Related papers: Lipschitz constant estimation for 1D convolutional…
We analyze the constant step size subgradient method on nonsmooth, nonconvex functions. We identify geometric assumptions on the objective function under which i) its domain admits a partition (stratification) into smooth manifolds (strata)…
Recent studies have shown that a Deep Convolutional Neural Network (DCNN) pretrained on a large image dataset can be used as a universal image descriptor, and that doing so leads to impressive performance for a variety of image…
We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the…
Techniques known as Nonlinear Set Membership prediction, Kinky Inference or Lipschitz Interpolation are fast and numerically robust approaches to nonparametric machine learning that have been proposed to be utilised in the context of system…
We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for…
Designing neural networks with bounded Lipschitz constant is a promising way to obtain certifiably robust classifiers against adversarial examples. However, the relevant progress for the important $\ell_\infty$ perturbation setting is…
We propose a new symplectic convolutional neural network (CNN) architecture by leveraging symplectic neural networks, proper symplectic decomposition, and tensor techniques. Specifically, we first introduce a mathematically equivalent form…
We investigate robustness of deep feed-forward neural networks when input data are subject to random uncertainties. More specifically, we consider regularization of the network by its Lipschitz constant and emphasize its role. We highlight…
One of the challenges in the study of Generative Adversarial Networks (GANs) is the difficulty of its performance control. Lipschitz constraint is essential in guaranteeing training stability for GANs. Although heuristic methods such as…
Empirical studies have widely demonstrated that neural networks are highly sensitive to small, adversarial perturbations of the input. The worst-case robustness against these so-called adversarial examples can be quantified by the Lipschitz…
The robustness of neural networks against input perturbations with bounded magnitude represents a serious concern in the deployment of deep learning models in safety-critical systems. Recently, the scientific community has focused on…
Precise estimation of the probabilistic structure of natural images plays an essential role in image compression. Despite the recent remarkable success of end-to-end optimized image compression, the latent codes are usually assumed to be…
Convolutional Neural Networks (CNNs) have been proven to be extremely successful at solving computer vision tasks. State-of-the-art methods favor such deep network architectures for its accuracy performance, with the cost of having massive…
We propose a generalized convolutional neural network (CNN) architecture that first decomposes the input signal into subbands by an adaptive filter bank structure, and then uses convolutional layers to extract features from each subband…
We describe the class of convexified convolutional neural networks (CCNNs), which capture the parameter sharing of convolutional neural networks in a convex manner. By representing the nonlinear convolutional filters as vectors in a…
Modern convolutional neural networks (CNNs) organize computation as a discrete stack of layers whose parameters are independently stored and learned, with the number of layers fixed as an architectural hyperparameter. In this work, we…
Model compression and acceleration are attracting increasing attentions due to the demand for embedded devices and mobile applications. Research on efficient convolutional neural networks (CNNs) aims at removing feature redundancy by…
The concept of compressing deep Convolutional Neural Networks (CNNs) is essential to use limited computation, power, and memory resources on embedded devices. However, existing methods achieve this objective at the cost of a drop in…
Exciting new work on the generalization bounds for neural networks (NN) given by Neyshabur et al. , Bartlett et al. closely depend on two parameter-depenedent quantities: the Lipschitz constant upper-bound and the stable rank (a softer…
We provide an inference procedure for the sharp regression discontinuity design (RDD) under monotonicity, with possibly multiple running variables. Specifically, we consider the case where the true regression function is monotone with…