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Controlling the spectral norm of the Jacobian matrix, which is related to the convolution operation, has been shown to improve generalization, training stability and robustness in CNNs. Existing methods for computing the norm either tend to…

Since the control of the Lipschitz constant has a great impact on the training stability, generalization, and robustness of neural networks, the estimation of this value is nowadays a real scientific challenge. In this paper we introduce a…

We pursue a line of research that seeks to regularize the spectral norm of the Jacobian of the input-output mapping for deep neural networks. While previous work rely on upper bounding techniques, we provide a scheme that targets the exact…

An increasing number of models require the control of the spectral norm of convolutional layers of a neural network. While there is an abundance of methods for estimating and enforcing upper bounds on those during training, they are…

Convolution neural networks have achieved remarkable performance in many tasks of computing vision. However, CNN tends to bias to low frequency components. They prioritize capturing low frequency patterns which lead them fail when suffering…

Deriving sharp and computable upper bounds of the Lipschitz constant of deep neural networks is crucial to formally guarantee the robustness of neural-network based models. We analyse three existing upper bounds written for the $l^2$ norm.…

This paper tackles the problem of Lipschitz regularization of Convolutional Neural Networks. Lipschitz regularity is now established as a key property of modern deep learning with implications in training stability, generalization,…

We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…

This paper leverages the use of \emph{Gram iteration} an efficient, deterministic, and differentiable method for computing spectral norm with an upper bound guarantee. Designed for circular convolutional layers, we generalize the use of the…

Convolutional neural network is a very important model of deep learning. It can help avoid the exploding/vanishing gradient problem and improve the generalizability of a neural network if the singular values of the Jacobian of a layer are…

The generalization error of deep neural networks via their classification margin is studied in this work. Our approach is based on the Jacobian matrix of a deep neural network and can be applied to networks with arbitrary non-linearities…

Deep neural networks (DNNs) play an important role in machine learning due to its outstanding performance compared to other alternatives. However, DNNs are not suitable for safety-critical applications since DNNs can be easily fooled by…

Normalized difference indices have been a staple in remote sensing for decades. They stay reliable under lighting changes produce bounded values and connect well to biophysical signals. Even so, they are usually treated as a fixed pre…

In convolutional neural networks, the linear transformation of multi-channel two-dimensional convolutional layers with linear convolution is a block matrix with doubly Toeplitz blocks. Although a "wrapping around" operation can transform…

Inverse problems arise in a number of domains such as medical imaging, remote sensing, and many more, relying on the use of advanced signal and image processing approaches -- such as sparsity-driven techniques -- to determine their…

Recent work has shown that tight concentration of the entire spectrum of singular values of a deep network's input-output Jacobian around one at initialization can speed up learning by orders of magnitude. Therefore, to guide important…

We characterize the singular values of the linear transformation associated with a standard 2D multi-channel convolutional layer, enabling their efficient computation. This characterization also leads to an algorithm for projecting a…

The recent theoretical analysis of deep neural networks in their infinite-width limits has deepened our understanding of initialisation, feature learning, and training of those networks, and brought new practical techniques for finding…

Recent studies suggest that artificial neural networks (ANNs) that match the spectral properties of the mammalian visual cortex -- namely, the $\sim 1/n$ eigenspectrum of the covariance matrix of neural activities -- achieve higher object…

Regularization techniques help prevent overfitting and therefore improve the ability of convolutional neural networks (CNNs) to generalize. One reason for overfitting is the complex co-adaptations among different parts of the network, which…