Smoothing Bounds
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
A New Approach to Code Smoothing Bounds
arXiv:2603.18077v2 Announce Type: replace Abstract: Code smoothing is a phenomenon in which an error distribution makes a code statistically close to the uniform distribution over the ambient space. This closeness is measured by total variation distance. Recently, Debris-Alazard et al.\ introduced a smoothing bound, which is an upper bound on this total variation distance.
Sharp First-Order Lower Bounds for Higher-Order Smooth Nonconvex Optimization
arXiv:2606.05438v1 Announce Type: new Abstract: We study the deterministic first-order oracle complexity of finding \(\epsilon\)-stationary points in smooth nonconvex optimization when the objective satisfies higher-order smoothness assumptions. While the classical \(\epsilon^{-2}\) rate is optimal under only Lipschitz gradients, higher-order smoothness leads to accelerated first-order upper bounds, most notably the \(\epsilon^{-7/4}\) rate under Lipschitz Hessians and the...
Efficiently Escaping Saddle Points under Generalized Smoothness via Self-Bounding Regularity
Announce Type: replace-cross Abstract: We study the optimization of non-convex functions that are not necessarily smooth (gradient and/or Hessian are Lipschitz) using first order methods. Smoothness is a restrictive assumption in machine learning in both theory and practice, motivating significant recent work on finding first order stationary points of functions satisfying generalizations of smoothness with first order methods. We develop a novel framework that lets us systematically study...
Near-Optimal Pure Machine Unlearning for Smooth Strongly Convex Losses
arXiv:2606.01527v1 Announce Type: new Abstract: Machine unlearning is motivated by legal and user-facing requirements to remove the influence of individuals' data from trained models, such as the right to be forgotten. Prior work has developed algorithms and error bounds for unlearning in smooth strongly convex stochastic optimization, but the fundamental statistical cost of unlearning has remained unclear. We nearly resolve this problem by proving upper and lower bounds on the excess...
STON'R Converges to First-Order Nash~Equilibria of Multiplayer Games
arXiv:2606.09565v1 Announce Type: new Abstract: Nonconcave games present a unique challenge, as neither pure Nash equilibria nor local Nash equilibria (LNE) are guaranteed to exist, even in zero-sum settings. Additionally, computing approximate LNE in smooth multiplayer games over bounded regions is PPAD-hard. These challenges, coupled with the inherent complexity, have driven recent research toward broader equilibrium concepts, such as min-max critical points, and first-order Nash...
A high-order Fourier Continuation (FC)-based spectral incompressible Smoothed Particle Hydrodynamics (ISPH) scheme for general boundary conditions in wall-bounded domains
arXiv:2606.06247v1 Announce Type: new Abstract: In this paper, a high-order Fourier Continuation (FC) algorithm is introduced into the spectral smoothed particle hydrodynamics (SPH) scheme to simulate the wall-bounded incompressible flows. This work aims to extend the spectral ISPH scheme towards the high-order simulation of flows with non-periodic wall boundary conditions. Herein, a polynomial-based Fourier continuation technique is applied to the velocity and pressure to make the domain...
OptMuon: Closed-Loop Orthogonalized Momentum Methods for Stochastic Optimization with Zero-Noise Optimality
arXiv:2606.08783v1 Announce Type: cross Abstract: Orthogonalized momentum updates, as used in Muon-style optimizers, have recently shown strong empirical stability in large-scale deep learning. However, existing orthogonalized methods are typically paired with constant or open-loop magnitude rules, and therefore do not explicitly calibrate their update magnitudes from the observed optimization trajectory.
Minimax optimal differentially private synthetic data for smooth queries
arXiv:2602.01607v3 Announce Type: replace-cross Abstract: Differentially private synthetic data enables the sharing and analysis of sensitive datasets while providing rigorous privacy guarantees for individual contributors. A central challenge is to achieve strong utility guarantees for meaningful downstream analysis. Many existing methods ensure uniform accuracy over broad query classes, such as all Lipschitz functions, but this level of generality often leads to suboptimal rates for...
Improved Guarantees for Langevin Monte Carlo with Average Smoothness
arXiv:2605.31413v1 Announce Type: cross Abstract: We establish improved nonasymptotic bounds for Langevin Monte Carlo in the strongly log-concave setting, when the error is measured by the Wasserstein distance. The main result shows that the discretization error is governed by an average coordinate-wise smoothness constant, rather than by the usual global smoothness constant. The proof is short and probabilistic, and relies on a refined use of the synchronous coupling.
Decentralized Online Riemannian Optimization Beyond Hadamard Manifolds
arXiv:2509.07779v2 Announce Type: replace-cross Abstract: We study decentralized online Riemannian optimization over manifolds with possibly positive curvature, going beyond the Hadamard manifold setting. Decentralized optimization techniques rely on a consensus step that is well understood in Euclidean spaces because of their linearity. However, in positively curved Riemannian spaces, a main technical challenge is that geodesic distances may not induce a globally convex structure.