Related papers: On Lipschitz Regularization of Convolutional Layer…
This paper proposes that Lipschitz continuity is a natural outcome of regularized least squares in kernel-based learning. Lipschitz continuity is an important proxy for robustness of input-output operators. It is also instrumental for…
This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks based upon non-Euclidean contraction theory. The basic idea is to cast the robustness analysis of a neural…
Deep learning has non-convex loss landscape and its optimization dynamics is hard to analyze or control. Nevertheless, the dynamics can be empirically convex-like across various tasks, models, optimizers, hyperparameters, etc. In this work,…
Many convolutional neural networks (CNNs) have a feed-forward structure. In this paper, a linear program that estimates the Lipschitz bound of such CNNs is proposed. Several CNNs, including the scattering networks, the AlexNet and the…
Imposing orthogonality on the layers of neural networks is known to facilitate the learning by limiting the exploding/vanishing of the gradient; decorrelate the features; improve the robustness. This paper studies the theoretical properties…
Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow…
This paper is concerned with the training of neural networks (NNs) under semidefinite constraints, which allows for NN training with robustness and stability guarantees. In particular, we focus on Lipschitz bounds for NNs. Exploiting the…
We introduce Parseval networks, a form of deep neural networks in which the Lipschitz constant of linear, convolutional and aggregation layers is constrained to be smaller than 1. Parseval networks are empirically and theoretically…
Deep neural networks are considered to be state of the art models in many offline machine learning tasks. However, their performance and generalization abilities in online learning tasks are much less understood. Therefore, we focus on…
Ensuring neural network robustness is essential for the safe and reliable operation of robotic learning systems, especially in perception and decision-making tasks within real-world environments. This paper investigates the robustness of…
We initiate the study of the inherent tradeoffs between the size of a neural network and its robustness, as measured by its Lipschitz constant. We make a precise conjecture that, for any Lipschitz activation function and for most datasets,…
Deep learning has achieved remarkable success across a wide range of domains, significantly expanding the frontiers of what is achievable in artificial intelligence. Yet, despite these advances, critical challenges remain -- most notably,…
Training convolutional neural networks with a Lipschitz constraint under the $l_{2}$ norm is useful for provable adversarial robustness, interpretable gradients, stable training, etc. While 1-Lipschitz networks can be designed by imposing a…
It has been shown that a neural network's Lipschitz constant can be leveraged to derive robustness guarantees, to improve generalizability via regularization or even to construct invertible networks. Therefore, a number of methods varying…
Recurrent neural networks (RNNs) are a class of nonlinear dynamical systems often used to model sequence-to-sequence maps. RNNs have excellent expressive power but lack the stability or robustness guarantees that are necessary for many…
We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output…
Attention is a powerful component of modern neural networks across a wide variety of domains. In this paper, we seek to quantify the regularity (i.e. the amount of smoothness) of the attention operation. To accomplish this goal, we propose…
Neural networks (NNs) have emerged as a state-of-the-art method for modeling nonlinear systems in model predictive control (MPC). However, the robustness of NNs, in terms of sensitivity to small input perturbations, remains a critical…
Explainability models are now prevalent within machine learning to address the black-box nature of neural networks. The question now is which explainability model is most effective. Probabilistic Lipschitzness has demonstrated that the…
Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz constant in neural…