Related papers: Wasserstein Diffusion Tikhonov Regularization
Recently, a variety of regularization techniques have been widely applied in deep neural networks, such as dropout, batch normalization, data augmentation, and so on. These methods mainly focus on the regularization of weight parameters to…
We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in…
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…
Human intelligence gradually accepts new information and accumulates knowledge throughout the lifespan. However, deep learning models suffer from a catastrophic forgetting phenomenon, where they forget previous knowledge when acquiring new…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…
Deep neural networks are known to be vulnerable to adversarial attacks (AA). For an image recognition task, this means that a small perturbation of the original can result in the image being misclassified. Design of such attacks as well as…
In this paper the problem of recovering a regularized solution of the Fredholm integral equations of the first kind with Hermitian and square-integrable kernels, and with data corrupted by additive noise, is considered. Instead of using a…
Domain generalization aims at learning a universal model that performs well on unseen target domains, incorporating knowledge from multiple source domains. In this research, we consider the scenario where different domain shifts occur among…
This paper focuses on the regularization of backward time-fractional diffusion problem on unbounded domain. This problem is well-known to be ill-posed, whence the need of a regularization method in order to recover stable approximate…
Dual gradient descent combined with early stopping represents an efficient alternative to the Tikhonov variational approach when the regularizer is strongly convex. However, for many relevant applications, it is crucial to deal with…
Equivariant and invariant deep learning models have been developed to exploit intrinsic symmetries in data, demonstrating significant effectiveness in certain scenarios. However, these methods often suffer from limited representation…
Off-policy evaluation and learning are concerned with assessing a given policy and learning an optimal policy from offline data without direct interaction with the environment. Often, the environment in which the data are collected differs…
Learning the governing equations from time-series data has gained increasing attention due to its potential to extract useful dynamics from real-world data. Despite significant progress, it becomes challenging in the presence of noise,…
In this paper, we study the Tikhonov regularization scheme in Hilbert scales for the nonlinear statistical inverse problem with a general noise. The regularizing norm in this scheme is stronger than the norm in Hilbert space. We focus on…
Domain adaptation aims at generalizing a high-performance learner on a target domain via utilizing the knowledge distilled from a source domain which has a different but related data distribution. One solution to domain adaptation is to…
Despite the recent success of deep neural networks, there remains a need for effective methods to enhance domain generalization using vision transformers. In this paper, we propose a novel domain generalization technique called Robust…
We present a framework to simultaneously align and smooth data in the form of multiple point clouds sampled from unknown densities with support in a d-dimensional Euclidean space. This work is motivated by applications in bioinformatics…
Discrete image tokenizers are commonly trained in two stages: first for reconstruction, and then with a prior model fitted to the frozen token sequences. This decoupling leaves the tokenizer unaware of the model that will later generate its…
This paper presents an error analysis of classical and learned Tikhonov regularization schemes for inverse problems. We first demonstrate, both theoretically and numerically, that using a fixed regularization parameter across varying noise…
Adversarial training and data augmentation with noise are widely adopted techniques to enhance the performance of neural networks. This paper investigates adversarial training and data augmentation with noise in the context of regularized…