Related papers: Trading Accuracy for Numerical Stability: Orthogon…

In this article, the problem of identifying the source term in transport processes given by a complete parabolic equation is studied mathematically from noisy measurements taken at an arbitrary fixed time. The problem is solved analytically…

Regularization is a well-established technique in machine learning (ML) to achieve an optimal bias-variance trade-off which in turn reduces model complexity and enhances explainability. To this end, some hyper-parameters must be tuned,…

In this work, our aim is to reconstruct the unknown initial value from terminal data. We develop a numerical framework on nonuniform time grids for fractional wave equations under the lower regularity assumptions. Then, we introduce a…

We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce…

Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…

The increasing size of neural networks has led to a growing demand for methods of efficient fine-tuning. Recently, an orthogonal fine-tuning paradigm was introduced that uses orthogonal matrices for adapting the weights of a pretrained…

While an explicit basis is common in the study of Euclidean spaces, it is usually implied in the study of inertial relativistic systems. There are some conceptual advantages to including the basis in the study of special relativistic…

In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…

This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy…

In this paper, we propose Selective Output Smoothing Regularization, a novel regularization method for training the Convolutional Neural Networks (CNNs). Inspired by the diverse effects on training from different samples, Selective Output…

Many modern datasets don't fit neatly into $n \times p$ matrices, but most techniques for measuring statistical stability expect rectangular data. We study methods for stability assessment on non-rectangular data, using statistical learning…

We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence…

Several generalizations of the traditional Tikhonov-Phillips regularization method have been proposed during the last two decades. Many of these generalizations are based upon inducing stability throughout the use of different penalizers…

We explore anisotropic regularisation methods in the spirit of [Holler & Kunisch, 14]. Based on ground truth data, we propose a bilevel optimisation strategy to compute the optimal regularisation parameters of such a model for the…

Standard deep learning models that employ the categorical cross-entropy loss are known to perform well at image classification tasks. However, many standard models thus obtained often exhibit issues like feature redundancy, low…

During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…

The Orthogonal Matching Pursuit (OMP) for compressed sensing iterates over a scheme of support augmentation and signal estimation. We present two novel matching pursuit algorithms with intrinsic regularization of the signal estimation step…

This primary purpose of this paper is to succinctly state a number of verifiable and tractable sufficient conditions under which a particular class of conservative signal processing structures may be readily used to solve a companion class…

Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…

Image registration is an ill-posed inverse problem which often requires regularisation on the solution space. In contrast to most of the current approaches which impose explicit regularisation terms such as smoothness, in this paper we…