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Orthogonal Convolutional Neural Networks (1911.12207v3)

Published 27 Nov 2019 in cs.CV

Abstract: Deep convolutional neural networks are hindered by training instability and feature redundancy towards further performance improvement. A promising solution is to impose orthogonality on convolutional filters. We develop an efficient approach to impose filter orthogonality on a convolutional layer based on the doubly block-Toeplitz matrix representation of the convolutional kernel instead of using the common kernel orthogonality approach, which we show is only necessary but not sufficient for ensuring orthogonal convolutions. Our proposed orthogonal convolution requires no additional parameters and little computational overhead. This method consistently outperforms the kernel orthogonality alternative on a wide range of tasks such as image classification and inpainting under supervised, semi-supervised and unsupervised settings. Further, it learns more diverse and expressive features with better training stability, robustness, and generalization. Our code is publicly available at https://github.com/samaonline/Orthogonal-Convolutional-Neural-Networks.

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Authors (4)
  1. Jiayun Wang (21 papers)
  2. Yubei Chen (32 papers)
  3. Rudrasis Chakraborty (30 papers)
  4. Stella X. Yu (65 papers)
Citations (171)

Summary

  • The paper presents an orthogonal regularization method that enhances CNN convergence and reduces feature redundancy.
  • The paper leverages a matrix-based view of convolution to achieve a uniform spectral distribution, yielding an IS of 8.63 and FID of 11.75 on CIFAR-10.
  • The paper demonstrates improved adversarial robustness by approximating a 1-Lipschitz function through enforced orthogonality.

Overview of Orthogonal Convolutional Neural Networks

The paper "Orthogonal Convolutional Neural Networks" presents an integrated approach to enhance the performance of Convolutional Neural Networks (CNNs) by applying orthogonality constraints to convolutional operations. The paper focuses on improving the convergence speed and robustness of Generative Adversarial Networks (GANs) through orthogonal regularization applied to convolutional kernels, which is accomplished by enforcing orthogonality in the transformation matrices of the convolutional layers.

Analysis of Convolutional Layer Transformations

At the heart of this work is the analysis of a convolutional layer that transforms input XX to output YY using a learnable kernel KK. By representing the convolution operation as a linear matrix multiplication, the authors highlight the importance of the spectrum of the transformation, K\mathcal{K}. They point out that conventional CNNs often suffer from imbalanced convolutional spectra, leading to varied scaling of inputs and potential issues with gradient stability.

The proposed orthogonality-enforcing approach demonstrates that maintaining a uniform K\mathcal{K} spectrum can significantly reduce feature redundancy. This reduction in redundancy paves the way for improved performance across various tasks, including image classification, retrieval, and generation, as well as enhanced robustness to adversarial perturbations.

Performance Evaluation in Image Generation

In the context of image generation, the authors evaluate the performance of their orthogonally regularized convolutional neural networks (OCNNs) using GANs trained on the CIFAR-10 dataset. It is evidenced that OCNNs achieve superior convergence rates and performance metrics compared to existing GAN architectures. Specifically, the model achieves an Inception Score (IS) of 8.63 and a Fréchet Inception Distance (FID) of 11.75, outperforming the baseline AutoGAN. These results substantiate the potential of orthogonal regularization to consistently enhance generative modeling capabilities.

Enhancing Robustness Against Adversarial Attacks

One of the notable contributions of the paper is the investigation of OCNNs' robustness to adversarial attacks. By creating a uniform spectrum that approximates a $1$-Lipschitz function, the OCNNs demonstrate increased resilience. Experiments with a simple black-box attack method reveal that adversaries require significantly more queries and greater time to achieve a similar success rate compared to baseline models. This robustness is attributed to the structured orthogonality that impedes rapid destabilization of the model under targeted perturbations.

Implications and Future Work

The findings of this paper have compelling implications for both theoretical advancements and practical applications in the field of neural networks. The application of orthogonality to alleviate gradient instability and feature redundancy addresses key challenges in deep learning, particularly as models become increasingly deeper and more complex. These insights could lead to new regularization techniques that maintain computational efficiency without compromising robustness or performance.

In terms of future developments, further exploration into orthogonality constraints across different model architectures and datasets could provide a broader understanding of its efficacy. Additionally, integrating these orthogonal regularizers with other state-of-the-art optimization techniques may offer a balanced approach to tackling complex, high-dimensional learning tasks.

Overall, the contribution of orthogonal convolutional neural networks is a noteworthy advancement toward more resilient and efficient deep learning models, steering the field towards more robust AI systems.