Related papers: Hessian Spectral Analysis at Foundation Model Scal…

Stellarator boundary optimization faces a fundamental numerical challenge: the extreme disparity between low- and high-mode amplitudes creates an optimization landscape in which direct full-spectrum approaches typically converge to poor…

Performance evaluations on the deterministic algorithms for 6-D problems are rarely found in literatures except some recent advances in the Vlasov and Boltzmann community [Dimarco et al. (2018), Kormann et al. (2019)], due to the extremely…

We study the mixed Hessian of the dispersionless Toda $\tau$-function for the one-harmonic $s$-fold symmetric conformal map $f(w)=rw+aw^{1-s}$. This Hessian is the susceptibility matrix generated by the inverse conformal map. Our spectral…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…

We present PYHESSIAN, a new scalable framework that enables fast computation of Hessian (i.e., second-order derivative) information for deep neural networks. PYHESSIAN enables fast computations of the top Hessian eigenvalues, the Hessian…

The Grism Lens-Amplified Survey from Space (GLASS) is a Hubble Space Telescope (HST) Large Program, which will obtain 140 orbits of grism spectroscopy of the core and infall regions of 10 galaxy clusters, selected to be among the very best…

First-order optimizers are reliable but slow in sharp, anisotropic regions. We study a curvature-adaptive method that periodically sketches a low-rank Hessian subspace via Hessian--vector products and preconditions gradients only in that…

We consider minimizing a smooth and strongly convex objective function using a stochastic Newton method. At each iteration, the algorithm is given an oracle access to a stochastic estimate of the Hessian matrix. The oracle model includes…

In this article we consider the development of unbiased estimators of the Hessian, of the log-likelihood function with respect to parameters, for partially observed diffusion processes. These processes arise in numerous applications, where…

Landslide detection from satellite imagery has advanced through deep learning, yet most models rely on large, highly correlated spectral-topographic inputs whose contributions remain poorly understood. The question of which channels are…

Spectral approximation and variational inducing learning for the Gaussian process are two popular methods to reduce computational complexity. However, in previous research, those methods always tend to adopt the orthonormal basis functions,…

Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…

Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this paper we unify these two approaches showing that the underlying…

In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless…

The specification of a covariance function is of paramount importance when employing Gaussian process models, but the requirement of positive definiteness severely limits those used in practice. Designing flexible stationary covariance…

The bispectrum vanishes for linear Gaussian fields and is thus a sensitive probe of non-linearities and non-Gaussianities in the cosmic density field. Hence, a detection of the bispectrum in the halo density field would enable tight…

Spectral clustering techniques are valuable tools in signal processing and machine learning for partitioning complex data sets. The effectiveness of spectral clustering stems from constructing a non-linear embedding based on creating a…

Non-gaussianity in the initial conditions of the universe is one of the most powerful mechanisms to discriminate among the competing theories of the early universe. Measurements using bispectrum of cosmic microwave background anisotropies…

We revisit the $k$-Hessian eigenvalue problem on a smooth, bounded, $(k-1)$-convex domain in $\mathbb R^n$. First, we obtain a spectral characterization of the $k$-Hessian eigenvalue as the infimum of the first eigenvalues of linear…