arXiv research

Study of marginally trapped surfaces in a perturbed Schwarzschild spacetime.

Improved neural network robustness with instance-specific perturbation margins.

MARGINATTACK improves zero-confidence adversarial attacks' accuracy and efficiency.

Advances robustness of metric learning by adversarial margin in input space.

The paper addresses online prediction in marginally stable systems with bounded perturbations.

High sensitivity of neural networks against malicious perturbations on inputs causes security concerns. To take a steady step towards robust classifiers, we aim to create neural network models provably defended from perturbations. Prior certification work requires strong assumptions on network structures and massive co…

Proves existence of solutions to Einstein constraints with specific boundary conditions and verifies Penrose inequality.

We consider the structured-output prediction problem through probabilistic approaches and generalize the "perturb-and-MAP" framework to more challenging weighted Hamming losses, which are crucial in applications. While in principle our approach is a straightforward marginalization, it requires solving many related MAP …

The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased" choice corresponds to the distribution of maximum entropy. The calculation of t…

As increasing amounts of sensitive personal information is aggregated into data repositories, it has become important to develop mechanisms for processing the data without revealing information about individual data instances. The differential privacy model provides a framework for the development and theoretical analy…

Adversarial training is a principled approach for training robust neural networks. Despite of tremendous successes in practice, its theoretical properties still remain largely unexplored. In this paper, we provide new theoretical insights of gradient descent based adversarial training by studying its computational prop…

Study on low-dimensional adversarial perturbations in classification models.

We show that any vacuum initial data set containing a marginally outer trapped surface S and satisfying a "no KIDs" condition can be perturbed near S so that S becomes strictly outer trapped in the new vacuum initial data set. This, together with the results in [9], gives a precise sense in which generic initial data c…

MACQ method explains deep learning models by analyzing feature contributions across prediction levels.

We study adversarial robustness of neural networks from a margin maximization perspective, where margins are defined as the distances from inputs to a classifier's decision boundary. Our study shows that maximizing margins can be achieved by minimizing the adversarial loss on the decision boundary at the "shortest succ…

Learnable token perturbations boost extrapolation in LLMs.

Study shows how transformers classify symbols without naming them, proving a margin-versus-collision criterion.

Black box variational inference (BBVI) with reparameterization gradients triggered the exploration of divergence measures other than the Kullback-Leibler (KL) divergence, such as alpha divergences. In this paper, we view BBVI with generalized divergences as a form of estimating the marginal likelihood via biased import…

We show that the maximal future development of asymptotically flat spherically symmetric black hole initial data for a self-gravitating nonlinear scalar field, also called a Higgs field, contains a connected, achronal marginally trapped tube which is asymptotic to the event horizon of the black hole, provided the initi…

Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize stability, we analyze and develop a computationally efficient implementation of Jac…

Data augmentation (DA) is commonly used during model training, as it significantly improves test error and model robustness. DA artificially expands the training set by applying random noise, rotations, crops, or even adversarial perturbations to the input data. Although DA is widely used, its capacity to provably impr…

New method improves deep neural networks' robustness to adversarial examples.

New method for analyzing compositional data, addressing biases in summary statistics.

Gradient noise improves privacy-protected optimization performance.

We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically successful results for both classification and regression tasks. However, most large m…

Robustness is an increasingly important property of machine learning models as they become more and more prevalent. We propose a defense against adversarial examples based on a k-nearest neighbor (kNN) on the intermediate activation of neural networks. Our scheme surpasses state-of-the-art defenses on MNIST and CIFAR-1…

Deep models, while being extremely versatile and accurate, are vulnerable to adversarial attacks: slight perturbations that are imperceptible to humans can completely flip the prediction of deep models. Many attack and defense mechanisms have been proposed, although a satisfying solution still largely remains elusive. …

Meta framework generates noise to improve multi-attack robustness.

Novel framework predicts cell responses to perturbations using GRNs.

The scalability of submodular optimization methods is critical for their usability in practice. In this paper, we study the reducibility of submodular functions, a property that enables us to reduce the solution space of submodular optimization problems without performance loss. We introduce the concept of reducibility…

Recently, the infinitesimal moduli space of heterotic $G_2$ compactifications was described in supergravity and related to the cohomology of a target space differential. In this paper we identify the marginal deformations of the corresponding heterotic nonlinear sigma model with cohomology classes of a worldsheet BRST …

Develops a new robustness criterion for VAEs and provides theoretical guarantees.

Paper improves variational inference by tightening bounds using perturbation theory.

The paper identifies potential adversarial samples near decision boundaries of neural networks.

The standard margin-based structured prediction commonly uses a maximum loss over all possible structured outputs. The large-margin formulation including latent variables not only results in a non-convex formulation but also increases the search space by a factor of the size of the latent space. Recent work has propose…

We propose a categorical data synthesizer with a quantifiable disclosure risk. Our algorithm, named Perturbed Gibbs Sampler, can handle high-dimensional categorical data that are often intractable to represent as contingency tables. The algorithm extends a multiple imputation strategy for fully synthetic data by utiliz…

The paper tackles adversarial attacks on recurrent neural networks.

We prove a version the Penrose inequality for black hole space-times which are perturbations of the Schwarzschild exterior in a slab around a null hypersurface $\underline{\mathcal{N}}_0$. $\underline{\mathcal{N}}_0$ terminates at past null infinity $\mathcal{I}^-$ and $\mathcal{S}_0:=\partial\underline{\mathcal{N}}_0$…

In recent work, the notion of Double Convexity for a foliation of a conical null hypersurface was introduced to give a proof, if satisfied, of the Null Penrose Inequality. Double Convexity constrains the geometry of a Marginally Outer Trapped Surface (MOTS), called a quasi-round MOTS. In the first part of this paper, f…

Develops a martingale expansion for stochastic volatility models.

Improved robustness of machine learning models with controlled Lipschitz constants.

Optimizes risk measures given known marginal distributions of two unknown factors.

Proposes a new method to improve deep model security against adversarial deformations.

State-of-the-art neural networks are vulnerable to adversarial examples; they can easily misclassify inputs that are imperceptibly different than their training and test data. In this work, we establish that the use of cross-entropy loss function and the low-rank features of the training data have responsibility for th…

FHBI enhances generalization in Bayesian inference with iterative steps in functional spaces.

Maximum entropy distributions with discrete support in $m$ dimensions arise in machine learning, statistics, information theory, and theoretical computer science. While structural and computational properties of max-entropy distributions have been extensively studied, basic questions such as: Do max-entropy distributio…

Estimates risk in finance using Wasserstein distance and parametric models.

The paper calibrates geophysical predictions using marginal distributions and machine learning.