A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper generalizes spectral section concepts to non-compact spaces.
Efficiently scales continuous kernels with sparse Fourier domain learning.
We consider a continuous curve of linear elliptic formally self-adjoint differential operators of first order with smooth coefficients over a compact Riemannian manifold with boundary together with a continuous curve of global elliptic boundary value problems. We express the spectral flow of the resulting continuous fa…
New method calculates eta invariant without analytic continuation.
Improved neural network predicts spectral functions more accurately than traditional methods.
The paper explains how continuous language models can produce discrete, interpretable meanings.
Lipschitz continuity recently becomes popular in generative adversarial networks (GANs). It was observed that the Lipschitz regularized discriminator leads to improved training stability and sample quality. The mainstream implementations of Lipschitz continuity include gradient penalty and spectral normalization. In th…
We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of the restriction to a finite codimensional closed subspace. We also discuss the case of restriction…
We consider a continuous curve of self-adjoint Fredholm extensions of a curve of closed symmetric operators with fixed minimal domain and fixed {\it intermediate} domain . Our main example is a family of symmetric generalized operators of Dirac type on a compact manifold with boundary with varying well-posed…
Paper shows stability of metric reconstruction for orbifolds from spectral data.
In this paper we propose the notion of continuous-time dynamic spectral risk-measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk-measures in terms of certain backward stochastic differential equations. By establishing a functional limit theorem, we show that DSRs may …
For a continuous curve of families of Dirac type operators we define a higher spectral flow as a -group element. We show that this higher spectral flow can be computed analytically by $\heta$-forms, and is related to the family index in the same way as the spectral flow is related to the index. We introduce a notion…
Unified framework for analyzing graph neural operators converging to graph limits.
Recently, there has been a surge of interest in using spectral methods for estimating latent variable models. However, it is usually assumed that the distribution of the observations conditioned on the latent variables is either discrete or belongs to a parametric family. In this paper, we study the estimation of an $m…
Study uses spectral risk for learning with heavy-tailed data.
New wavelet frames constructed from reproducing kernels for continuous and discrete domains.
The paper analyzes the generalization performance of spectral clustering algorithms and proposes new methods to improve their effectiveness.
Recently, we proposed short-time Fourier transform (STFT)-based loss functions for training a neural speech waveform model. In this paper, we generalize the above framework and propose a training scheme for such models based on spectral amplitude and phase losses obtained by either STFT or continuous wavelet transform …
The spectral flow theorem is applied to operators on finite intervals.
We obtain a Bonnet-Myers theorem under a spectral condition: a closed Riemannian manifold for which the lowest eigenvalue of the Ricci tensor is such that the Schrödinger operator is positive has finite fundamental group. As a continuation of our earlier results, we obtain isoperimetric inequa…
A federated model learns shared archetypes from heterogeneous clients in continual learning.
In this paper, we introduce the concept of \emph{Poissonian occupation times} below level 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…
We consider the optimal stopping of a class of spectrally negative jump diffusions. We state a set of conditions under which the value is shown to have a representation in terms of an ordinary nonlinear programming problem. We establish a connection between the considered problem and a stopping problem of an associated…
We consider the Whitham equations for deformations of hyperelliptic spectral curves, which preserve all periods of a meromorphic differential. If the meromorphic differential has a root at a fixed point of the hyperelliptic involution, then the Whitham flow has a singularity. We prove that the stable and unstable manif…
It is a well-known fact that on a bounded spectral interval the Dirac spectrum can be described locally by a non-decreasing sequence of continuous functions of the Riemannian metric. In the present article we extend this result to a global version. We think of the spectrum of a Dirac operator as a function from the int…
New optimizer SF-NorMuon matches tuned AdamW across various horizons.
The paper develops spectral networks in symplectic topology and their relation to Lagrangian fillings.
SG-NTF completes HDI tensors with spectral mapping and spatio-temporal gating.
This paper analyzes optimal stopping regions for American options with Poisson exercise opportunities.
An important form of prior information in clustering comes in form of cannot-link and must-link constraints. We present a generalization of the popular spectral clustering technique which integrates such constraints. Motivated by the recently proposed -spectral clustering for the unconstrained problem, our method is…
A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although they are not presented this way, can be viewed as spectral methods on matrices bui…
In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary kernels, and propose a family of spectral kernels that extends existing approac…
We continue the study of the spectral theory associated to integrable metrics, started in our previous paper arXiv:1301.1793 [math.SP]. We introduce the notion of 1-integrable metric on line-bundles on a compact Riemann surface. We extend the spectral theory of generalized Laplacians to line-bundles equipped with 1-int…
Summary of a talk given at the International Seminar "Analysis of spectral invariants and related operator theory", Tokyo University of Science, Unga Campus, 5-6 Oct. 2009
The paper extends spectral estimates to hyperbolic surfaces with hyperbolic ends.
Novel Haar-Laplacian for directed graphs enhances spectral graph applications.
Estimates for Schrödinger operators on manifolds with bounded Ricci curvature.
Spectral images captured by satellites and radio-telescopes are analyzed to obtain information about geological compositions distributions, distant asters as well as undersea terrain. Spectral images usually contain tens to hundreds of continuous narrow spectral bands and are widely used in various fields. But the vast…
Analysis of DPPs and k-DPPs via spectral decomposition reveals identifiable parameters and non-identifiability gaps.
Wave operators and spectral stability for Dirac operators under Ricci flow.
New framework detects directional influence in multivariate time series.
Study heat kernel on manifolds with fibred boundary metrics.
We provide two examples of spectral analysis techniques of Schroedinger operators applied to geometric Laplacians. In particular we show how to adapt the method of analytic dilation to Laplacians on complete manifolds with corners of codimension 2 finding the absence of singular continuous spectrum for these operators,…
New spectral invariants recover Calabi invariant for surface dynamics.
This paper gives new concentration inequalities for the spectral norm of a wide class of matrix martingales in continuous time. These results extend previously established Freedman and Bernstein inequalities for series of random matrices to the class of continuous time processes. Our analysis relies on a new supermarti…
Muon dynamics study uses spectral Wasserstein flow for optimization stability.
This paper re-visits the spectral method for learning latent variable models defined in terms of observable operators. We give a new perspective on the method, showing that operators can be recovered by minimizing a loss defined on a finite subset of the domain. A non-convex optimization similar to the spectral method …
New neural architectures invariant to sign flips and basis symmetries for graph representation learning.