Related papers: Hessian Spectral Analysis at Foundation Model Scal…
Laser speckle, the granular intensity pattern arising from random optical interference, provides a high-dimensional encoding of spectral information that can be exploited for precision metrology. Speckle-based spectrometers have advanced…
We propose a new approach to quantum phase transitions in terms of the density-functional fidelity, which measures the similarity between density distributions of two ground states in parameter space. The key feature of the approach, as we…
Feature selection of high-dimensional labeled data with limited observations is critical for making powerful predictive modeling accessible, scalable, and interpretable for domain experts. Spectroscopy data, which records the interaction…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…
Approximating the action of a matrix function $f(\mathbf{A})$ on a vector $\mathbf{b}$ is an increasingly important primitive in machine learning, data science, and statistics, with applications such as sampling high dimensional Gaussians,…
To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…
We present initial results from the Herschel GT key program: Herschel observations of EXtra-Ordinary Sources (HEXOS) and outline the promise and potential of spectral surveys with Herschel/HIFI. The HIFI instrument offers unprecedented…
The Herschel SPIRE Fourier transform spectrometer (FTS) performs spectral imaging in the 447-1546 GHz band. It can observe in three spatial sampling modes: sparse mode, with a single pointing on sky, or intermediate or full modes with 1 and…
We extend traditional complexity analyses of trust-region methods for unconstrained, possibly nonconvex, optimization. Whereas most complexity analyses assume uniform boundedness of the model Hessians, we work with potentially unbounded…
Well-calibrated spectropolarimetry studies at resolutions of $R>$10,000 with signal-to-noise ratios (SNRs) better than 0.01\% across individual line profiles, are becoming common with larger aperture telescopes. Spectropolarimetric studies…
The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral analysis in a translation invariant closed linear subspace of additive/multiadditive functions containing the…
The rapidly growing interest in simulating condensed-phase materials using quantum chemistry methods calls for a library of high-quality Gaussian basis sets suitable for periodic calculations. Unfortunately, most standard Gaussian basis…
We study algorithms for approximating the spectral density of a symmetric matrix $A$ that is accessed through matrix-vector product queries. By combining a previously studied Chebyshev polynomial moment matching method with a deflation step…
Understanding the spectral properties of kernels offers a principled perspective on generalization and representation quality. While deep models achieve state-of-the-art accuracy in molecular property prediction, kernel methods remain…
The pseudospectral method is a powerful tool for finding highly precise solutions of Schr\"{o}dinger's equation for few-electron problems. We extend the method's scope to wave functions with non-zero angular momentum and test it on several…
Understanding the curvature evolution of the loss landscape is fundamental to analyzing the training dynamics of neural networks. The most commonly studied measure, Hessian sharpness ($\lambda_{\max}^H$) -- the largest eigenvalue of the…
We introduce computational strategies for measuring the ``size'' of the spectrum of bounded self-adjoint operators using various metrics such as the Lebesgue measure, fractal dimensions, the number of connected components (or gaps), and…
The distribution of the eigenvalues of a Hermitian matrix (or of a Hermitian matrix pencil) reveals important features of the underlying problem, whether a Hamiltonian system in physics, or a social network in behavioral sciences. However,…
High-harmonic spectroscopy (HHS) is a nonlinear all-optical technique with inherent attosecond temporal resolution, which has been applied successfully to a broad variety of systems in the gas phase and solid state. Here, we extend HHS to…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…