arXiv research

New method for estimating covariance with robustness to outliers.

Enhances robustness of deep neural networks with randomized smoothing.

New algorithms learn stability certificates from data, avoiding complex dynamics.

Improved neural network robustness certification through tighter convex relaxations.

Develops structured noise for more accurate graph classifier robustness certificates.

New method closes certification gap for adversarially trained models.

While neural networks have achieved high performance in different learning tasks, their accuracy drops significantly in the presence of small adversarial perturbations to inputs. Defenses based on regularization and adversarial training are often followed by new attacks to defeat them. In this paper, we propose attack-…

Bayesian method synthesizes barrier certificates for unknown systems with latent states.

CITE algorithm provides anytime-valid certification of model outputs.

Adaptive Bernstein copulas improve risk management by preventing overfitting and reducing simulation effort.

Paper develops tighter risk certificates for contrastive learning models.

Develops local population-risk certificates for model updates

The performance of a reinforcement learning algorithm can vary drastically during learning because of exploration. Existing algorithms provide little information about the quality of their current policy before executing it, and thus have limited use in high-stakes applications like healthcare. We address this lack of …

Survey Bernstein-type theorems for graphical surfaces in Euclidean and Lorentz-Minkowski spaces.

In this paper we study nonconvex penalization using Bernstein functions. Since the Bernstein function is concave and nonsmooth at the origin, it can induce a class of nonconvex functions for high-dimensional sparse estimation problems. We derive a threshold function based on the Bernstein penalty and give its mathemati…

New method provides tighter robustness guarantees for adversarial attacks.

In this paper we study nonconvex penalization using Bernstein functions whose first-order derivatives are completely monotone. The Bernstein function can induce a class of nonconvex penalty functions for high-dimensional sparse estimation problems. We derive a thresholding function based on the Bernstein penalty and di…

Ancient solutions to mean curvature flow have unique shapes.

TUV Austria proposes certification for ML applications to ensure reliability.

Valid certifies LLMs' domain adherence, bounding out-of-domain behavior.

The study models insurance dependence using Bernstein copulas.

Improved understanding of translating solitons using new techniques.

We summarize results concerning the Bernstein property of differential equations.

Explains Bernstein theorems for various geometric PDEs.

Improved analysis of UCRL2 with empirical Bernstein inequality reduces exploration-exploitation regret.

Paper provides efficient robustness certificates for neural networks.

Ancient symplectic solutions to mean curvature flow are flat.

In this paper, we prove some Bernstein type results for $n$-dimensional minimal Lagrangian graphs in quaternion Euclidean space $H^n\cong R^{4n}$. In particular, we also get a new Bernstein Theorem for special Lagrangian graphs in $C^n$

New attack tricks certifiably robust models into mislabeling images.

We present Bernstein-Sato identities for scalar-, spinor- and differential form-valued distribution kernels on Euclidean space associated to conformal symmetry breaking operators. The associated Bernstein-Sato operators lead to partially new formulae for conformal symmetry breaking differential operators on functions, …

Conformal Candidate Certification advances offline MBO by certifying candidate designs with statistical guarantees.

New robustness certificates for streaming models with a sliding window.

The paper proves Calabi-Bernstein type results for minimal and maximal surfaces in 3D and 3D-L spacetime.

Article provides Bernstein gradient estimates for heat equations with potential terms.

Survey examines challenges of ML in avionic systems certification.

Geometric technique determines exactness of SDP robustness certificate.

Randomized classifiers have been shown to provide a promising approach for achieving certified robustness against adversarial attacks in deep learning. However, most existing methods only leverage Gaussian smoothing noise and only work for $\ell_2$ perturbation. We propose a general framework of adversarial certificati…

The paper improves risk certificate tightness for neural networks using PAC-Bayes bounds.

The paper solves Bernstein problems for specific submanifolds in high-dimensional spaces.

Study adversarial perturbations in classification, analyzing learning and certification.

New method improves robustness of smoothed classifiers against adversarial attacks.

New framework certifies robustness for regression models.

Sharp inequalities for matrix means with unknown variance.

For entire spacelike stationary 2-dimensional graphs in Minkowski spaces, we establish Bernstein type theorems under specific boundedness assumptions either on the W-function or on the total (Gaussian) curvature. These conclusions imply the classical Bernstein theorem for minimal surfaces in 3-dimensional Euclidean spa…

SREC markets are a relatively novel market-based system to incentivize the production of energy from solar means. A regulator imposes a floor on the amount of energy each regulated firm must generate from solar power in a given period and provides them with certificates for each generated MWh. Firms offset these certif…

In this paper, we study the properties of potential function of the translating soliton $M$ in $R^{n+1}$ and the volume growth of the intersection of Euclidean balls with $M$. We give a condition to obtain the Bernstein theorem for the translating solitons. We also give an outline of a simple proof of the Bernstein the…

Paper proves stable minimal surfaces in 3D are flat.

This paper develops a general theoretical framework to analyze structured sparse recovery problems using the notation of dual certificate. Although certain aspects of the dual certificate idea have already been used in some previous work, due to the lack of a general and coherent theory, the analysis has so far only be…