arXiv research

New scalable Lipschitz bounds improve neural network robustness analysis.

The paper calculates upper bounds on ReLU network Lipschitz constants.

Geodesically complete spaces with curvature bounded above have maps with finite energy that are Lipschitz.

Investigates Lipschitz continuity in neural networks across various settings.

New parameterization of neural networks with Lipschitz bounds for robustness.

Efficient local Lipschitz bounds improve neural network robustness.

New method for differentially private optimization with general Lipschitz conditions.

This paper bounds the Lipschitz constants of neural networks and their gradients.

The thesis defines and proves invariants for manifolds of bounded geometry.

The study connects polyhedral manifolds to Riemannian ones with geometric bounds.

We examine the impact of learning Lipschitz continuous models in the context of model-based reinforcement learning. We provide a novel bound on multi-step prediction error of Lipschitz models where we quantify the error using the Wasserstein metric. We go on to prove an error bound for the value-function estimate arisi…

Neural networks are dense among Lipschitz functions with fixed Lipschitz constant.

We prove a Lipschitz-Volume rigidity theorem for the non-collapsed Gromov-Hausdorff limits of manifolds with Ricci curvature bounded from below. This is a counterpart of the Lipschitz-Volume rigidity in Alexandrov geometry.

Scalable method bounds Lipschitz constant of generative models.

Improved DP SO with large Lipschitz parameters, handling outliers and heavy-tailed data.

New MIP formulations for neural network Lipschitz constant estimation.

New method tightens Lipschitz bounds for CNNs efficiently.

This paper studies bounds for the Lipschitz constant of random neural networks.

The study examines the limitations of bi-Lipschitz Normalizing Flows in approximating certain distributions.

The study examines metrics on Riemannian spaces with bounded properties and finds conditions for Lipschitz and uniform bounds.

Study risk-sensitive reinforcement learning with Lipschitz dynamic risk measures, establishing regret bounds.

Improved robustness of 1D CNNs for heart arrhythmia classification.

Uniform heat kernel bounds lead to synthetic Ricci curvature conditions for Lipschitz manifolds.

The paper calculates bounds on the local Lipschitz constants of neural network layers.

Method approximates Lipschitz domains with smoother shapes.

The paper establishes a uniform Lipschitz bound on the square root of the systole function in Teichmüller space.

The paper proposes a method to train NNs with a small Lipschitz constant to improve robustness.

An $e^ε$-Lipschitz and co-Lipschitz map, as a metric analogue of an $ε$-Riemannian submersion, naturally arises from a sequence of Alexandrov spaces with curvature uniformly bounded below that converges to a space of only weak singularities. In this paper we prove its homotopy lifting property and its homotopy stabilit…

New Lipschitz bound for ReLU networks resists weight rescaling.

Paper investigates Lipschitz constants of self-attention modules in neural networks.

We investigate contextual online learning with nonparametric (Lipschitz) comparison classes under different assumptions on losses and feedback information. For full information feedback and Lipschitz losses, we design the first explicit algorithm achieving the minimax regret rate (up to log factors). In a partial feedb…

In this paper we consider Llarull's theorem in the foliation case and get a lower bound of the Lipschitz constant of the map $M\to S^n$ in the foliation case under the spin condition.

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

Smooths metrics on manifolds with curvature bounds and injectivity radius constraints.

New algorithms for online learning without boundedness or Lipschitz loss assumptions.

Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning controllers. Existing methods in the literature for estimating the Lipschitz constant su…

CLIP controls neural network stability by bounding Lipschitz constants.

The study shows that certain graphs are regular at boundary points.

New algorithm tackles delayed feedback in Lipschitz bandits with sublinear regret.

Sharp Lipschitz bounds for flow-matching and diffusion models with optimal sampling rates.

Considering the Teichmüller space of a surface equipped with Thurston's Lipschitz metric, we study geodesic segments whose endpoints have bounded combinatorics. We show that these geodesics are cobounded, and that the closest-point projection to these geodesics is strongly contracting. Consequently, these geodesics are…

Algorithm tackles adaptive discretization in adversarial Lipschitz bandits for dynamic pricing and auctions.

We construct a smooth compact n-dimensional manifold Y with one point singularity such that all its Lipschitz homotopy groups are trivial, but Lipschitz mappings Lip(S^n,Y) are not dense in the Sobolev space W^{1,n}(S^n,Y). On the other hand we show that if a metric space Y is Lipschitz (n-1)-connected, then Lipschitz …

We prove a quantitative bi-Lipschitz nonembedding theorem for the Heisenberg group with its Carnot-Carathéodory metric and apply it to give a lower bound on the integrality gap of the Goemans-Linial semidefinite relaxation of the Sparsest Cut problem.

Proposes a weaker version of Strong Cosmic Censorship with curvature bounds.

Optimizes privacy-preserving optimization for heavy-tailed data.

LipKernel adds robustness to CNNs by enforcing Lipschitz bounds.

The paper studies Lipschitz bounds for integral kernels under differentiability assumptions.