Related papers: Numerical analytic continuation: Answers to well-p…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
We develop a method for multidimensional optimisation using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimising functional correspond to fixed points of the…
We study the maximum entropy (MaxEnt) approach for analytical continuation of spectral data from imaginary times to real frequencies. The total error is divided in a statistical error, due to the noise in the input data, and a systematic…
Numerical software are widely used in safety-critical systems such as aircrafts, satellites, car engines and so on, facilitating dynamics control of such systems in real time, it is therefore absolutely necessary to verify their…
Continual learning is inherently a constrained learning problem. The goal is to learn a predictor under a no-forgetting requirement. Although several prior studies formulate it as such, they do not solve the constrained problem explicitly.…
We precisely quantify the impact of statistical error in the quality of a numerical approximation to a random matrix eigendecomposition, and under mild conditions, we use this to introduce an optimal numerical tolerance for residual error…
We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. It has been shown that exact recovery is possible by…
Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…
Numerical Question Answering is the task of answering questions that require numerical capabilities. Previous works introduce general adversarial attacks to Numerical Question Answering, while not systematically exploring numerical…
Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with…
Spectral methods provide an elegant and efficient way of numerically solving differential equations of all kinds. For smooth problems, truncation error for spectral methods vanishes exponentially in the infinity norm and $L_2$-norm.…
The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior.…
In this paper, we consider the approximate weighted graph matching problem and introduce stable and informative first and second order compatibility terms suitable for inclusion into the popular integer quadratic program formulation. Our…
A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows to overcome these…
As machine learning models are increasingly considered for high-stakes domains, effective explanation methods are crucial to ensure that their prediction strategies are transparent to the user. Over the years, numerous metrics have been…
The article gives an overview of the parameter numerical continuation methodology applied to setpoint control and parameter identification of nonlinear systems. The control problems for affine systems as well as general (nonaffine)…
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…