Constructs perturbations of a minimal surface with triple junctions.
problem Minimal surfaces with triple junctions in curved spaces.
method Constructs stationary perturbations with given boundary conditions.
result Constructs minimal surfaces with triple junctions in R2imesS1. Perturbing non-minimal bridge positions of a knot ensures similar behavior for its cable links.
problem Ensuring similar non-minimal bridge positions for cable links.
method Perturbing non-minimal bridge positions of a knot K and analyzing (2,2q)-cable links L. result Every non-minimal bridge position of a (2,2q)-cable link L is perturbed. Perturbs area-minimizing hypersurfaces to reduce singular set's dimension.
problem Reduces the dimension of the singular set of area-minimizing hypersurfaces.
method Perturbs a smooth hypersurface to minimize the Minkowski dimension of the singular set.
result The singular set of the perturbed minimizing current has Minkowski dimension less than n-9.
Minimal token perturbations reveal how Transformer models process information.
problem Understanding information propagation in Transformer models for interpretability.
method Study of minimal token perturbations on embedding space.
result Rare tokens cause larger shifts, and input information mixes deeper.
Singularities of area minimizing hypersurfaces can be smoothed in dimensions 9 and 10.
problem Singularities of area minimizing hypersurfaces.
method Perturbation of singularities.
result Singularities can be perturbed away 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.
problem Counting minimal tori in Riemannian manifolds.
method Introduces a function to count minimal tori and shows invariance under metric perturbations.
result The count function is invariant under metric perturbations.
New method μP2 improves neural network training by scaling perturbations layerwise.
problem Improving neural network performance as models scale up.
method Layerwise perturbation scaling in the infinite-width limit of neural networks.
result Layerwise perturbation scaling ensures all layers are effectively perturbed in the limit.
Local minimizers are convex and close to Wulff shapes.
problem Finding local minimizers in anisotropic isoperimetric problems.
method Showed local minimizers are geodesically convex and small smooth perturbations of tangent Wulff shapes.
result Local minimizers are quantitatively 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.
problem Understanding the difference between perturbed convex functions and their Γ-regularizations.
method Analyzing the compactly supported perturbation and the Γ-regularization of a strictly convex function.
result The optimal estimate of the distance between perturbed convex functions and their Γ-regularizations is shown to be o(ε). 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.
problem Identifying minimal surfaces near quadratic cones.
method Analyzing minimal hypersurfaces inside the unit ball with perturbed boundary conditions.
result Minimal surfaces are uniquely determined by their boundary conditions.
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.
problem Proving uniqueness of special Lagrangians and minimal Lagrangians.
method Hamiltonian perturbations using Imagi, Joyce, and Oliveira dos Santos method.
result Generalized uniqueness theorem for special and minimal Lagrangians.
Generic smooth minimal hypersurfaces exist in 8D manifolds.
problem Existence of smooth minimal hypersurfaces in high-dimensional manifolds.
method Global perturbation argument and a novel geometric invariant.
result Generic metrics on 8D manifolds admit smooth minimal hypersurfaces.
Improved algorithm speeds up generation of universal adversarial perturbations.
problem Slow generation of universal adversarial perturbations.
method Optimized algorithm based on orientation of perturbation vectors.
result Significantly faster generation of universal perturbations with higher fooling rates.
This work improves structured prediction by learning the balance between signal and random noise.
problem Structured prediction with random perturbations.
method Learning the variance of randomized structured predictors to balance signal and noise.
result Learning the balance improves structured prediction effectiveness.
Paper proposes methods to estimate minimal adversarial perturbations for deep neural networks.
problem Quantifying robustness of deep neural networks against adversarial attacks.
method Proposes two lightweight strategies to find minimal adversarial perturbation.
result Approximates theoretical distance for samples close to classification boundary, providing robustness guarantees.
Construct minimal Lagrangian surfaces in complex projective plane via loop group method.
problem Construct minimal Lagrangian immersions from arbitrary Riemann surfaces into complex projective plane.
method Loop group method, perturbed equivariant minimal Lagrangian surfaces, Delaunay cylinders approximation.
result Construct a class of minimal Lagrangian cylinders approximating Delaunay cylinders.
Paper proposes a new method for WDRO with local perturbations, achieving better accuracy.
problem Wasserstein distributionally robust optimization's theoretical understanding needs improvement.
method Develops a new approximation theorem and risk consistency results for WDRO.
result The proposed method achieves significantly higher accuracy on noisy datasets.
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.
problem Finding links with minimal bridge positions.
method Applying Takao et al.'s criterion to create links with locally minimal n-bridge and globally minimal m-bridge positions. result Provided an infinite family of links with specific bridge positions.
AMP regularization improves deep learning models by favoring flat minima.
problem Improving deep learning model generalization and avoiding overfitting.
method AMP regularization uses adversarial model perturbation to minimize a norm-bounded perturbation of the empirical risk.
result AMP regularization leads to state-of-the-art performance across various deep architectures.
The paper proves prevalent existence and partially determines moduli space of area-minimizing surfaces with fractal singular sets.
problem Existence and moduli space of area-minimizing surfaces with fractal singular sets.
method Proof of prevalent existence, determination of moduli space, refinement of strata.
result Sharp results on moduli space and refinement of strata, showing fractal singularities do not completely dissolve under generic perturbations.
New non-existence results for harmonic maps into perturbed cones.
problem Proper harmonic maps into perturbed cones in \(\mathbb{R}^n\), horospheres in \(\mathbb{H}^n\).
method Extension of foliated maximum principle to non-compact settings.
result New non-existence results for proper harmonic maps.
Paper improves variational inference by tightening bounds using perturbation theory.
problem Improving variational inference's bias and KL divergence approximation.
method Revisits perturbation theory to derive corrections that tighten variational bounds.
result New bounds are tighter and more mass-covering, leading to higher likelihoods.
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.
problem Understanding the long-term behavior of mean curvature flows in closed 3-manifolds.
method The approach involves constructing piecewise almost regular flows and applying perturbative arguments.
result The study constructs minimal surfaces in 3-manifolds via parabolic methods.
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…
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.
problem Challenges in designing effective regularization schemes for adversarial robustness.
method Adversarial Labelling of Perturbed Samples (ALPS) using synthetic samples and min-max formulation.
result ALPS achieves state-of-the-art regularization performance and adversarial robustness.
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.
problem The behavior of singular minimal hypersurfaces in dimensions 7 and above.
method Analyzes the local behavior of minimal hypersurfaces under perturbations and convergence of families of hypersurfaces.
result Existence and smoothness of nearby minimal hypersurfaces under perturbations, uniqueness of homological minimization, and existence of Jacobi fields.
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…
SmoothFool efficiently computes smooth adversarial perturbations for deep networks.
problem Vulnerability of deep neural networks to adversarial attacks with specific statistical properties.
method SmoothFool: a general and computationally efficient framework for computing smooth adversarial perturbations.
result Smoothness significantly enhances robustness against adversarial attacks and improves transferability.
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.
problem Protecting both training data and model parameters while maintaining privacy.
method Add noise to training data and train with perturbed data for differential privacy.
result Achieves (ε,δ)-differential privacy on the final model with privacy on original data.
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.
problem Underexplored statistical properties of Gumbel-Softmax and Gumbel-Argmax distributions.
method Investigates convexity and differentiability to determine completeness and minimality of these distributions.
result Identifies parameters that admit complete and minimal representation of probability distributions.
The study shows that certain metrics on spheres prevent stable tangent cones for area-minimizing boundaries.
problem Preventing stable tangent cones for area-minimizing boundaries under specific metrics.
method Developed a perturbation theorem and used spectral theory and compactness arguments.
result A residual set of metrics on Sn+1 precludes linearly 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.
problem Improving model explanations for black box classifiers.
method Neural network approach that returns minimal adversarial perturbations.
result EMAP provides more interpretable explanations and faster than sampling-based methods.
Develops new methods to create imperceptible image changes that fool classifiers.
problem Improving the robustness of image classifiers by creating subtle changes undetectable to humans.
method Two methods: Edge-Aware and Color-Aware, designed to reduce detectability of image perturbations.
result Demonstrated that the new methods effectively cause misclassification and are computationally efficient.
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 lp-norms for $p \in…
Study on adversarial training's impact on deep neural reinforcement learning policies.
problem Vulnerability of deep neural reinforcement learning policies to imperceptible adversarial perturbations.
method Two parallel approaches: Fourier spectrum analysis and feature sensitivity measurement.
result Adversarially trained policies are more sensitive to low frequency perturbations.