Related papers: Spectral analysis of 2D outlier layout
Neural networks are notorious for being overconfident predictors, posing a significant challenge to their safe deployment in real-world applications. While feature normalization has garnered considerable attention within the deep learning…
Persistent homology has been widely used to study the topology of point clouds in $\mathbb{R}^n$. Standard approaches are very sensitive to outliers, and their computational complexity depends badly on the number of data points. In this…
Outliers widely occur in big-data applications and may severely affect statistical estimation and inference. In this paper, a framework of outlier-resistant estimation is introduced to robustify an arbitrarily given loss function. It has a…
It has become routine in neuroscience studies to measure brain networks for different individuals using neuroimaging. These networks are typically expressed as adjacency matrices, with each cell containing a summary of connectivity between…
The randomized quantum marginal problem asks about the joint distribution of the partial traces ("marginals") of a uniform random Hermitian operator with fixed spectrum acting on a space of tensors. We introduce a new approach to this…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
In this paper we study a class of non-effectively hyperbolic operators vanishing of order 2 on a manifold, on a sub-region of which the spectral structure of the Hamilton map changes type. Suitable normal symplectic coordinates are found…
We propose a simple distributed algorithm for balancing indivisible tokens on graphs. The algorithm is completely deterministic, though it tries to imitate (and enhance) a random algorithm by keeping the accumulated rounding errors as small…
The theory of quaternionic operators has applications in several different fields such as quantum mechanics, fractional evolution problems, and quaternionic Schur analysis, just to name a few. The main difference between complex and…
Several areas have been improved with Deep Learning during the past years. Implementing Deep Neural Networks (DNN) for non-safety related applications have shown remarkable achievements over the past years; however, for using DNNs in safety…
The transformer's remarkable ability to perform in-context learning (ICL) has sparked a wide range of studies designed to understand its strengths and limitations. However, a theoretical understanding of when ICL can and cannot generalize…
Outlier detection and cluster number estimation is an important issue for clustering real data. This paper focuses on spectral clustering, a time-tested clustering method, and reveals its important properties related to outliers. The…
In this work, we explore the use of operator splitting algorithms for solving regularized structural topology optimization problems. The context is the classical structural design problems (e.g., compliance minimization and compliant…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded semidefinite perturbation is considered. A variant of the Davis-Kahan $ \sin2\Theta $ theorem from [SIAM J. Numer. Anal. 7 (1970), 1--46]…
We study statistical properties of energy spectra of a tight-binding model on the two-dimensional quasiperiodic Ammann-Beenker tiling. Taking into account the symmetries of finite approximants, we find that the underlying universal…
In this paper, we introduce and study a new class of bounded linear operators on complex Hilbert spaces, which we call 2-C-normal operators. This class is inspired by and closely related to the notion of 2-normal operators, with additional…
Outlier Detection is a critical and cardinal research task due its array of applications in variety of domains ranging from data mining, clustering, statistical analysis, fraud detection, network intrusion detection and diagnosis of…
Let $\mathcal{H}$ be a right quaternionic Hilbert space and let $T$ be a quaternionic normal operator with the domain $\mathcal{D}(T) \subset \mathcal{H}$. Then for a fixed unit imaginary quaternion $m$, there exists a Hilbert basis…
We establish a new perturbation theory for orthogonal polynomials using a Riemann--Hilbert approach and consider applications in numerical linear algebra and random matrix theory. This new approach shows that the orthogonal polynomials with…
Several areas have been improved with Deep Learning during the past years. For non-safety related products adoption of AI and ML is not an issue, whereas in safety critical applications, robustness of such approaches is still an issue. A…