Related papers: Hessian Spectral Analysis at Foundation Model Scal…
Neural networks (NNs) are central to modern machine learning and achieve state-of-the-art results in many applications. However, the relationship between loss geometry and generalization is still not well understood. The local geometry of…
Feshbach resonances are commonly described by a single-resonance Feshbach model, and open-channel resonances are not taken into account explicitly. However, an open-channel resonance near threshold limits the range of validity of this…
Understanding the evolution of the Milky Way calls for the precise abundance determination of many elements in many stars. A common perception is that deriving more than a few elemental abundances ([Fe/H], [$\alpha$/Fe], perhaps [C/H],…
Recent advances in spectroscopic instrumentation and calibration methods dramatically improve the quality of quasar spectra. Supercomputer calculations show that, at high spectral resolution, procedures used in some previous analyses of…
The General Spectral Modeling (GSM) code employs the quasi-static approximation, a standard, low-density methodology that assumes the ionization balance is separable from a determination of the excited-state populations that give rise to…
Kernel spectral clustering corresponds to a weighted kernel principal component analysis problem in a constrained optimization framework. The primal formulation leads to an eigen-decomposition of a centered Laplacian matrix at the dual…
Spectroscopy has played the key role in revealing, and thereby understanding, the structure of atoms and molecules. A central drive in this field is the pursuit of higher precision and accuracy so that ever more subtle effects might be…
Novel view synthesis has recently been revolutionized by 3D Gaussian Splatting (3DGS), which enables real-time rendering through explicit primitive rasterization. However, existing methods tie visual fidelity strictly to the number of…
As attention-based deep learning models scale in size and complexity, diagnosing their faults becomes increasingly challenging. In this work, we conduct an empirical study to evaluate the potential of Hessian-based analysis for diagnosing…
Recently, it has been observed that when training a deep neural net with SGD, the majority of the loss landscape's curvature quickly concentrates in a tiny *top* eigenspace of the loss Hessian, which remains largely stable thereafter.…
Investigating the performance of different methods is a fundamental problem in graph partitioning. In this paper, we estimate the so-called detectability threshold for the spectral method with both unnormalized and normalized Laplacians in…
Hybrid density functional (HDF) approximations usually deliver higher accuracy than local and semilocal approximations to the exchange-correlation functional, but this comes with drastically increased computational cost. Practical…
A systematic programme of calibration observations was carried out to monitor the performance of the SPIRE FTS instrument on board the Herschel Space Observatory. Observations of planets (including the prime point-source calibrator,…
Using the Fundamental-Measure Density Functional Theory, we have studied theoretically the phase behavior of extremely confined mixtures of parallel hard squares in slit geometry. The pore width is chosen such that configurations consisting…
Absorption-line systems detected in high resolution quasar spectra can be used to compare the value of dimensionless fundamental constants such as the fine-structure constant, alpha, and the proton-to-electron mass ratio, mu = m_p/m_e, as…
Spectral unmixing is an important and challenging problem in hyperspectral data processing. This topic has been extensively studied and a variety of unmixing algorithms have been proposed in the literature. However, the lack of publicly…
We study linear spectral statistics of high dimensional sample covariance matrices in a regime where the empirical spectral distribution remains governed by the classical sample covariance law but the fluctuation theory is nonclassical. Our…
Mining large-scale high-throughput tandem mass spectrometry data sets is a very important problem in mass spectrometry based protein identification. One of the fundamental problems in large scale mining of spectra is to design appropriate…
Classical approximation bases such as Chebyshev polynomials provide principled and interpretable representations, but their multivariate tensor-product constructions scale exponentially with dimension and impose axis-aligned structure that…
Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method…