Almost-Orthogonal Layers for Efficient General-Purpose Lipschitz Networks

• URL: http://arxiv.org/abs/2208.03160v2
• Date: Fri, 1 Sep 2023 08:13:48 GMT
• Title: Almost-Orthogonal Layers for Efficient General-Purpose Lipschitz Networks
• Authors: Bernd Prach and Christoph H. Lampert
• Abstract summary: We propose a new technique for constructing deep networks with a small Lipschitz constant. It provides formal guarantees on the Lipschitz constant, it is easy to implement and efficient to run, and it can be combined with any training objective and optimization method. Experiments and ablation studies in the context of image classification with certified robust accuracy confirm that AOL layers achieve results that are on par with most existing methods.
• Score: 23.46030810336596
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It is a highly desirable property for deep networks to be robust against small input changes. One popular way to achieve this property is by designing networks with a small Lipschitz constant. In this work, we propose a new technique for constructing such Lipschitz networks that has a number of desirable properties: it can be applied to any linear network layer (fully-connected or convolutional), it provides formal guarantees on the Lipschitz constant, it is easy to implement and efficient to run, and it can be combined with any training objective and optimization method. In fact, our technique is the first one in the literature that achieves all of these properties simultaneously. Our main contribution is a rescaling-based weight matrix parametrization that guarantees each network layer to have a Lipschitz constant of at most 1 and results in the learned weight matrices to be close to orthogonal. Hence we call such layers almost-orthogonal Lipschitz (AOL). Experiments and ablation studies in the context of image classification with certified robust accuracy confirm that AOL layers achieve results that are on par with most existing methods. Yet, they are simpler to implement and more broadly applicable, because they do not require computationally expensive matrix orthogonalization or inversion steps as part of the network architecture. We provide code at https://github.com/berndprach/AOL.

Related papers

• Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iteration [122.51142131506639]
  We introduce a precise, fast, and differentiable upper bound for the spectral norm of convolutional layers using circulant matrix theory. We show through a comprehensive set of experiments that our approach outperforms other state-of-the-art methods in terms of precision, computational cost, and scalability. It proves highly effective for the Lipschitz regularization of convolutional neural networks, with competitive results against concurrent approaches.
  arXiv  Detail & Related papers  (2023-05-25T15:32:21Z)
• A Unified Algebraic Perspective on Lipschitz Neural Networks [88.14073994459586]
  This paper introduces a novel perspective unifying various types of 1-Lipschitz neural networks. We show that many existing techniques can be derived and generalized via finding analytical solutions of a common semidefinite programming (SDP) condition. Our approach, called SDP-based Lipschitz Layers (SLL), allows us to design non-trivial yet efficient generalization of convex potential layers.
  arXiv  Detail & Related papers  (2023-03-06T14:31:09Z)
• Improved techniques for deterministic l2 robustness [63.34032156196848]
  Training convolutional neural networks (CNNs) with a strict 1-Lipschitz constraint under the $l_2$ norm is useful for adversarial robustness, interpretable gradients and stable training. We introduce a procedure to certify robustness of 1-Lipschitz CNNs by replacing the last linear layer with a 1-hidden layer. We significantly advance the state-of-the-art for standard and provable robust accuracies on CIFAR-10 and CIFAR-100.
  arXiv  Detail & Related papers  (2022-11-15T19:10:12Z)
• Rethinking Lipschitz Neural Networks for Certified L-infinity Robustness [33.72713778392896]
  We study certified $ell_infty$ from a novel perspective of representing Boolean functions. We develop a unified Lipschitz network that generalizes prior works, and design a practical version that can be efficiently trained.
  arXiv  Detail & Related papers  (2022-10-04T17:55:27Z)
• Training Certifiably Robust Neural Networks with Efficient Local Lipschitz Bounds [99.23098204458336]
  Certified robustness is a desirable property for deep neural networks in safety-critical applications. We show that our method consistently outperforms state-of-the-art methods on MNIST and TinyNet datasets.
  arXiv  Detail & Related papers  (2021-11-02T06:44:10Z)
• Skew Orthogonal Convolutions [44.053067014796596]
  Training convolutional neural networks with a Lipschitz constraint under the $l_2$ norm is useful for provable adversarial robustness, interpretable gradients, stable training, etc. Methodabv allows us to train provably Lipschitz, large convolutional neural networks significantly faster than prior works.
  arXiv  Detail & Related papers  (2021-05-24T17:11:44Z)
• Orthogonalizing Convolutional Layers with the Cayley Transform [83.73855414030646]
  We propose and evaluate an alternative approach to parameterize convolutional layers that are constrained to be orthogonal. We show that our method indeed preserves orthogonality to a high degree even for large convolutions.
  arXiv  Detail & Related papers  (2021-04-14T23:54:55Z)
• On Lipschitz Regularization of Convolutional Layers using Toeplitz Matrix Theory [77.18089185140767]
  Lipschitz regularity is established as a key property of modern deep learning. computing the exact value of the Lipschitz constant of a neural network is known to be NP-hard. We introduce a new upper bound for convolutional layers that is both tight and easy to compute.
  arXiv  Detail & Related papers  (2020-06-15T13:23:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.