arXiv research

Constructs perturbations of a minimal surface with triple junctions.

Perturbing non-minimal bridge positions of a knot ensures similar behavior for its cable links.

Perturbs area-minimizing hypersurfaces to reduce singular set's dimension.

Minimal token perturbations reveal how Transformer models process information.

Singularities of area minimizing hypersurfaces can be smoothed in dimensions 9 and 10.

We show that except for $n = 2$ if a bridge surface for a knot is an index $n$ topologically minimal surface, then after a perturbation it is still topologically minimal with index at most $n+1$.

Counts minimal tori in Riemannian manifolds with 6 or more dimensions.

New method $μP^2$ improves neural network training by scaling perturbations layerwise.

Local minimizers are convex and close to Wulff shapes.

The change in Holographic entanglement entropy (HEE) for small fluctuations about pure anti De Sitter (AdS) is obtained by a perturbative expansion of the area functional in terms of the change in the bulk metric and the embedded extremal surface. However, it is known that change in the embedding appears in second orde…

Optimally shows the distance between perturbed convex functions and their Γ-regularizations.

Differential privacy is concerned about the prediction quality while measuring the privacy impact on individuals whose information is contained in the data. We consider differentially private risk minimization problems with regularizers that induce structured sparsity. These regularizers are known to be convex but they…

We introduce a new concept, data irrecoverability, and show that the well-studied concept of data privacy is sufficient but not necessary for data irrecoverability. We show that there are several regularized loss minimization problems that can use perturbed data with theoretical guarantees of generalization, i.e., loss…

Unique minimal surfaces near quadratic cones are identified.

In this paper we investigate the usage of adversarial perturbations for the purpose of privacy from human perception and model (machine) based detection. We employ adversarial perturbations for obfuscating certain variables in raw data while preserving the rest. Current adversarial perturbation methods are used for dat…

Generalizes Thomas-Yau theorem for special and minimal Lagrangians.

Generic smooth minimal hypersurfaces exist in 8D manifolds.

Improved algorithm speeds up generation of universal adversarial perturbations.

This work improves structured prediction by learning the balance between signal and random noise.

Paper proposes methods to estimate minimal adversarial perturbations for deep neural networks.

Construct minimal Lagrangian surfaces in complex projective plane via loop group method.

Paper proposes a new method for WDRO with local perturbations, achieving better accuracy.

We extend the results of Hardt and Simon on area-minimizing cones to prove that isolated singularities of stationary one-sided area-minimizing hypersurfaces can be locally perturbed away on the side that they are minimizing.

Researchers found infinite links with specific bridge positions.

AMP regularization improves deep learning models by favoring flat minima.

The paper proves prevalent existence and partially determines moduli space of area-minimizing surfaces with fractal singular sets.

New non-existence results for harmonic maps into perturbed cones.

Deep neural networks are easily fooled high confidence predictions for adversarial samples

The study examines the long-term behavior of mean curvature flows in closed 3-manifolds.

MAP perturbation models have emerged as a powerful framework for inference in structured prediction. Such models provide a way to efficiently sample from the Gibbs distribution and facilitate predictions that are robust to random noise. In this paper, we propose a provably polynomial time randomized algorithm for learn…

Variational inference has become one of the most widely used methods in latent variable modeling. In its basic form, variational inference employs a fully factorized variational distribution and minimizes its KL divergence to the posterior. As the minimization can only be carried out approximately, this approximation i…

We propose a novel framework for the differentially private ERM, input perturbation. Existing differentially private ERM implicitly assumed that the data contributors submit their private data to a database expecting that the database invokes a differentially private mechanism for publication of the learned model. In i…

ALPS improves neural network robustness and generalization.

We consider a communication scenario, in which an intruder tries to determine the modulation scheme of the intercepted signal. Our aim is to minimize the accuracy of the intruder, while guaranteeing that the intended receiver can still recover the underlying message with the highest reliability. This is achieved by per…

The paper studies deformations of singular minimal hypersurfaces in dimensions 7 and above.

Variance reduction has been commonly used in stochastic optimization. It relies crucially on the assumption that the data set is finite. However, when the data are imputed with random noise as in data augmentation, the perturbed data set be- comes essentially infinite. Recently, the stochastic MISO (S-MISO) algorithm i…

Deep neural networks are susceptible to adversarial manipulations in the input domain. The extent of vulnerability has been explored intensively in cases of $\ell_p$-bounded and $\ell_p$-minimal adversarial perturbations. However, the vulnerability of DNNs to adversarial perturbations with specific statistical properti…

We show the existence of various families of properly embedded singly periodic minimal surfaces in R^3 with finite arbitrary genus and Scherk type ends in the quotient. The proof of our results is based on the gluing of small perturbations of pieces of already known minimal surfaces.

Paper introduces input perturbation for privacy in machine learning models.

A new approach to maximum likelihood learning of discrete graphical models and RBM in particular is introduced. Our method, Perturb and Descend (PD) is inspired by two ideas (I) perturb and MAP method for sampling (II) learning by Contrastive Divergence minimization. In contrast to perturb and MAP, PD leverages trainin…

Investigates statistical properties of perturb-softmax and perturb-argmax distributions.

The study shows that certain metrics on spheres prevent stable tangent cones for area-minimizing boundaries.

Given a minimal Lagrangian submanifold L in a negative Kaehler--Einstein manifold M, we show that any small Kaehler--Einstein perturbation of M induces a deformation of L which is minimal Lagrangian with respect to the new structure. This provides a new source of examples of minimal Lagrangians. More generally, the sam…

Neural networks are vulnerable to adversarial examples and researchers have proposed many heuristic attack and defense mechanisms. We address this problem through the principled lens of distributionally robust optimization, which guarantees performance under adversarial input perturbations. By considering a Lagrangian …

EMAP finds minimal perturbations to change model predictions, combining feature weighting and counterfactuals.

Develops new methods to create imperceptible image changes that fool classifiers.

The evaluation of robustness against adversarial manipulation of neural networks-based classifiers is mainly tested with empirical attacks as methods for the exact computation, even when available, do not scale to large networks. We propose in this paper a new white-box adversarial attack wrt the $l_p$-norms for $p \in…

Study on adversarial training's impact on deep neural reinforcement learning policies.