tasks and signals, i.e., images, graphs, and audio. When used in conjunction with activation functions, $Π$-Nets produce state-of-the-art results in challenging tasks, such as image generation. Lastly, our framework elucidates why recent generative models, such as StyleGAN, improve upon their predecessors, e.g., ProGAN.