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.
Polynomial decay of correlations shown for curved surfaces.
Study on scalar curvature decay on non-compact manifolds linked at infinity.
Study on massless Vlasov equation on Reissner-Nordström spacetimes, showing decay rates and non-decay phenomena.
Study on Kähler manifolds connects curvature decay with growth of holomorphic functions.
New bounds for KRR condition number reveal overfitting phenomena.
We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards the iden…
Minimax optimal convergence rates for classes of stochastic convex optimization problems are well characterized, where the majority of results utilize iterate averaged stochastic gradient descent (SGD) with polynomially decaying step sizes. In contrast, SGD's final iterate behavior has received much less attention desp…
We study a notion of a Lipschitz, permutation-invariant "centroid" for triples of points in mapping class groups MCG(S), which satisfies a certain polynomial growth bound. A consequence (via work of Drutu-Sapir or Chatterji-Ruane) is the Rapid Decay Property for MCG(S).
Riemannian stochastic gradient descent converges faster with increasing batch size.
We study the geodesic X-ray transform on Cartan-Hadamard manifolds, and prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the sectional curvature is bounded, and polynomially decaying if the sectional curvature de…
Paper shows existence of vortex solutions with specific decay properties.
Develops exact convex optimization formulations for neural networks.
In this work, we consider solutions of the Maxwell equations on the Schwarzschild-de Sitter family of black hole spacetimes. We prove that, in the static region bounded by black hole and cosmological horizons, solutions of the Maxwell equations decay to stationary Coulomb solutions at a super-polynomial rate, with deca…
In this paper, we study harmonic and caloric functions of polynomial growth on a complete non-compact gradient shrinking Ricci soliton. On one hand, when the scalar curvature satisfies at least quadratic decay, we prove that the space of harmonic functions with fixed polynomial growth degree is finite dimensional. We a…
Last SGD iterate bounds for overparameterized linear regression.
In this paper, we prove the linear stability to gravitational and electromagnetic perturbations of the Reissner-Nordström family of charged black holes with small charge. Solutions to the linearized Einstein-Maxwell equations around a Reissner-Nordström solution arising from regular initial data remain globally bounded…
We extend Eardley and Moncrief's estimates for the conformally invariant Yang-Mills-Higgs equations to the Einstein cylinder. Our method is to first work on Minkowski space and localise their estimates, and then carry them to the Einstein cylinder by a conformal transformation. By patching local estimates to…
This paper deals with two related problems, namely distance-preserving binary embeddings and quantization for compressed sensing . First, we propose fast methods to replace points from a subset , associated with the Euclidean metric, with points in the cube and we associa…
Study shows neural networks trained with GD converge to Gaussian processes with polynomial decay.
The paper extends Bonnet-Myers theorem for manifolds with nonnegative Ricci curvature.
Paper develops an online learning algorithm for functional data models.
Study on instability of extreme Reissner-Nordström spacetime perturbations.
New polynomial-time solutions found for training ReLU networks, mirroring Max-Cut complexity.
We investigate if kernel regularization methods can achieve minimax convergence rates over a source condition regularity assumption for the target function. These questions have been considered in past literature, but only under specific assumptions about the decay, typically polynomial, of the spectrum of the the kern…
Link invariants fail to detect most links with high probability.
We give a purely complex geometric proof of the existence of the Bergman kernel expansion. Our method provides a sharper estimate, and in the case that the metrics are real analytic, we prove that the remainder decays faster than any polynomial.
We study the behavior of hyperbolic affine automorphisms of a translation surface which is infinite in area and genus that is obtained as a limit of surfaces built from regular polygons studied by Veech. We find that hyperbolic affine automorphisms are not recurrent and yet their action restricted to cylinders satisfie…
In this paper, we study the online learning algorithm without explicit regularization terms. This algorithm is essentially a stochastic gradient descent scheme in a reproducing kernel Hilbert space (RKHS). The polynomially decaying step size in each iteration can play a role of regularization to ensure the generalizati…
Study analyzes learnability of RKHS under L∞ norm for kernel methods.
Stochastic (sub)gradient methods require step size schedule tuning to perform well in practice. Classical tuning strategies decay the step size polynomially and lead to optimal sublinear rates on (strongly) convex problems. An alternative schedule, popular in nonconvex optimization, is called \emph{geometric step decay…
The authors prove that the logarithmic Monge-Ampère flow with uniformly bound and convex initial data satisfies uniform decay estimates away from time . Then applying the decay estimates, we conclude that every entire classical strictly convex solution of the equation {equation*} \det D^{2}u=\exp\{n(-u+1/2\sum_{i=…
Eigenvalues of random hyperbolic surface covers converge to hyperbolic plane's.
New theory sharpens Q-learning with LDTZ rate, proving it's best of both worlds.
Adaptive algorithm identifies best arm with abstention, showing phase transition from polynomial to exponential error probability.
The Matérn covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Matérn class is that it is possible to get precise control over the degree of mean-square differentiability of the random process. However, the Matérn class possesses e…
The paper constructs Ricci-flat Kähler manifolds with specific decay properties.
Study efficient neural operator learning using variation spaces.
We prove in this paper the linear stability of the celebrated Schwarzschild family of black holes in general relativity: Solutions to the linearisation of the Einstein vacuum equations around a Schwarzschild metric arising from regular initial data remain globally bounded on the black hole exterior and in fact decay to…
The paper establishes curvature estimates for solitons in higher dimensions.
Unified analysis of kernel-based and locally adaptive bandit optimization methods.
This work improves polynomial approximations for functions with asymmetric behavior.
New method models fat-tailed distributions with anisotropic tail-adaptive flows.
New ensemble method improves model stability exponentially.
We consider solutions to the linear wave equation on a non-extremal maximally extended Schwarzschild-de Sitter spacetime arising from arbitrary smooth initial data prescribed on an arbitrary Cauchy hypersurface. (In particular, no symmetry is assumed on initial data, and the support of the solutions may con…
We prove boundedness and polynomial decay statements for solutions to the spin Teukolsky-type equation projected to the spherical harmonic on Reissner-Nordström spacetime. The equation is verified by a gauge-invariant quantity which we identify and which involves the electromagnetic and curvature tensor…
Motivated by the Strong Cosmic Censorship Conjecture for asymptotically AdS spacetimes, we initiate the study of massive scalar waves satisfying on the interior of Anti-de Sitter (AdS) black holes. We prescribe initial data on a spacelike hypersurface of a Reissner--Nordström--AdS black hole and impose…
We prove that the mapping torus group $\FN \rtimes_α \Z$ of any automorphism of a free group $\FN$ of finite rank is weakly hyperbolic relative to the canonical (up to conjugation) family of subgroups of $\FN$ which consists of (and contains representatives of all) conjugacy classes that …
As the success of deep learning reaches more grounds, one would like to also envision the potential limits of deep learning. This paper gives a first set of results proving that certain deep learning algorithms fail at learning certain efficiently learnable functions. The results put forward a notion of cross-predictab…