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.
Paper proves min-vol NMF robust to noise under expanded condition.
Scattering networks maximize separation on low-dimensional data.
Paper checks SSC for matrix factorizations using Gurobi.
We develop the scattering theory of general conformally compact metrics. For low frequencies, the domain of the scattering matrix is shown to be frequency dependent. In particular, generalized eigenfunctions exhibit L^2 decay in directions where the asymptotic curvature is sufficiently negative. The scattering matrix i…
In this letter, we propose a new identification criterion that guarantees the recovery of the low-rank latent factors in the nonnegative matrix factorization (NMF) model, under mild conditions. Specifically, using the proposed criterion, it suffices to identify the latent factors if the rows of one factor are \emph{suf…
New method uses broken scattering to uniquely identify Finsler manifolds.
We prove that if two non-trapping obstacles in satisfy some rather weak non-degeneracy conditions and the scattering rays in their exteriors have (almost) the same travelling times or (almost) the same scattering length spectrum, then they coincide.
Establishes scattering theory for de Sitter vacuum solutions in even dimensions.
Unified geometric scattering model for measure spaces.
Paper develops formulas for shape derivatives in wave scattering.
We provide a simple way to obtain the meromorphic extension of Eisenstein series and Scattering matrices under conditions which generalize the case of discrete groups acting convex cocompactly on hyperbolic spaces.
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of the success of convolutional neural networks (ConvNets) in image data analysis and other tasks. Inspired by recent interest in geometric deep learning, which aims to generalize ConvNets to manifold and gra…
Study fixed angle inverse scattering with Riemannian metrics, proving uniqueness and stability.
Scattering theory for linearised gravity on Schwarzschild black hole exterior.
Wavelet scattering spectra model non-Gaussian time-series, proving scale invariance for self-similar processes.
This paper is devoted to the study of the Reissner-Nordstrøm-de Sitter black holes and their maximal analytic extensions. In particular, we study some of their properties that lays the groundwork for separate papers where we obtain decay results and construct conformal scattering theories for test fields on such spacet…
Regularizes 3D inverse scattering with tangent-point energy for better solutions.
Solves a challenging problem in imaging and communication.
We study the first-order scattering transform as a candidate for reducing the signal processed by a convolutional neural network (CNN). We show theoretical and empirical evidence that in the case of natural images and sufficiently small translation invariance, this transform preserves most of the signal information nee…
In this paper we introduce a notion of scattering theory for the Laplace-Beltrami operator on non-compact, connected and complete Riemannian manifolds. A principal condition is given by a certain positive lower bound of the second fundamental form of angular submanifolds at infinity. Another condition is certain bounds…
Gaussian belief propagation (BP) has been widely used for distributed inference in large-scale networks such as the smart grid, sensor networks, and social networks, where local measurements/observations are scattered over a wide geographical area. One particular case is when two neighboring agents share a common obser…
In this paper, we study the problem of multi-band (frequency-variant) covariance interpolation with a particular emphasis towards massive MIMO applications. In a massive MIMO system, the communication between each BS with antennas and each single-antenna user occurs through a collection of scatterers in the e…
New model predicts radiative properties of nanoparticle layers with high accuracy and uncertainty.
We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be computable. This paper will demonstrate the potential of the scattering symplect…
We introduce general scattering transforms as mathematical models of deep neural networks with l2 pooling. Scattering networks iteratively apply complex valued unitary operators, and the pooling is performed by a complex modulus. An expected scattering defines a contractive representation of a high-dimensional probabil…
Paper explains scattering diagrams' role in mirror symmetry.
GSAN learns adaptive node representations using geometric scattering and attention.
New method learns soliton dynamics from scattering data without assuming known equations.
Scattering representations simplify SBI for images without extra compression.
We consider solutions to the anti-self-dual Yang Mills (ASDYM) equations in split signature that are global on the double cover of the appropriate conformally compactified Minkowski space $\widetilde\M$. Ward's ASDYM twistor construction is adapted to this geometry by using a correspondence between points of $\widetild…
Billiard trajectories (broken generalised geodesics) are considered in the exterior of an obstacle with smooth boundary on an arbitrary Riemannian manifold. We prove a generalisation of the well-known Santalo's formula. As a consequence, it is established that if the set of trapped points has positive measure, then…
New algorithms for SSMF with weaker identifiability conditions than SSC.
The paper establishes scattering theory for wave equations on Schwarzschild spacetime.
Study scattering rigidity on stationary manifolds using geodesics.
MODWST improves classification tasks with wavelet scattering.
Study on scattering geodesics on modular surface and their sojourn times.
Scattering theory on Riemann surfaces with explicit matrix and generalized period mappings.
Study on recovering Lorentzian metrics from scattering data.
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric…
Bayesian Scattering offers a simple baseline for image data uncertainty.
The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. Recently, several works have introduced generalizations of the scattering transform for non-Euclidean settings such as graphs. Our work builds upon these constructions by introducin…
We construct continuous families of scattering manifolds with the same scattering phase. The manifolds are compactly supported metric perturbations of Euclidean for . The metric perturbation may have arbitrarily small support.
Model predicts stable molecules with AI and physics constraints.
Scattering theory for harmonic one-forms on Riemann surfaces.
Paper shows how scattering maps of Schrödinger equations relate to metrics.
The problem of recovering the asymptotics of a short range perturbation of the Euclidean metric on R^n from fixed energy scattering data is studied. It is shown that if two such metrics, g1, g2, have scattering data at some fixed energy which are equal up to smoothing, then there exists a diffeomorphism ψ`fixing infini…
Scattering theory developed for linearised gravity near Schwarzschild black hole.
We develop a geometric scattering theory for a geometrically finite group acting on (a vector bundle over) a symmetric space of negative curvature. In particular, we obtain the meromorphic continuation of Eisenstein series and scattering matrices and their functional equations.