arXiv research

Study linear perturbations of Spin(7) metrics, finding only rank one nilpotent matrices.

Study linear perturbations in Schwarzschild black hole spacetime.

Refined theorem on linear perturbations with applications in singularity theory and optimization.

EVILL uses randomised perturbations to improve exploration in bandit problems.

Improved online Lasso reduces regret in sparse linear contextual bandits.

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

The paper constructs new bimetric conformal invariants using metric perturbations.

New approach reduces unconstrained linear bandits to simpler optimization problems.

We propose a new online algorithm for cumulative regret minimization in a stochastic linear bandit. The algorithm pulls the arm with the highest estimated reward in a linear model trained on its perturbed history. Therefore, we call it perturbed-history exploration in a linear bandit (LinPHE). The perturbed history is …

Paper analyzes GCNN sensitivity to probabilistic graph perturbations.

In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out a recursive approximation to an arbitrarily highe…

TULiP estimates uncertainty for deep learning models safely.

We build blowing-up solutions for linear perturbation of the Yamabe problem on manifolds with boundary, provided the dimension of the manifold is n>6 and the trace-free part of the second fundamental form is non-zero everywhere on the boundary.

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

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…

This work proves Kerr black holes are dynamically stable under certain perturbations.

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…

Unified algorithm for linear bandits with improved regret bound.

Adversarial training augments the training set with perturbations to improve the robust error (over worst-case perturbations), but it often leads to an increase in the standard error (on unperturbed test inputs). Previous explanations for this tradeoff rely on the assumption that no predictor in the hypothesis class ha…

New operators help focus on specific areas in complex math problems.

Researchers found a way to measure energy in black hole perturbations.

Charge measurements for instantons and gravitational perturbations.

In this paper, we address the issue of linear stability of Schwarzschild space- time subject to certain axisymmetric perturbations. In particular, we prove that associ- ated solutions to the linearized vacuum Einstein equations centered at a Schwarzschild metric, with suitably regular initial data, decay to a linearize…

Paper addresses eigenvector perturbation in small eigen-gap scenarios.

We derive a system of equations governing the coupled gravitational and electromagnetic perturbations of Reissner-Nordström spacetime. The equations are derived in the context of global non-linear stability of Reissner-Nordström under axially symmetric polarized perturbations, as a generalization of the recent work on …

New bounds for nearly-linear networks without training.

The paper studies the asymptotic behavior of adversarial training under $\ell_\infty$-perturbation.

State-of-art deep neural networks (DNN) are vulnerable to attacks by adversarial examples: a carefully designed small perturbation to the input, that is imperceptible to human, can mislead DNN. To understand the root cause of adversarial examples, we quantify the probability of adversarial example existence for linear …

Based on the Hamiltonian dimensional reduction of $3+1$ axially symmetric, Ricci-flat Lorentzian spacetimes to a $2+1$ Einstein-wave map system with the (negatively curved) hyperbolic 2-plane target, we construct a positive-definite, (spacetime) gauge-invariant energy functional for linear axially symmetric perturbatio…

Investigates fluid flow perturbations using geometric theory.

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

This work presents a novel approach to train invertible linear layers by adding rank-one perturbations.

In his celebrated paper "Generic projections", John Mather has shown that almost all linear projections from a submanifold of a vector space into a subspace are transverse with respect to a given modular submanifold. In this paper, an improvement of Mather's result is stated. Namely, we show that almost all linear pert…

In this paper, we propose an efficient Monte Carlo implementation of non-linear FBSDEs as a system of interacting particles inspired by the ideas of branching diffusion method. It will be particularly useful to investigate large and complex systems, and hence it is a good complement of our previous work presenting an a…

Study perturbs Dirac operators in any dimension, focusing on Majorana fermions.

New metric scores perturbations across populations, not cells, improving model comparison.

Adversarial training can lead to overfitting without compromising robustness.

We build blowing-up solutions for linear perturbation of the Yamabe problem on manifolds with umbilic boundary, provided the Weyl tensor is nonzero everywhere on the boundary and the dimension of the manifold is n>10.

Paper develops robust Bayesian models for linear regression under adversarial perturbations.

This work examines how adversarial vulnerability changes with the dimensionality of the subspace of perturbations.

We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and angular momentum equal to any preassigned values measured with respect to a fixed affine frame at infinity. This is in contrast to the axisym…

New geometric interpretation explains over-parameterized models and adversarial perturbations.

We present an algorithm for computing class-specific universal adversarial perturbations for deep neural networks. Such perturbations can induce misclassification in a large fraction of images of a specific class. Unlike previous methods that use iterative optimization for computing a universal perturbation, the propos…

We consider the problem of controlling an unknown linear dynamical system in the presence of (nonstochastic) adversarial perturbations and adversarial convex loss functions. In contrast to classical control, the a priori determination of an optimal controller here is hindered by the latter's dependence on the yet unkno…

The SPS method constructs confidence regions for true parameters with optimal sample complexity.

The paper tackles extrapolation of gene knockouts effects on RNA counts.

Enhances GBDT robustness with one-hot encoding and regularization.

This paper contains the second part of a two-part series on the stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. We continue our study of solutions to the linear wave equation on a suitable globally hyperbolic subset of such a spacetime, arising from regular initial da…