arXiv research

DBPA assesses LLM perturbations using frequentist hypothesis testing.

Improved online Lasso reduces regret in sparse linear contextual bandits.

Study analyzes perturbations in singular subspaces under random noise.

Deep networks have recently been shown to be vulnerable to universal perturbations: there exist very small image-agnostic perturbations that cause most natural images to be misclassified by such classifiers. In this paper, we propose the first quantitative analysis of the robustness of classifiers to universal perturba…

New method proves inequalities for self-shrinkers using perturbation.

This study benchmarks transcriptomics models for perturbation analysis, finding scVI and PCA superior.

Study magnetic perturbations in Riemannian and Lorentzian Calderón problems.

Study reveals class-dependent effects in perturbation-based feature attribution metrics for time series classification.

BioBO optimizes gene perturbation design using Bayesian optimization with biological priors.

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…

The problem of attribution is concerned with identifying the parts of an input that are responsible for a model's output. An important family of attribution methods is based on measuring the effect of perturbations applied to the input. In this paper, we discuss some of the shortcomings of existing approaches to pertur…

In this paper, we take the first steps towards a novel unified framework for the analysis of perturbations in both the Time and Frequency domains. The identification of type and source of such perturbations is fundamental for monitoring reactor cores and guarantee safety while running at nominal conditions. A 3D Convol…

PAC-Bayesian bounds estimate adversarial robustness.

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

Study metric perturbations to make degenerate harmonic forms non-degenerate.

Paper addresses eigenvector perturbation in small eigen-gap scenarios.

Automates perturbation analysis for neural networks, enabling certified robustness on complex architectures.

Study stability of contingent claim solutions under probabilistic perturbations.

Paper analyzes GCNN sensitivity to probabilistic graph perturbations.

Paper develops robust estimators and strategies for stochastic MABs with heavy-tailed rewards.

Despite the tremendous success of deep neural networks in various learning problems, it has been observed that adding an intentionally designed adversarial perturbation to inputs of these architectures leads to erroneous classification with high confidence in the prediction. In this work, we propose a general framework…

PerturBench benchmarks ML models for cellular perturbation analysis.

Improved perturbation reduces matrix condition number to O(n) with minimal storage.

The paper examines fair pricing and hedging stability under small numéraire perturbations.

Recent work has extensively shown that randomized perturbations of neural networks can improve robustness to adversarial attacks. The literature is, however, lacking a detailed compare-and-contrast of the latest proposals to understand what classes of perturbations work, when they work, and why they work. We contribute…

Adding node feature kernels improves GCN robustness to graph perturbations.

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…

Short proof shows how ridge regression works with random data.

Analyzes perturbed contact instantons with Legendrian boundary conditions using geometric analysis.

The universal perturbative invariants of rational homology spheres can be extracted from the Chern-Simons partition function by combining perturbative and nonperturbative results. We spell out the general procedure to compute these invariants, and we work out in detail the case of Seifert spaces. By extending some prev…

We regard pre-trained residual networks (ResNets) as nonlinear systems and use linearization, a common method used in the qualitative analysis of nonlinear systems, to understand the behavior of the networks under small perturbations of the input images. We work with ResNet-56 and ResNet-110 trained on the CIFAR-10 dat…

Study on stability of GCNNs under graph perturbations.

Paper examines stability of Bayesian posterior measures using integral probability metrics.

New technique stabilizes singular values in concatenated matrices.

In this paper we prescribe a fourth order conformal invariant on the standard $n-$sphere, with $n\geq5$, and study the related fourth order elliptic equation. We first find some existence results in the perturbative case. After some blow up analysis we build a homotopy to pass from the perturbative case to the non-pert…

Paper develops a new kernel approximation framework.

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 …

We study the perturbations of two classes of static black ellipsoid solutions of four dimensional vacuum Einstein equations. Such solutions are described by generic off--diagonal metrics which are generated by anholonomic transforms of diagonal metrics. The analysis is performed in the approximation of small eccentrici…

Advances FTPL results for bandit problems with unbounded perturbations.

We propose a new input perturbation mechanism for publishing a covariance matrix to achieve $(ε,0)$-differential privacy. Our mechanism uses a Wishart distribution to generate matrix noise. In particular, We apply this mechanism to principal component analysis. Our mechanism is able to keep the positive semi-definitene…

In this work we prove the fact that, for a short time, it is possible to construct a smooth parametrized family of isometric embeddings of an arbitrary smooth parametrized family of Riemannian metrics on a smooth closed manifold into an Euclidean space. In order to prove this statement we work out stability estimates w…

Constructing an efficient parameterization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parameterization using the local tangent plane. Principal component analysis (PCA) is often the tool of choice, as…

The inverse statistical problem of finding direct interactions in complex networks is difficult. In the natural sciences, well-controlled perturbation experiments are widely used to probe the structure of complex networks. However, our understanding of how and why perturbations aid inference remains heuristic, and we l…

Unified analysis of removal-based feature attributions robustness.

SGD generalization bounds derived from information theory.

Study privacy and accuracy in high-dimensional LASSO with perturbation mechanisms.

Despite achieving impressive performance, state-of-the-art classifiers remain highly vulnerable to small, imperceptible, adversarial perturbations. This vulnerability has proven empirically to be very intricate to address. In this paper, we study the phenomenon of adversarial perturbations under the assumption that the…

Improved FTPL algorithm reduces regret in predictable minimax games.