Papers › $Π-$nets: Deep Polynomial Neural Networks

$Π-$nets: Deep Polynomial Neural Networks

8 Mar 2020arXiv:2003.03828archive 2025-07-28

Grigorios G. Chrysos, Stylianos Moschoglou, Giorgos Bouritsas, Yannis Panagakis, Jiankang Deng, Stefanos Zafeiriou

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.

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grigorisg9gr/polynomial_nets officialmxnetNOASSERTION report
kzkadc/poly-nets mentioned on GitHubpytorchMIT report

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Tasks

Audio ClassificationGraph Representation LearningImage ClassificationImage GenerationPolynomial Neural Networks

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Graph Representation Learning COMA Pi-net-linear Error (mm) 0.474 #1 of 1 Archive leaderboard report
Image Generation CIFAR-10 Pi-net FID 16.79 #48 of 78 Archive leaderboard report

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