arXiv research

The paper learns perturbation sets from data to improve robustness in machine learning.

Study robust learning without knowing perturbation sets, using interactions with attackers.

Advances FTPL results for bandit problems with unbounded perturbations.

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

FTPL with Fréchet perturbation achieves near optimal regret bounds for m-set semi-bandit problems.

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

The paper strengthens a theorem on crossings under linear perturbations with Hausdorff measure estimates.

Differentiable clustering method using perturbed spanning forests.

Study a modified Laplacian equation in spacetime.

Improved online Lasso reduces regret in sparse linear contextual bandits.

If we consider the moduli space of flat connections of a non trivial principal SO(3)-bundle over a surface, then we can define a map from the set of perturbed closed geodesics, below a given energy level, into families of perturbed Yang-Mills connections depending on a small parameter. In this paper we show that this m…

We study the problem of finding a universal (image-agnostic) perturbation to fool machine learning (ML) classifiers (e.g., neural nets, decision tress) in the hard-label black-box setting. Recent work in adversarial ML in the white-box setting (model parameters are known) has shown that many state-of-the-art image clas…

Adversarial perturbations fool deepfake detectors with high accuracy.

Study adversarial perturbations in classification, analyzing learning and certification.

Study robust online learning with adversarial perturbations.

Study of mean curvature flow with obstacles using singular perturbation.

PerturBench benchmarks ML models for cellular perturbation analysis.

We investigate the optimality of perturbation based algorithms in the stochastic and adversarial multi-armed bandit problems. For the stochastic case, we provide a unified regret analysis for both sub-Weibull and bounded perturbations when rewards are sub-Gaussian. Our bounds are instance optimal for sub-Weibull pertur…

The paper examines how gradient descent stabilizes low-rank matrix factorization in noisy conditions.

In a previous paper on coupled gravitational and electromagnetic perturbations of Reissner-Nordström spacetime in a polarized setting, we derived a system of wave equations for two independent quantities, one related to the Weyl curvature and one related to the Ricci curvature of the perturbed spacetime. We analyze her…

In this paper we study the property of phase retrievability by redundant sysems of vectors under perturbations of the frame set. Specifically we show that if a set $\fc$ of $m$ vectors in the complex Hilbert space of dimension n allows for vector reconstruction from magnitudes of its coefficients, then there is a pertu…

DEceit constructs effective universal pixel-restricted perturbations for deep image classifiers.

New metrics produce discrete zero sets for nondegenerate harmonic forms.

Adversarial training, in which a network is trained on both adversarial and clean examples, is one of the most trusted defense methods against adversarial attacks. However, there are three major practical difficulties in implementing and deploying this method - expensive in terms of extra memory and computation costs; …

New method learns robustly with less data, bridging theory and practice.

The paper smooths out equations on 4-manifolds to show smooth moduli spaces.

Study magnetic perturbations in Riemannian and Lorentzian Calderón problems.

We consider a classifier whose test set is exposed to various perturbations that are not present in the training set. These test samples still contain enough features to map them to the same class as their unperturbed counterpart. Current architectures exhibit rapid degradation of accuracy when trained on standard data…

Learnable token perturbations boost extrapolation in LLMs.

Unified algorithm for linear bandits with improved regret bound.

Deep neural networks (DNNs) have achieved superior performance in various prediction tasks, but can be very vulnerable to adversarial examples or perturbations. Therefore, it is crucial to measure the sensitivity of DNNs to various forms of perturbations in real applications. We introduce a novel perturbation manifold …

Classical matrix perturbation results, such as Weyl's theorem for eigenvalues and the Davis-Kahan theorem for eigenvectors, are general purpose. These classical bounds are tight in the worst case, but in many settings sub-optimal in the typical case. In this paper, we present perturbation bounds which consider the natu…

We introduce an efficient message passing scheme for solving Constraint Satisfaction Problems (CSPs), which uses stochastic perturbation of Belief Propagation (BP) and Survey Propagation (SP) messages to bypass decimation and directly produce a single satisfying assignment. Our first CSP solver, called Perturbed Blief …

SGD converges with perturbed forward-backward passes, explained by geometric amplification.

New framework maximizes perturbed samples for inverse classification with budget constraints.

We come up with infinite-dimensional prequantum line bundles and moment map interpretations of three different sets of equations - the generalised Monge-Amp`ere equation, the almost Hitchin system, and the Calabi-Yang-Mills equations. These are all perturbations of already existing equations. Our construction for the g…

LoRA fine-tuning explained with gradient dynamics for low-rank perturbations.

Study efficient learning of robust halfspaces with noise.

We present CROSSGRAD, a method to use multi-domain training data to learn a classifier that generalizes to new domains. CROSSGRAD does not need an adaptation phase via labeled or unlabeled data, or domain features in the new domain. Most existing domain adaptation methods attempt to erase domain signals using technique…

Improved generalization with semantic perturbations using normalizing flows.

Introduces TPV to analyze model robustness without labels.

State-of-the-art machine learning models frequently misclassify inputs that have been perturbed in an adversarial manner. Adversarial perturbations generated for a given input and a specific classifier often seem to be effective on other inputs and even different classifiers. In other words, adversarial perturbations s…

We prove a Freed-Uhlenbeck style generic smoothness theorem for the moduli space of solutions to the Vafa--Witten equations on a closed symplectic four-manifold by using a method developed by Feehan for the study of the $PU(2)$-monopole equations on smooth closed four-manifolds. We introduce a set of perturbation terms…

New framework for fair classification in adversarial settings with provable guarantees.

The paper proves the existence and uniqueness of certain spacelike hypersurfaces with specific curvature and boundary conditions.

This paper examines how graph topology affects adversarial attacks on vertex classification.

Defenses against adversarial examples, such as adversarial training, are typically tailored to a single perturbation type (e.g., small $\ell_\infty$-noise). For other perturbations, these defenses offer no guarantees and, at times, even increase the model's vulnerability. Our aim is to understand the reasons underlying…

New framework robustly handles outliers in Wasserstein DRO for better decision-making.