Deep polynomial neural networks
File(s)
Author(s)
Type
Journal Article
Abstract
Deep convolutional neural networks (DCNNs) are 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 function approximators based on polynomial expansions. Π-Nets are polynomial neural networks, i.e., the output is a high-order polynomial of the input. The unknown parameters, which are naturally represented by high-order tensors, are estimated through a collective tensor factorization with factors sharing. We introduce three tensor decompositions that significantly reduce the number of parameters and show how they can be efficiently implemented by hierarchical neural networks. We empirically demonstrate that Π-Nets are very expressive 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 three challenging tasks, i.e., image generation, face verification and 3D mesh representation learning. The source code is available at https://github.com/grigorisg9gr/polynomial_nets.
Date Issued
2022-08-01
Date Acceptance
2021-02-11
Citation
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022, 44 (8), pp.4021-4034
ISSN
0162-8828
Publisher
Institute of Electrical and Electronics Engineers
Start Page
4021
End Page
4034
Journal / Book Title
IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume
44
Issue
8
Copyright Statement
Copyright © 2021 IEEE. This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for the watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000820522900001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=a2bf6146997ec60c407a63945d4e92bb
Grant Number
EP/S010203/1
Subjects
Computer Science
Computer Science, Artificial Intelligence
discriminative models
Engineering
Engineering, Electrical & Electronic
face verification
generative models
high-order polynomials
MODEL
Polynomial neural networks
RECOGNITION
Science & Technology
Technology
tensor decompositions
Publication Status
Published
Date Publish Online
2021-02-11