Timezone: »
Normalization techniques have become a basic component in modern convolutional neural networks (ConvNets). In particular, many recent works demonstrate that promoting the orthogonality of the weights helps train deep models and improve robustness. For ConvNets, most existing methods are based on penalizing or normalizing weight matrices derived from concatenating or flattening the convolutional kernels. These methods often destroy or ignore the benign convolutional structure of the kernels; therefore, they are often expensive or impractical for deep ConvNets. In contrast, we introduce a simple and efficient ``Convolutional Normalization'' (ConvNorm) method that can fully exploit the convolutional structure in the Fourier domain and serve as a simple plug-and-play module to be conveniently incorporated into any ConvNets. Our method is inspired by recent work on preconditioning methods for convolutional sparse coding and can effectively promote each layer's channel-wise isometry. Furthermore, we show that our ConvNorm can reduce the layerwise spectral norm of the weight matrices and hence improve the Lipschitzness of the network, leading to easier training and improved robustness for deep ConvNets. Applied to classification under noise corruptions and generative adversarial network (GAN), we show that the ConvNorm improves the robustness of common ConvNets such as ResNet and the performance of GAN. We verify our findings via numerical experiments on CIFAR and ImageNet. Our implementation is available online at \url{https://github.com/shengliu66/ConvNorm}.
Author Information
Sheng Liu (NYU)
Xiao Li (University of Michigan)
Simon Zhai (UC Berkeley)
Chong You (University of California, Berkeley)
Zhihui Zhu (University of Denver)
Carlos Fernandez-Granda (NYU)
Qing Qu (University of Michigan)
More from the Same Authors
-
2021 Spotlight: A Geometric Analysis of Neural Collapse with Unconstrained Features »
Zhihui Zhu · Tianyu Ding · Jinxin Zhou · Xiao Li · Chong You · Jeremias Sulam · Qing Qu -
2022 Poster: Neural Collapse with Normalized Features: A Geometric Analysis over the Riemannian Manifold »
Can Yaras · Peng Wang · Zhihui Zhu · Laura Balzano · Qing Qu -
2022 Poster: Are All Losses Created Equal: A Neural Collapse Perspective »
Jinxin Zhou · Chong You · Xiao Li · Kangning Liu · Sheng Liu · Qing Qu · Zhihui Zhu -
2022 Poster: StrokeRehab: A Benchmark Dataset for Sub-second Action Identification »
Aakash Kaku · Kangning Liu · Avinash Parnandi · Haresh Rengaraj Rajamohan · Kannan Venkataramanan · Anita Venkatesan · Audre Wirtanen · Natasha Pandit · Heidi Schambra · Carlos Fernandez-Granda -
2022 Poster: Error Analysis of Tensor-Train Cross Approximation »
Zhen Qin · Alexander Lidiak · Zhexuan Gong · Gongguo Tang · Michael B Wakin · Zhihui Zhu -
2022 Poster: Revisiting Sparse Convolutional Model for Visual Recognition »
xili dai · Mingyang Li · Pengyuan Zhai · Shengbang Tong · Xingjian Gao · Shao-Lun Huang · Zhihui Zhu · Chong You · Yi Ma -
2021 Poster: A Geometric Analysis of Neural Collapse with Unconstrained Features »
Zhihui Zhu · Tianyu Ding · Jinxin Zhou · Xiao Li · Chong You · Jeremias Sulam · Qing Qu -
2021 Poster: Only Train Once: A One-Shot Neural Network Training And Pruning Framework »
Tianyi Chen · Bo Ji · Tianyu Ding · Biyi Fang · Guanyi Wang · Zhihui Zhu · Luming Liang · Yixin Shi · Sheng Yi · Xiao Tu -
2021 Poster: Rank Overspecified Robust Matrix Recovery: Subgradient Method and Exact Recovery »
Lijun Ding · Liwei Jiang · Yudong Chen · Qing Qu · Zhihui Zhu -
2021 Poster: Adaptive Denoising via GainTuning »
Sreyas Mohan · Joshua L Vincent · Ramon Manzorro · Peter Crozier · Carlos Fernandez-Granda · Eero Simoncelli -
2020 Poster: Early-Learning Regularization Prevents Memorization of Noisy Labels »
Sheng Liu · Jonathan Niles-Weed · Narges Razavian · Carlos Fernandez-Granda -
2020 Poster: Robust Recovery via Implicit Bias of Discrepant Learning Rates for Double Over-parameterization »
Chong You · Zhihui Zhu · Qing Qu · Yi Ma -
2020 Spotlight: Robust Recovery via Implicit Bias of Discrepant Learning Rates for Double Over-parameterization »
Chong You · Zhihui Zhu · Qing Qu · Yi Ma -
2020 Poster: Learning Diverse and Discriminative Representations via the Principle of Maximal Coding Rate Reduction »
Yaodong Yu · Kwan Ho Ryan Chan · Chong You · Chaobing Song · Yi Ma -
2019 : Poster Session »
Jonathan Scarlett · Piotr Indyk · Ali Vakilian · Adrian Weller · Partha P Mitra · Benjamin Aubin · Bruno Loureiro · Florent Krzakala · Lenka Zdeborová · Kristina Monakhova · Joshua Yurtsever · Laura Waller · Hendrik Sommerhoff · Michael Moeller · Rushil Anirudh · Shuang Qiu · Xiaohan Wei · Zhuoran Yang · Jayaraman Thiagarajan · Salman Asif · Michael Gillhofer · Johannes Brandstetter · Sepp Hochreiter · Felix Petersen · Dhruv Patel · Assad Oberai · Akshay Kamath · Sushrut Karmalkar · Eric Price · Ali Ahmed · Zahra Kadkhodaie · Sreyas Mohan · Eero Simoncelli · Carlos Fernandez-Granda · Oscar Leong · Wesam Sakla · Rebecca Willett · Stephan Hoyer · Jascha Sohl-Dickstein · Sam Greydanus · Gauri Jagatap · Chinmay Hegde · Michael Kellman · Jonathan Tamir · Nouamane Laanait · Ousmane Dia · Mirco Ravanelli · Jonathan Binas · Negar Rostamzadeh · Shirin Jalali · Tiantian Fang · Alex Schwing · Sébastien Lachapelle · Philippe Brouillard · Tristan Deleu · Simon Lacoste-Julien · Stella Yu · Arya Mazumdar · Ankit Singh Rawat · Yue Zhao · Jianshu Chen · Xiaoyang Li · Hubert Ramsauer · Gabrio Rizzuti · Nikolaos Mitsakos · Dingzhou Cao · Thomas Strohmer · Yang Li · Pei Peng · Gregory Ongie -
2019 Poster: Distributed Low-rank Matrix Factorization With Exact Consensus »
Zhihui Zhu · Qiuwei Li · Xinshuo Yang · Gongguo Tang · Michael B Wakin -
2019 Poster: A Nonconvex Approach for Exact and Efficient Multichannel Sparse Blind Deconvolution »
Qing Qu · Xiao Li · Zhihui Zhu -
2019 Spotlight: A Nonconvex Approach for Exact and Efficient Multichannel Sparse Blind Deconvolution »
Qing Qu · Xiao Li · Zhihui Zhu -
2019 Poster: A Linearly Convergent Method for Non-Smooth Non-Convex Optimization on the Grassmannian with Applications to Robust Subspace and Dictionary Learning »
Zhihui Zhu · Tianyu Ding · Daniel Robinson · Manolis Tsakiris · René Vidal -
2019 Poster: Data-driven Estimation of Sinusoid Frequencies »
Gautier Izacard · Sreyas Mohan · Carlos Fernandez-Granda -
2018 Poster: Dual Principal Component Pursuit: Improved Analysis and Efficient Algorithms »
Zhihui Zhu · Yifan Wang · Daniel Robinson · Daniel Naiman · René Vidal · Manolis Tsakiris -
2018 Poster: Dropping Symmetry for Fast Symmetric Nonnegative Matrix Factorization »
Zhihui Zhu · Xiao Li · Kai Liu · Qiuwei Li