arXiv research

New method GSAT improves robustness against structured perturbations.

The paper proves stability of certain singularities in integrable systems.

We study the general structure of formal perturbative solutions to the Hamiltonian perturbations of spatially one-dimensional systems of hyperbolic PDEs. Under certain genericity assumptions it is proved that any bihamiltonian perturbation can be eliminated in all orders of the perturbative expansion by a change of coo…

This work improves structured prediction by learning the balance between signal and random noise.

Study of free particle's geometry and its perturbations using complex projective structures.

In this paper we will perturb the scalar curvature of compact Kahler manifolds by incorporating it with higher Chern forms, and then show that the perturbed scalar curvature has many common properties with the unperturbed scalar curvature. In particular the perturbed scalar curvature becomes a moment map, with respect …

Simple perturbation of Vafa-Witten equations leads to transversality.

Graph neural networks detect structural perturbations from time series data.

In \cite{LZ2} it is proved that for certain class of perturbations of the hyperbolic equation $u_t=f(u) u_x$, there exist changes of coordinate, called quasi-Miura transformations, that reduce the perturbed equations to the unperturbed one. We prove in the present paper that if in addition the perturbed equations posse…

Charge measurements for instantons and gravitational perturbations.

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

CausalRegNet generates accurate data for gene perturbation experiments, improving CSL methods.

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…

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…

We explain how deformation theories of geometric objects such as complex structures, Poisson structures and holomorphic bundle structures lead to differential Gerstenhaber or Poisson algebras. We use homological perturbation theory to obtain $A_{\infty}$ algebra structures and some canonically defined deformations of s…

Constructs perturbed Fefferman spaces on almost CR manifolds.

EVILL uses randomised perturbations to improve exploration in bandit problems.

The study explains why signature methods work in commodity futures term structure classification.

This paper establishes transversality for perturbed Vafa-Witten moduli spaces on 4-manifolds.

Adding node feature kernels improves GCN robustness to graph perturbations.

New adversarial examples with structured distortion sets improve robustness and perceptibility.

The paper smooths out equations on 4-manifolds to show smooth moduli spaces.

When generating adversarial examples to attack deep neural networks (DNNs), Lp norm of the added perturbation is usually used to measure the similarity between original image and adversarial example. However, such adversarial attacks perturbing the raw input spaces may fail to capture structural information hidden in t…

Improved online Lasso reduces regret in sparse linear contextual bandits.

Adversarial examples are perturbed inputs designed to fool machine learning models. Most recent works on adversarial examples for image classification focus on directly modifying pixels with minor perturbations. A common requirement in all these works is that the malicious perturbations should be small enough (measured…

EBMs trained on discrete data using heat equations on graph structures.

The paper proves transversality for special Lagrangian submanifolds in a 6D manifold.

We prove a theorem which asserts that the Lie algebra of all holomorphic vector fields on a compact Kähler manifold with a perturbed extremal metric has the structure similar to the case of an unperturbed extremal Kähler metric proved by Calabi.

Study on stability of GCNNs under graph perturbations.

The Davis-Kahan-Wedin $\sin Θ$ theorem describes how the singular subspaces of a matrix change when subjected to a small perturbation. This classic result is sharp in the worst case scenario. In this paper, we prove a stochastic version of the Davis-Kahan-Wedin $\sin Θ$ theorem when the perturbation is a Gaussian rando…

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…

Framework for causal discovery using multi-modal data.

This work analyzes the stability of graph filters under large perturbations.

New method for robustly interpreting ML models using quantile constraints and Wasserstein projections.

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…

A new framework explains GNN predictions by simulating graph structure and feature changes.

Improved generalization with semantic perturbations using normalizing flows.

Paper analyzes GCNN sensitivity to probabilistic graph perturbations.

Adversarial examples are intentionally perturbed images that mislead classifiers. These images can, however, be easily detected using denoising algorithms, when high-frequency spatial perturbations are used, or can be noticed by humans, when perturbations are large. In this paper, we propose EdgeFool, an adversarial im…

The paper explores hidden torus symmetries in integrable systems and their stability.

Classifies Ricci solitons on specific Lorentzian Lie groups.

Differential privacy is concerned about the prediction quality while measuring the privacy impact on individuals whose information is contained in the data. We consider differentially private risk minimization problems with regularizers that induce structured sparsity. These regularizers are known to be convex but they…

Novel tensor perturbation bounds for orthogonal iteration methods.

Modifying the method of [21], we compute the perturbed $HF^+$ for some special classes of fibered three manifolds in the second highest spin$^c$-structures $S_{g-2}$. The special classes considered in this paper include the mapping tori of Dehn twists along a single non-separating curve and along a transverse pair of c…

State entropy regularization improves robustness in reinforcement learning, especially under structured perturbations.

New method stabilizes private LASSO for high-dimensional data with diverse covariate scales.

A new method for generating SPX and VIX risk scenarios using perturbed optimal transport.

A new method trains discrete EBMs without sampling.