arXiv research

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

Simple perturbation of Vafa-Witten equations leads to transversality.

Adversarial training adds dynamic perturbations to neural networks for robustness.

We examine the issue of sensitivity with respect to model parameters for the problem of utility maximization from final wealth in an incomplete Samuelson model and mainly, but not exclusively, for utility functions of positive power-type. The method consists in moving the parameters through change of measure, which we …

Gradient-based methods introduce noise that penalizes models sensitive to weight perturbations.

Charge measurements for instantons and gravitational perturbations.

We consider uncorrelated Stein-Stein, Heston, and Hull-White models and their perturbations by compound Poisson processes with jump amplitudes distributed according to a double exponential law. Similar perturbations of the Black-Scholes model were studied by S. Kou. For perturbed stochastic volatility models, we obtain…

Diffeomorphism freedom induces a gauge dependence in the theory of spacetime perturbations. We derive a compact formula for gauge transformations of perturbations of arbitrary order. To this end, we develop the theory of Taylor expansions for one-parameter families (not necessarily groups) of diffeomorphisms. First, we…

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…

PEP improves deep network performance and calibration by perturbing optimal parameters.

BPN defends against adversarial attacks by generating beneficial perturbations.

Introduces TPV to analyze model robustness without labels.

Study robust estimation of principal components under adversarial perturbations.

We study the problem of existence of surfaces in ${\bf R}^3$ parametrized on the sphere ${\mathbb S}^2$ with prescribed mean curvature $H$ in the perturbative case, i.e. for $H=H_0+εH_1$, where $H_0$ is a nonzero constant, $H_1$ is a $C^2$ function and $ε$ is a small perturbation parameter.

Study on function sensitivity in random DNNs using large deviation theory.

We study the point of transition between complete and incomplete financial models thanks to Dirichlet Forms methods. We apply recent techniques, developped by Bouleau, to hedging procedures in order to perturbate parameters and stochastic processes, in the case of a volatility parameter fixed but uncertain for traders;…

A new efficient PGD method generates smaller perturbation adversarial examples.

A new exploration strategy for contextual bandits reduces regret and is computationally efficient.

Perturbative GAN reduces training complexity and improves image quality.

DEKF maintains stability in LSTM learning with bounded perturbations.

A fast method computes class-specific adversarial perturbations for deep networks.

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…

EVILL uses randomised perturbations to improve exploration in bandit problems.

Node-perturbation learning is a type of statistical gradient descent algorithm that can be applied to problems where the objective function is not explicitly formulated, including reinforcement learning. It estimates the gradient of an objective function by using the change in the object function in response to the per…

The paper explores how polynomial roots and operator eigenvalues change with parameters.

Paper presents an analytical solution to Merton Garman model using symmetries.

Herding defines a deterministic dynamical system at the edge of chaos. It generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted as "samples" from an associated MRF model. Herding differs from maximum likelihoo…

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…

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

Improved MoE performance through perturbing cosine router.

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…

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…

Improved online Lasso reduces regret in sparse linear contextual bandits.

Learnable token perturbations boost extrapolation in LLMs.

Bayesian optimisation generates saliency maps for black-box models.

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 …

Many machine learning image classifiers are vulnerable to adversarial attacks, inputs with perturbations designed to intentionally trigger misclassification. Current adversarial methods directly alter pixel colors and evaluate against pixel norm-balls: pixel perturbations smaller than a specified magnitude, according t…

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…

Perturbation theory improves nonparametric instrumental variable estimation accuracy.

The paper introduces extremal perturbations for better attribution analysis in deep networks.

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…

Investigates statistical properties of perturb-softmax and perturb-argmax distributions.

SapAugment learns adaptive augmentation policies for better model training.

Proves existence and uniqueness of rotating fluid bodies in GR to second order.

Efficient method defends privacy in federated learning without accuracy loss.

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…

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 …

DSPG improves SPSA for distributed optimization with wireless delays.