arXiv research

New bound relaxes uniform gradient norm assumptions for PAC-Bayesian bounds.

Gradient bounds and Liouville theorems for quasi-linear equations on manifolds with nonnegative Ricci curvature.

The study classifies specific types of solitons with bounded scalar curvature.

The study finds a lower bound for the diameter of gradient ρ-Einstein solitons.

The paper provides gradient estimates for solutions on manifolds with integral Ricci bounds.

Paper establishes a generalization bound for gradient flow using a data-dependent kernel.

Generalizes smoothness conditions for optimization methods.

Sharp Gaussian bounds derived for Schrödinger kernel on Ricci solitons.

Derives gradient bounds for f-heat equations on manifolds with Bakry-Emery Ricci curvature.

Proves convergence of gradient Ricci shrinkers with uniform bounds.

5D shrinking solitons with bounded curvature are rigid.

Characterizes Kähler-hyperbolicity of bounded symmetric domains based on rank and genus.

Lower bounds show many sampling algorithms need many gradient queries.

In this paper, we prove the compactness theorem for gradient Ricci solitons. Let $(M_α, g_α)$ be a sequence of compact gradient Ricci solitons of dimension $n\geq 4$, whose curvatures have uniformly bounded $L^{\frac{n}{2}}$ norms, whose Ricci curvatures are uniformly bounded from below with uniformly lower bounded vol…

In this work we revisit gradient regularization for adversarial robustness with some new ingredients. First, we derive new per-image theoretical robustness bounds based on local gradient information. These bounds strongly motivate input gradient regularization. Second, we implement a scaleable version of input gradient…

New decay estimates for scalar curvature of steady gradient Ricci solitons.

New bounds for model generalization under deterministic gradient descent.

Improved bounds for proximal gradient algorithms with computational errors.

Short note on soft-max and policy gradients in bandit problems using Lyapunov functions.

Improved Gaussian process regression with tighter log marginal likelihood bounds.

We lower bound the complexity of finding $ε$-stationary points (with gradient norm at most $ε$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions through queries to an unbiased stochastic gradient oracle with bounded variance, we prove that (i…

Paper relaxes stability and generalization assumptions for SGD.

New research shows existing information-theoretic methods can't establish minimax rates for gradient descent in stochastic convex optimization.

Unified bounds for random subset generalization error and improved SGD Langevin dynamics.

New oracles improve stochastic optimization with noisy or biased measurements.

The natural gradient of ELBO vanishes in unconstrained optimization, simplifying learning.

In this very short note we prove a lower bound for the scalar curvature of certain steady gradient Ricci solitons.

Maxout networks study gradients and propose initialization strategies.

Gradient descent fails to learn simple neural networks efficiently.

Improved DP algorithms for non-convex optimization with tighter generalization bounds.

Paper formalizes and analyzes a new bound for variational inference.

New findings show margins are not sufficient for explaining gradient boosting performance.

SGD handles label noise with bounds improving over SGLD.

New algorithm guarantees performance on noisy data.

Many continuous control tasks have bounded action spaces. When policy gradient methods are applied to such tasks, out-of-bound actions need to be clipped before execution, while policies are usually optimized as if the actions are not clipped. We propose a policy gradient estimator that exploits the knowledge of action…

New bounds show BBVI's gradient variance matches SGD conditions, improving parameterization efficiency.

Optimizes shortfall risk using gradient-based methods.

Paper extends Aronson-Bénilan estimates for porous medium equations on manifolds with negative curvature.

Researchers estimate gradients of solutions to a Finslerian Allen-Cahn equation.

Paper develops probabilistic bounds for a stochastic gradient algorithm in non-convex problems.

SGD generalization bounds derived from information theory.

Sharp Lipschitz bounds and gradient estimates for fully nonlinear parabolic equations.

This work bounds the run-time of nonconvex optimization with early stopping.

The paper proves gradient estimates for a weighted p-Laplacian equation on Riemannian manifolds.

DIFF2 improves differential privacy in nonconvex optimization with better utility bounds.

Paper investigates conditions for independence of weak gradients on metric spaces.

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

Study 4D solitons with specific curvature properties, proving curvature bounds and classifying solutions.