A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
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 …
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…
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.
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 precisely characterizes and improves the tradeoff between robustness and accuracy in linear regression.
problem Tradeoff between robustness and accuracy in adversarial training.
method Characterizes the effect of augmentation on standard error in linear regression; proves RST improves robust error without sacrificing standard error.
result RST improves both standard and robust error for neural networks under various 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…
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…
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 …
The paper studies the asymptotic behavior of adversarial training under ℓ∞-perturbation.
problem Theoretical guarantees for sparsity-recovery in adversarial training.
method Investigation of the asymptotic distribution of the adversarial training estimator in generalized linear models.
result The asymptotic distribution of the adversarial training estimator under ℓ∞-perturbation could have a positive probability mass at 0 when the true parameter is 0.
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…
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…
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.
This work examines how adversarial vulnerability changes with the dimensionality of the subspace of perturbations.
problem Understanding adversarial vulnerability in constrained input spaces.
method Investigates adversarial vulnerability in subspace V of the input space X with varying dimensions, using PGD attacks and analyzing the dependence on ε and dim(V)/dim(X).
result Adversarial success of PGD attacks is a monotonically increasing function of $ε( rac{dim(V)}{dim(X)})^{ rac{1}{q}}$.
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…
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…
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…