Related papers: Foundations of Polar Linear Algebra

We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…

The ability of having a sparse representation for a certain class of signals has many applications in data analysis, image processing, and other research fields. Among sparse representations, the cosparse analysis model has recently gained…

Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…

A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…

Linear (spectro) polarimetry is usually performed using separate photon flux measurements after spatial or temporal polarization modulation. Such classical polarimeters are limited in sensitivity and accuracy by systematic effects and…

We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…

By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as…

A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…

This report showcases the role of, and future directions for, the field of Randomized Numerical Linear Algebra (RNLA) in a selection of scientific applications. These applications span the domains of imaging, genomics and dynamical systems,…

A periodic linear graph operator acts on states (functions) defined on the vertices of a graph equipped with a free translation action. Fourier transform with respect to the translation group reveals the central spectral objects, Bloch and…

Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing,…

We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…

We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…

In real-world applications with large state and action spaces, reinforcement learning (RL) typically employs function approximations to represent core components like the policies, value functions, and dynamics models. Although powerful…

We present in this paper the motivation and theory of nonlinear spectral representations, based on convex regularizing functionals. Some comparisons and analogies are drawn to the fields of signal processing, harmonic analysis and sparse…

We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory. We suggest a unifying approach using operators where we allow the…

While machine learning can accurately model process systems, models for decision making should also be structurally simple and physically interpretable. In process control, for example, (nearly) linear models are favored than nonlinear…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

We consider a new class of Parareal algorithms, which use ideas from localized reduced basis methods to construct the coarse solver from spectral approximations of the transfer operators mapping initial values for a given time interval to…