Related papers: Trading Accuracy for Numerical Stability: Orthogon…
Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…
The aim of this paper is to present a new fast-convergent numerically stable space-time adaptive processing (STAP) algorithm derived using a novel technique of feedback orthogonalization. The main advantages of this approach lie in its…
Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
Updating machine learning models with new information usually improves their predictive performance, yet, in many applications, it is also desirable to avoid changing the model predictions too much. This property is called stability. In…
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…
Numerous regularization methods for deformable image registration aim at enforcing smooth transformations, but are difficult to tune-in a priori and lack a clear physical basis. Physically inspired strategies have emerged, offering a sound…
The orthogonalization process is an essential building block in Krylov space methods, which takes up a large portion of the computational time. Commonly used methods, like the Gram-Schmidt method, consider the projection and normalization…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
We consider orthogonal transformations of arbitrary square matrices to a form where all diagonal entries are equal. In our main results we treat the simultaneous transformation of two matrices and the symplectic orthogonal transformation of…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
In this article we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of…
This paper seeks to answer the question: as the (near-) orthogonality of weights is found to be a favorable property for training deep convolutional neural networks, how can we enforce it in more effective and easy-to-use ways? We develop…
Orthogonality regularization has been developed to prevent deep CNNs from training instability and feature redundancy. Among existing proposals, kernel orthogonality regularization enforces orthogonality by minimizing the residual between…
Deep-learning-based nonlinear system identification has shown the ability to produce reliable and highly accurate models in practice. However, these black-box models lack physical interpretability, and a considerable part of the learning…
A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and…
Point processes are stochastic models generating interacting points or events in time, space, etc. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on…
Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter.…
Householder orthogonalization plays an important role in numerical linear algebra. It attains perfect orthogonality regardless of the conditioning of the input. However, in the context of a non-standard inner product, it becomes difficult…