Related papers: Basis set extrapolation from the vanishing counter…
The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is…
We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…
We present a very simple yet powerful generalization of a previously described model and algorithm for estimation of multiple dipoles from magneto/electro-encephalographic data. Specifically, the generalization consists in the introduction…
This paper addresses the problem of basis correction in the context of LSS identification from input-output data. It is often the case that identification algorithms for the LSSs from input-output data operate locally. The individually…
Test-time scaling offers a promising path to improve LLM reasoning by utilizing more compute at inference time; however, the true promise of this paradigm lies in extrapolation (i.e., improvement in performance on hard problems as LLMs keep…
This paper presents a new view of Explanation-Based Learning (EBL) of natural language parsing. Rather than employing EBL for specializing parsers by inferring new ones, this paper suggests employing EBL for learning how to reduce ambiguity…
This article revisits the fundamental problem of parameter selection for Gaussian process interpolation. By choosing the mean and the covariance functions of a Gaussian process within parametric families, the user obtains a family of…
Basis set convergence of the Hartree-Fock and the correlation energy is examined for the hydrogen bonded infinite bent chains (HF)_infinity and (HCl)_infinity. We employ series of correlation consistent basis sets up to quintuple zeta…
The Bethe-Salpeter equation (BSE) based on GW quasiparticle levels is a successful approach for calculating the optical gaps and spectra of solids and also for predicting the neutral excitations of small molecules. We here present an…
In modern communication systems such as the Internet, random losses of information can be mitigated by oversampling the source. This is equivalent to expanding the source using overcomplete systems of vectors (frames), as opposed to the…
Calculations in field theory are usually accomplished by employing some variants of perturbation theory, for instance using loop expansions. These calculations result in asymptotic series in powers of small coupling parameters, which as a…
The application of error-free transformation (EFT) is recently being developed to solve ill-conditioned problems. It can reduce the number of arithmetic operations required, compared with multiple precision arithmetic, and also be applied…
We consider bounds on the generalization performance of the least-norm linear regressor, in the over-parameterized regime where it can interpolate the data. We describe a sense in which any generalization bound of a type that is commonly…
In this paper, we study the conditional stochastic optimization (CSO) problem which covers a variety of applications including portfolio selection, reinforcement learning, robust learning, causal inference, etc. The sample-averaged gradient…
Certain quasi-exactly solvable systems exhibit an energy reflection property that relates the energy levels of a potential or of a pair of potentials. We investigate two sister potentials and show the existence of this energy reflection…
We explore the robustness of the correlation matrix Hamiltonian reconstruction technique with respect to the choice of operator basis, studying the effects of bases that are undercomplete and over-complete -- too few or too many operators…
This paper presents a Bayesian framework for assessing the adequacy of a model without the necessity of explicitly enumerating a specific alternate model. A test statistic is developed for tracking the performance of the model across…
A scheme to provide various mean-field-type approximation algorithms is presented by employing the Bethe free energy formalism to a family of replicated systems in conjunction with analytical continuation with respect to the number of…
We review the Bethe-Salpeter equation (BSE) approach to the calculation of electronic excitation energies of molecular systems. We recall the general Green's function many-theory formalism and give the working equations of the BSE approach…
Refining one's hypotheses in the light of data is a common scientific practice; however, the dependency on the data introduces selection bias and can lead to specious statistical analysis. An approach for addressing this is via conditioning…