arXiv research

Spectral Independence Criterion helps infer cause-effect relationships in time series.

Study spectral distances on compact RCD spaces.

The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we propose a powerful and efficient spectral kernel learning framework and learned ke…

Combining known spectral sequences with a new spectral sequence relating reduced and unreduced sl(N)-homology yields a relationship between the Homflypt-homology of a knot and its sl(N)-concordance invariants. As an application, some of the sl(N)-concordance invariants are shown to be linearly independent.

New method tests conditional independence using spectral representations.

Muon optimizer simplifies matrix optimization with spectral orthogonalization.

We study a spectral generalization of classical combinatorial graph spanners to the spectral setting. Given a set of vectors $V\subseteq \Re^d$, we say a set $U\subseteq V$ is an $α$-spectral spanner if for all $v\in V$ there is a probability distribution $μ_v$ supported on $U$ such that $$vv^\intercal \preceq α\cdot\m…

In this paper we study the spectral asymmetry of (possibly nonselfadjoint) elliptic PsiDO's in terms of the difference of zeta functions coming from different cuttings. Refining previous formulas of Wodzicki in the case of odd class elliptic PsiDO's, our main results have several consequence concerning the local indepe…

The study reveals a persistent bias in the distribution of holonomy on compact hyperbolic 3-manifolds.

New ICA method for sources with mixed spectra.

Two proofs of Melrose-Piazza theorem on spectral sections.

We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as $\l…

In this paper, we introduce the concept of \emph{Poissonian occupation times} below level $0$ of spectrally negative Lévy processes. In this case, occupation time is accumulated only when the process is observed to be negative at arrival epochs of an independent Poisson process. Our results extend some well known conti…

Proves spectral sequence for real Heegaard Floer homology.

Ozsváth, Rasmussen and Szabó constructed odd Khovanov homology. It is a link invariant which has the same reduction modulo 2 as (even) Khovanov homology. Szabó introduced a spectral sequence with mod 2 coefficients from mod 2 Khovanov homology to another link homology. He got his spectral sequence from a chain complex …

DOODL learns shared spectral dynamics across related dynamical systems.

New bounds for KRR condition number reveal overfitting phenomena.

New 2-representations link spectral enhancements in link homology.

Considering the kinematics of the moving frame associated with a constant mean curvature surface immersed in S^3 we derive a linear problem with the spectral parameter corresponding to elliptic sinh-Gordon equation. The spectral parameter is related to the radius R of the sphere S^3. The application of the Sym formula …

New method detects and analyzes correlation in multiple network data.

New method for analyzing complex data spaces.

SPQR improves Q-ensemble diversity in reinforcement learning.

A spectral sequence is established, from Bar-Natan's variant of Khovanov homology to a deformation of instanton homology for knots and links. This spectral sequence arises as a specialization of a spectral sequence from a characteristic-2 version of $F_5$ homology, in Khovanov'sclassification. Concordance invariants of…

We consider a version of the stochastic inventory control problem for a spectrally positive Lévy demand process, in which the inventory can only be replenished at independent exponential times. We show the optimality of a periodic barrier replenishment policy that restocks any shortage below a certain threshold at each…

Essential principal components simplify spectral analysis with minimal training data.

Algorithm learns dynamics from past observations.

Spectral methods that are based on eigenvectors and eigenvalues of discrete graph Laplacians, such as Diffusion Maps and Laplacian Eigenmaps are often used for manifold learning and non-linear dimensionality reduction. It was previously shown by Belkin and Niyogi \cite{belkin_niyogi:2007} that the eigenvectors and eige…

Reconstruction based subspace clustering methods compute a self reconstruction matrix over the samples and use it for spectral clustering to obtain the final clustering result. Their success largely relies on the assumption that the underlying subspaces are independent, which, however, does not always hold in the appli…

Calculates spectral flow bounds for reducible solutions to Vafa-Witten equations.

Bayesian framework integrates spectral deconvolution with expert reasoning for robust peak estimation.

Ozsvath, Rasmussen and Szabo constructed odd Khovanov homology. It is a link invariant which has the same reduction modulo 2 as (even) Khovanov homology. Szabo introduced a spectral sequence with mod 2 coefficients from mod 2 Khovanov homology to another link homology. He got his spectral sequence from a chain complex …

We construct a map from the suspension $G$-spectrum $Σ_G^\infty M$ of a smooth compact $G$-manifold to the equivariant $A$-theory spectrum $A_G(M)$, and we show that its fiber is, on fixed points, a wedge of stable $h$-cobordism spectra. This map is constructed as a map of spectral Mackey functors, which is compatible …

A fast, robust AMP algorithm for quadratic optimization problems.

Proposes a deep network for multi-class classification using spectral training and Gaussian kernel.

Proves accuracy guarantees for self-supervised learning with correlated positive pairs.

Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among brain regions. In this paper, we develop a non-asymptotic theory for regularize…

The paper analyzes neural networks for solving high-dimensional Schrödinger eigenvalue problems.

Spectral algorithms improve under covariate shift with novel weighted techniques.

This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition technique yields consistent parameter estimates from low-order observable moments, wit…

Spectral methods improve signal recovery in mixed GLMs with precise asymptotics.

New method controls linear systems with adversarial disturbances.

New empirical PAC-Bayes bound for Markov chains with finite state space.

In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a certain "contrast function" over the unit sphere. These algorithms, partly inspired by…

Study spectral and index properties of Hodge-Dirac operator on compact manifolds.

A new method for spectral positional encodings in directed graphs using Hermitian block Krylov subspaces.

New rigidity theorem for sharp spectral gap in nonnegatively curved spaces.

PolyNSD improves Neural Sheaf Diffusion with polynomial operators and spectral rescaling.

The random dot product graph (RDPG) is an independent-edge random graph that is analytically tractable and, simultaneously, either encompasses or can successfully approximate a wide range of random graphs, from relatively simple stochastic block models to complex latent position graphs. In this survey paper, we describ…