In this paper we continue our study of the Laplacian on manifolds with axial analytic asymptotically cylindrical ends initiated in~arXiv:1003.2538. By using the complex scaling method and the Phragmén-Lindelöf principle we prove exponential decay of the eigenfunctions corresponding to the non-threshold eigenvalues of t…
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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.
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48 results for “exponentially decaying thresholding”
A new method for estimating sparse inverse covariance matrices.
problem Recovering the connectivity and non-connectivity graph of covariates.
method Adaptive thresholding in a transformed domain of the inverse covariance matrix.
result The proposed method outperforms state-of-the-art methods in accuracy.
New method creates vacuum data at minimal and borderline decay thresholds.
problem Creating vacuum initial data at specific decay thresholds.
method Conical solution-operator method applied to vacuum asymptotically flat initial data.
result Demonstrates global and exterior stability of Minkowski spacetime.
It will be discussed the statistics of the extreme values in time series characterized by finite-term correlations with non-exponential decay. Precisely, it will be considered the results of numerical analyses concerning the return intervals of extreme values of the fluctuations of resistance and defect-fraction displa…
The study shows that the visible range from a point on harmonic manifolds follows an exponential distribution.
problem Understanding the visible range from a point on harmonic manifolds.
method Analyzing Poisson Boolean models on harmonic manifolds, focusing on the geometric mechanism of tube volumes around geodesic segments.
result The visible range from a point on harmonic manifolds follows an exponential distribution.
A random walk on a separable, geodesic hyperbolic metric space converges to the boundary with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes positive linear progress. Progress is known to be linear with exponential decay when …
Existence of Solutions to the Seiberg-Witten Vortex Equations with Exponential Decay on the Planemath.AP
Paper shows existence of vortex solutions with specific decay properties.
problem Existence of solutions to Seiberg-Witten equations with specific decay properties.
method Dimensional reduction of Seiberg-Witten equations on the plane.
result Contains both exponentially decayed and polynomial growth solutions.
New method trains neural networks with threshold activation functions efficiently.
problem Training neural networks with threshold activation functions is challenging due to zero gradients.
method We study weight decay regularized training problems of deep neural networks with threshold activations, showing they can be formulated as convex optimization problems.
result Regularized deep threshold network training problems can be formulated as standard convex optimization problems, paralleling the LASSO method.
We show that the probability that a finitely supported random walk on a non-elementary subgroup of the the mapping class group gives a non-pseudo-Anosov element decays exponentially in the length of the random walk. More generally, we show that if R is a set of mapping class group elements with an upper bound on their …
In this paper, we examine the dependence of standard gluing process for pseudoholomorphic curves under the change of the length of the neck-region with respect to the cylindrical metrics associated to the given analytic coordinates near the punctures in the setting of bordered open Riemann surface with boundary pun…
Weight decay stabilizes training dynamics by slowing progressive sharpening.
problem Understanding how weight decay affects training stability in deep learning models.
method Analyzing weight decay effects at the Edge of Stability, developing a mathematical framework.
result Weight decay dampens oscillations and stabilizes sharpness in CNNs, causing a phase transition in MLPs.
We prove exponential decay of correlations for Hölder continuous observables with respect to any Gibbs measure for contact Anosov flows admitting Pesin sets with exponentially small tails. This is achieved by establishing strong spectral estimates for certain Ruelle transfer operators for such flows.
AdamNX improves Adam's stability by adjusting its learning rate.
problem Adam's tendency to converge to non-flat minima in large-scale models.
method Proposes a novel exponential decay mechanism for Adam's second-order moment estimate.
result AdamNX outperforms Adam and its variants in stability and performance.
A new accelerated method with simpler momentum update rules.
problem Optimizing parameters in machine learning models.
method Proposes a novel accelerated stochastic gradient method with simpler momentum update rules.
result The method outperforms Sgdm and Adam in practical problems.
Unified framework for analyzing gradient flows of measures with exponential decay of entropy.
problem Analyzing exponential decay of entropy functionals in gradient flows of measures.
method Characterization of global exponential decay behaviors using Hellinger-Kantorovich geometry, shape-mass decomposition, and Polyak-Łojasiewicz-type inequalities.
result Unified theoretical framework for gradient flows with complete analysis of exponential decay behaviors.
The paper examines the optimality of kernel methods in high-dimensional clustering.
problem Understanding the optimality of kernel methods in high-dimensional data clustering.
method High-dimensional Gaussian clustering, exponential kernel function, kernel k-means, semi-definite relaxation.
result The exponential kernel function optimally recovers clusters in high-dimensional data, matching information-theoretic limits up to a factor of √2.
New exponential decay estimate for Hermitian Yang-Mills metrics near branch points.
problem Understanding the behavior of Hermitian Yang-Mills metrics near branch points.
method Local radial solutions, global gluing construction, exponential estimate near branch points.
result Exponential decay estimate for local radial solutions near branch points.
In a financial market, for agents with long investment horizons or at times of severe market stress, it is often changes in the asset price that act as the trigger for transactions or shifts in investment position. This suggests the use of price thresholds to simulate agent behavior over much longer timescales than are…
We consider Hitchin's hyperkähler metric on the -Hitchin moduli space moduli space over a compact Riemann surface. We prove that the difference between the metric and a simpler "semiflat" hyperkähler metric is exponentially-decaying along generic rays in the Hitchin moduli s…
The goal of this paper is to prove a result conjectured in Föllmer and Schachermayer [FS07], even in slightly more general form. Suppose that S is a continuous semimartingale and satisfies a large deviations estimate; this is a particular growth condition on the mean-variance tradeoff process of S. We show that S then …
Approximations to utility indifference prices are provided for a contingent claim in the large position size limit. Results are valid for general utility functions on the real line and semi-martingale models. It is shown that as the position size approaches infinity, the utility function's decay rate for large negative…
Study on U-statistics with heavy-tailed samples, providing tail bounds and LDP.
problem Deviation of U-statistics with heavy-tailed samples.
method Exponential tail bounds and Large Deviation Principle (LDP) for U-statistics.
result Obtained an exponential upper bound for U-statistics tail decay, showing two regions of decay.
Study improves the exponential rate of metric difference in Higgs bundles.
problem Improving the exponential rate of metric difference in Higgs bundles.
method Analyzes the Hitchin metric and semi-flat metric in rank two Higgs bundles.
result Exponential rate of metric difference is improved.
Global exponential stability for the three-dimensional Navier-Stokes equations on hyperbolic spacemath-ph
Global stability proved for Navier-Stokes equations on hyperbolic space.
problem Stability of the Navier-Stokes equations on hyperbolic space.
method Proved global stability with exponential decay rate for small initial data.
result Exponential decay rate of $μλ_\Def^{(3)}$ for Navier-Stokes equations on hyperbolic space.
New research shows fixed-budget best-arm identification cannot match static oracle performance.
problem Fixed-budget best-arm identification's performance limitations.
method Analysis of various adaptive and static algorithms for best-arm identification.
result For any algorithm, there exists at least one instance where the error decay rate is at most \((1 + \frac{\log(K)}{8})^{-1}\) times that of the static oracle.
The paper studies Teichmüller TQFT for hyperbolic knots, proving exponential decay of partition functions.
problem Analyzing Teichmüller TQFT for hyperbolic knots with generalized FAMED triangulations.
method Introducing generalized FAMED property, proving exponential decay of partition functions in semi-classical limit.
result Partition functions decay exponentially with the volume of knot complements, and the 1-loop invariant emerges.
We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution has generically a stretched-exponential form, but can assume also an algebraic …
Solutions to the wave equation on de Sitter-Schwarzschild space with smooth initial data on a Cauchy surface are shown to decay exponentially to a constant at temporal infinity, with corresponding uniform decay on the appropriately compactified space.
New bounds for KRR condition number reveal overfitting phenomena.
problem Characterizing overfitting in KRR with varying kernel spectral decay.
method Derived new bounds for kernel matrices, enhanced test error bounds, and identified feature independence role.
result Identified tempered and catastrophic overfitting phenomena.
On the Polynomial and Exponential Decay of Eigen-Forms of Generalized Time-Harmonic Maxwell Problemsmath.AP
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…
We found that factors decay over time, with momentum fitting best.
problem Understanding how factors decay over time and their impact on performance.
method Derived a hyperbolic decay model for factors, tested against linear and exponential alternatives.
result Momentum exhibits hyperbolic decay, outperforming linear and exponential models.
SAD-DPSGD improves model performance on imbalanced medical datasets like HAM10000.
problem Data leakage and imbalanced distribution in medical image classification datasets.
method SAD-DPSGD uses a linear decaying mechanism for noise and clipping thresholds to enhance performance.
result SAD-DPSGD outperforms Auto-DPSGD on HAM10000, improving accuracy by 2.15%.
The study analyzes when Bayesian averaging over decision trees is reliable.
problem When do Bayesian model averaging weights over decision trees provide reliable information?
method Closed-form solution for Bayesian decision trees with Catalan-exponential priors.
result Established a complete non-asymptotic theory of rational commitment thresholds.
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…
New ensemble method improves model stability exponentially.
problem Improving model stability for discontinuous base learners.
method Selecting the most frequently generated model from subsamples.
result Exponentially decaying tails for excess risk.
Optimal execution of portfolio transactions is the essential part of algorithmic trading. In this paper we present in simple analytical form the optimal trajectory for risk-averse trader with the assumption of exponential market recovery and short-time investment horizon.
Decision trees and shallow neural networks have different geometric complexities, impacting their interpretability and accuracy.
problem The geometric simplicity of decision boundaries in decision trees conflicts with the approximation capabilities of shallow neural networks.
method Analysis of the Radon total variation (RTV) seminorm to compare geometric complexity of decision regions and neural network approximations.
result Smooth barrier scores can approximate decision regions with finite RTV, but their performance depends on the tube-mass condition near the decision boundary.
Sharp large deviations and Gibbs conditioning for portfolio credit risk models.
problem Analyzing the risk of default in financial portfolios with dependent factors.
method Sharp large deviation estimates and conditional Bahadur-Rao estimates for threshold models with diverging latent factors.
result Conditioned on a large exceedance event, default indicators become asymptotically i.i.d., and loss-given-default is exponentially tilted.
Study on biharmonic heat equation on manifolds with curvature constraints.
problem Analyzing entire solutions of biharmonic heat equation on manifolds.
method Exponential decay estimates for biharmonic heat kernel under Ricci curvature and noncollapsing conditions. Proving uniqueness criteria for Cauchy problem.
result Conservation law for biharmonic heat kernel and uniform L-infinity estimate for entire solutions.
We improve deep threshold networks' memorization capacity exponentially.
problem Memorizing datasets with randomized labels using deep neural networks.
method Using Gaussian random weights in the first layer and binary or integer weights in subsequent layers, we prove a new dependence on minimum distance.
result We show that neurons and weights are sufficient.
Analyzes dynamics of quantum neural networks, predicting exponential decay of training error.
problem Understanding convergence rate of quantum neural networks training.
method Analytic theory for gradient descent dynamics of wide quantum neural networks.
result Simple analytic formula predicts exponential decay of training error.
New model explains volatility after extreme stock market events.
problem Understanding volatility dynamics after extreme stock market events.
method Proposed a new dynamical model using high frequency minute data.
result Volatility after extreme events follows a stretched exponential decay initially and a power law decay later.
We consider a random walk on the mapping class group of a surface of finite type. We assume that the random walk is determined by a probability measure whose support is finite and generates a non-elementary subgroup . We further assume that is not consisting only of lifts with respect to any one covering. Then w…
VISTA learns causal structures by integrating local subgraphs, improving accuracy and efficiency.
problem Efficiently learning causal structures from high-dimensional observational data.
method VISTA decomposes the global causal structure learning problem into local subgraphs based on Markov Blankets, integrating them via a weighted voting mechanism.
result VISTA achieves notable improvements in accuracy and efficiency over existing methods.
Constructs index for elliptic operators using rapidly decaying kernels.
problem Index of elliptic operators in Fréchet algebra.
method Uses heat operators and heat kernel asymptotics.
result Index can be represented by an idempotent involving heat operators.
The paper establishes a nearly-sharp statistical threshold for efficient learning in Latent MDPs with separated components.
problem Learning Latent Markov Decision Processes (LMDPs) with separated components.
method The paper considers various notions of separation and establishes a nearly-sharp statistical threshold for efficient learning. It also presents a quasi-polynomial algorithm with time complexity scaling in terms of the statistical threshold under a weaker assumption of separability under the optimal policy, and a near-matching time complexity lower bound under the exponential time hypothesis.
result Establishes a nearly-sharp statistical threshold for efficient learning in Latent MDPs with separated components.
Simplicial persistence of financial markets: filtering, generative processes and portfolio riskq-fin.ST
Simplicial persistence measures financial market dynamics, revealing long-term structure evolution.
problem Understanding the long-term structure evolution of financial markets.
method Simplicial persistence, null models, TMFG filtering, thresholding, generative process analysis.
result More liquid markets exhibit slower persistence decay, suggesting higher fragility to systemic shocks.
The L1 loss landscape of neural nets near local minima behaves differently, revealing exponential decay and increased vertex density.
problem Understanding the L1 loss landscape of neural nets near local minima.
method Iterative minimization of the loss function on adjacent vertices of the Deep ReLU Simplex algorithm.
result Exponential decay of loss levels and increased vertex density around local minima.