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 introduces kernel deformed exponential families for sparse continuous attention.
Researchers derived heat kernel expansions for non-compact spaces using Witten deformation.
Inspired by Berndtsson's work on the subharmonicity property of the Bergman kernel, we give a local variation formula of the full Bergman kernels associated to deformations of complex manifolds. In compact case, it follows from the reproducing property of the Bergman kernel and the curvature formula of the 0-th direct …
Deformations of compact Riemann surfaces are considered using a Čech cohomology sliding overlaps approach. Cocycles are calculated for conformal cutting and regluing deformations at zeros of Abelian differentials. A second order deformation expansion is presented for the Riemann period matrix. A complete deformation ex…
The study examines the geometry of Lichnerowicz Laplacian's kernel on various spaces.
The paper studies neural networks with wide layers and finds a deformed semicircle law.
New system uses microwave radar for hand gesture recognition, improving accuracy and reducing processing time.
The geometric approach to diffeomorphic image registration known as "large deformation by diffeomorphic metric mapping" (LDDMM) is based on a left action of diffeomorphisms on images, and a right-invariant metric on a diffeomorphism group, usually defined using a reproducing kernel. We explore the use of left-invariant…
Introduces a new spectral geometry framework with dissipative data.
Hodge numbers of Sasakian manifolds remain unchanged under deformations.
Study deformations of G2-instantons on nearly G2 manifolds.
We formulate the deformation theory for instantons on nearly Kähler six-manifolds using spinors and Dirac operators. Using this framework we identify the space of deformations of an irreducible instanton with semisimple structure group with the kernel of an elliptic operator, and prove that abelian instantons are rigid…
Study instantons on asymptotically conical Spin(7)-manifolds, identifying deformation spaces.
Analyzes complex structure deformations using cohomology contraction methods.
Wiatowski and Bölcskei, 2015, proved that deformation stability and vertical translation invariance of deep convolutional neural network-based feature extractors are guaranteed by the network structure per se rather than the specific convolution kernels and non-linearities. While the translation invariance result appli…
Following Donaldson's oppenness theorem on deforming a conical Kähler-Einstein metric, we prove a parabolic Schauder-type estimate with respect to conical metrics. As a corollary, we show that the conical Kähler-Ricci Flow exists for short time. The key is to establish the relevant heat kernel estimates, where we use t…
Study shows how to reduce data needed for learning under geometric constraints.
The paper analyzes Kähler-Ricci flow near Kähler-Ricci solitons under complex structure deformation.
Study the inductive bias of neural networks using neural tangent kernels.
Novel drift detection method using deformation analysis in ML models.
A new method for non-rigid point set registration reduces computational complexity.
2L-FUSE enhances feature sparsity through kernel learning.
This paper is dedicated to the study of deformations of coassociative 4-folds in a G_2 manifold which have conical singularities. We stratify the types of deformations allowed into three problems. The main result for each problem states that the moduli space is locally homeomorphic to the kernel of a smooth map between…
Researchers resolve string theory ambiguities and define a new metric for massless spectrum.
Study on deformation of weighted scalar curvature, proving geometric results and stability.
We prove a local index theorem of Atiyah-Singer type for Dirac operators on manifolds with a Lie structure at infinity (Lie manifolds for short). With the help of a renormalized supertrace, defined on a suitable class of regularizing operators, the proof of the index theorem relies on a rescaling technique similar in s…
The paper introduces new metric structures on -foliations and uses a flow to deform them.
Bayesian neural networks explore rare fluctuations for better feature learning.
We give a condition which ensures that the Paneitz operator of an embedded three-dimensional CR manifold is nonnegative and has kernel consisting only of the CR pluriharmonic functions. Our condition requires uniform positivity of the Webster scalar curvature and the stability of the CR pluriharmonic functions for a re…
Let (M,g) be a compact Riemannian spin manifold. The Atiyah-Singer index theorem yields a lower bound for the dimension of the kernel of the Dirac operator. We prove that this bound can be attained by changing the Riemannian metric g on an arbitrarily small open set.
A new method uses Gaussian Processes for feature-based nonrigid image registration.
Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size of the data. Many natural measures of similarity between pairs of samples are not…
Study instantons on -manifolds, proving uniqueness.
We study coassociative 4-folds N in R^7 which are asymptotically conical to a cone C with rate lambda<1. If lambda is in the interval [-2,1) and generic, we show that the moduli space of coassociative deformations of N which are also asymptotically conical to C with rate lambda is a smooth manifold, and we calculate it…
We consider finite area convex Euclidean circular sectors. We prove a variational Polyakov formula which shows how the zeta-regularized determinant of the Laplacian varies with respect to the opening angle. Varying the angle corresponds to a conformal deformation in the direction of a conformal factor with a logarithmi…
Unified theory for adaptive image convolutions using metric perspectives.
New geometric Joyce structures on moduli spaces of quadratic differentials.
Informative and discriminative feature descriptors play a fundamental role in deformable shape analysis. For example, they have been successfully employed in correspondence, registration, and retrieval tasks. In the recent years, significant attention has been devoted to descriptors obtained from the spectral decomposi…
Given an associative 3-fold in R^7 which is asymptotically conical with generic rate less than 1, we show that its moduli space of deformations is locally homeomorphic to the kernel of a smooth map between smooth manifolds. Moreover, the virtual dimension of the moduli space is computed and shown to be non-negative for…
We obtain a family of matrix integrals which decompose to a product of Gamma-functions (they have some relations with S.G.Gindikin 'Beta', but generally speaking essentially differ from it). We obtain Plancherel formula for Berezin representations for all series of classical groups (for large values of parameters of re…
Kernel Flows approximates unknown functions using numerical kernel selection.
By a theorem of Mclean, the deformation space of an associative submanifold Y of an integrable G_2 manifold (M,φ) can be identified with the kernel of a Dirac operator D:Ω^{0}(ν) -->Ω^{0}(ν) on the normal bundle νof Y. Here, we generalize this to the non-integrable case, and also show that the deformation space becomes…
Optimizes metric in LDDMM for better image registration and classification.
The success of deep convolutional architectures is often attributed in part to their ability to learn multiscale and invariant representations of natural signals. However, a precise study of these properties and how they affect learning guarantees is still missing. In this paper, we consider deep convolutional represen…
Study moduli space of quadratic differentials with new geometric insights.
The paper discusses methods to compute Green's function on algebraic surfaces using Schottky uniformization.
We extend our analysis in [arXiv:0801.4782] and show that the chiral algebras of (0,2) sigma models are totally trivialized by worldsheet instantons for all complete flag manifolds of compact semisimple Lie groups. Consequently, supersymmetry is spontaneously broken. Our results verify Stolz's idea that there are no ha…
Gradient descent reshapes the function space of neural networks.