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.
Introduces spectral-domain Wasserstein distance and Gelbrich bound for elliptical processes.
Estimates spectral gap for Brownian motion on sticky-reflecting domains.
Deep learning's success has been widely recognized in a variety of machine learning tasks, including image classification, audio recognition, and natural language processing. As an extension of deep learning beyond these domains, graph neural networks (GNNs) are designed to handle the non-Euclidean graph-structure whic…
Efficiently scales continuous kernels with sparse Fourier domain learning.
The paper bridges spectral and spatial graph convolutions, improving model capacity and transferability.
Corners can be identified by a drum's sound spectrum.
Paper proposes a forecasting model combining autoregressive models with spectral attention.
New method optimizes portfolios for non-stationary markets.
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…
SpGAT learns graph representations using spectral attention for efficiency.
Cross-domain recommendation can alleviate the data sparsity problem in recommender systems. To transfer the knowledge from one domain to another, one can either utilize the neighborhood information or learn a direct mapping function. However, all existing methods ignore the high-order connectivity information in cross-…
Study proves spectral determination of triangles and quadrilaterals, with restrictions on higher-order polygons.
Previous research has shown that computation of convolution in the frequency domain provides a significant speedup versus traditional convolution network implementations. However, this performance increase comes at the expense of repeatedly computing the transform and its inverse in order to apply other network operati…
Study finds finitely many non-congruent polygonal domains with same Steklov spectrum.
Dimensionality reduction (DR) methods have attracted extensive attention to provide discriminative information and reduce the computational burden of the hyperspectral image (HSI) classification. However, the DR methods face many challenges due to limited training samples with high dimensional spectra. To address this …
Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.
Domains in infinite jets present the simplest class of diffieties with boundary. In this note some basic elements of geometry of these domains are introduced and an analogue of the C-spectral sequence in this context is studied. This, in particular, allows cohomological interpretation and analysis of initial data, boun…
Data vectors are obtained from multiple domains. They are feature vectors of images or vector representations of words. Domains may have different numbers of data vectors with different dimensions. These data vectors from multiple domains are projected to a common space by linear transformations in order to search clos…
The article proves a conjecture about the fundamental gap for horoconvex domains in hyperbolic space.
New method trains neural networks in spectral domain for improved performance.
Lattice formulation captures Atiyah-Patodi-Singer index.
Multi-output Gaussian processes (MOGPs) are an extension of Gaussian Processes (GPs) for predicting multiple output variables (also called channels, tasks) simultaneously. In this paper we use the convolution theorem to design a new kernel for MOGPs, by modeling cross channel dependencies through cross convolution of t…
We prove the Fundamental Gap Conjecture, which states that the difference between the first two Dirichlet eigenvalues (the spectral gap) of a Schrödinger operator with convex potential and Dirichlet boundary data on a convex domain is bounded below by the spectral gap on an interval of the same diameter with zero poten…
FreDN separates trends and periodicities in non-stationary time series forecasts.
Study of spectral flow in symmetric Toeplitz operator families.
Bayesian model reconstructs time and frequency data robustly.
We show that the (graded) spectral flow of a family of Toeplitz operators on a complete Riemannian manifold is equal to the index of a certain Callias-type operator. When the dimension of the manifold is even this leads to a cohomological formula for the spectral flow. As an application, we compute the spectral flow of…
The paper detects changes in graph signal means offline.
HyFAD improves time series imputation by combining time and frequency diffusion.
Study spectral properties of sub-Laplacians in Carnot groups.
A novel unsupervised domain adaptation method using hierarchical optimal transport.
Partial convexification improves tractability of low-rank spectral optimization problems.
Symplectic homology matches dual capacities for convex domains.
Sharp lower bound for Hodge Laplacian on Kähler hyperbolic manifolds.
Paper develops Riemannian geometry for SPSD matrices with DA applications.
Deep learning speeds spectral density estimation for large 2D/3D grids.
Discrete Fourier transforms provide a significant speedup in the computation of convolutions in deep learning. In this work, we demonstrate that, beyond its advantages for efficient computation, the spectral domain also provides a powerful representation in which to model and train convolutional neural networks (CNNs).…
New equivariant filters improve graph classification.
Hyperspectral images (HSI) contain a wealth of information over hundreds of contiguous spectral bands, making it possible to classify materials through subtle spectral discrepancies. However, the classification of this rich spectral information is accompanied by the challenges like high dimensionality, singularity, lim…
New kernels capture both local and non-local interactions efficiently.
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…
This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in arbitrary dimensions. Second, we connect the proposed metric (defined in the spatia…
Develops a dynamical method to prove the sharp Berezin-Li-Yau inequality.
We propose a new framework for manifold denoising based on processing in the graph Fourier frequency domain, derived from the spectral decomposition of the discrete graph Laplacian. Our approach uses the Spectral Graph Wavelet transform in order to per- form non-iterative denoising directly in the graph frequency domai…
New neural network rates for unbounded domains with weighted Sobolev spaces.
Gaussian processes classify graphs using vertex and edge features.
In this paper we construct compact manifolds with fixed boundary geometry which admit Riemannian metrics of unit volume with arbitrarily large Steklov spectral gap. We also study the effect of localized conformal deformations that fix the boundary geometry. For instance, we prove that it is possible to make the spectra…
This paper establishes the consistency of spectral approaches to data clustering. We consider clustering of point clouds obtained as samples of a ground-truth measure. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. We investigate the…