arXiv research

Extends Minkowski stability proof to minimal decay assumptions.

New method creates vacuum data at minimal and borderline decay thresholds.

Unique solutions found for wave-like decaying null infinity equations.

New findings on flatness of certain metrics with fast decay.

Study on curvature decay in steady Ricci solitons, proving dichotomy.

Cautious Weight Decay modifies weight decay for better optimization.

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.

Introduces gradient decay in Softmax for better generalization.

Study examines wave equation decay and Strichartz estimates on conic manifolds.

Study shows uniform decay rate for singular mean curvature flows.

Weight decay stabilizes training dynamics by slowing progressive sharpening.

Polynomial decay of correlations shown for curved surfaces.

Last SGD iterate bounds for overparameterized linear regression.

Optimal learning rates decay to zero in easy tasks and maintain a warmup phase in hard tasks.

We found that factors decay over time, with momentum fitting best.

The paper predicts and explains the decay of stock anomaly performance over time.

Sharp decay found for solutions of a specific equation in Lie groups.

We give conditions which imply that a complete noncompact manifold with quadratic curvature decay has finite topological type. In particular, we find links between the topology of a manifold with quadractic curvature decay and some properties of the asymptotic cones of such a manifold.

The paper extends decay estimates to graphs with positive spectrum.

The paper studies harmonic map heat flow stability and decay rates.

In this paper, we give a description for steady Ricci solitons with a linear decay of sectional curvature. In particular, we classify all 3-dimensional steady Ricci solitons and 4-dimensional $κ$-noncollpased steady Ricci solitons with nonnegative sectional curvature under the linear curvature decay.

Extends global stability of Minkowski spacetime to minimal decay assumptions.

SHIFT framework identifies subgroups with large ML model performance decay.

New Sobolev inequalities found for curved spaces.

New inequality shows energy growth and decay in geometric problems.

Study on optimal ReLU networks with weight decay for interpolation.

We consider a model for linear transient price impact for multiple assets that takes cross-asset impact into account. Our main goal is to single out properties that need to be imposed on the decay kernel so that the model admits well-behaved optimal trade execution strategies. We first show that the existence of such s…

Sharp decay constant for positive scalar curvature metrics on manifolds.

Novel Adam-family method with decoupled weight decay for training neural networks.

Constructs index for elliptic operators using rapidly decaying kernels.

Regularization in the optimization of deep neural networks is often critical to avoid undesirable over-fitting leading to better generalization of model. One of the most popular regularization algorithms is to impose L-2 penalty on the model parameters resulting in the decay of parameters, called weight-decay, and the …

Study shows decay of correlations on specific types of flows.

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…

Study optimizes decay estimates for minimizing currents in submanifolds.

Paper shows existence of vortex solutions with specific decay properties.

SGD and weight decay encourage neural networks to learn low-rank weight matrices.

We get decay rate of higher derivatives of nonlinear massless Dirac equations with a kind of "good" spin null form. The method we rely on is similar to that of Li and Zang. However, they only give the decay rate of solution itself to nonlinear massless Dirac system.

Weight decay is one of the standard tricks in the neural network toolbox, but the reasons for its regularization effect are poorly understood, and recent results have cast doubt on the traditional interpretation in terms of $L_2$ regularization. Literal weight decay has been shown to outperform $L_2$ regularization for…

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…

Forward construction of vacuum initial data with limited decay

The paper improves energy decay estimates for Dir-stationary Q-valued functions and applies them to Liouville-type theorems and continuity.

Step decay schedules improve convergence in non-convex optimization.

A new method to improve deep neural networks using weight rescaling.

Study finds solutions to inequality decay to zero on warped cylinders.

Previous work of the authors establishes a criterion on the fundamental group of a knot complement that determines when Dehn surgery on the knot will have a fundamental group that is not left-orderable. We provide a refinement of this criterion by introducing the notion of a decayed knot; it is shown that Dehn surgery …

The paper studies steady solitons with curvature decay and proves their smoothness.

This paper reveals periodic behavior in neural network training with BN and weight decay.