arXiv research

New examples of knots with special bridge positions found.

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 …

We study general linear perturbations of a class of 4d real-dimensional hyperkahler manifolds obtainable by the (generalized) Legendre transform method. Using twistor methods, we show that deformations can be encoded in a set of holomorphic functions of 2d+1 variables, as opposed to the functions of d+1 variables contr…

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.

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…

Adversarial training is by far the most successful strategy for improving robustness of neural networks to adversarial attacks. Despite its success as a defense mechanism, adversarial training fails to generalize well to unperturbed test set. We hypothesize that this poor generalization is a consequence of adversarial …

EMPIR combines low and full precision DNNs to enhance robustness against adversarial attacks.

Adversarial robustness has become a central goal in deep learning, both in the theory and the practice. However, successful methods to improve the adversarial robustness (such as adversarial training) greatly hurt generalization performance on the unperturbed data. This could have a major impact on how the adversarial …

We establish a canonical gluing procedure for Seiberg-Witten monopoles on the two pieces of a closed, oriented 4-manifold X which is split along a 3-dimensional closed, oriented submanifold. We only assume that the (unperturbed) character variety is Kuranishi-smooth and the limiting maps are transversal -- then we will…

We study the determination of the second-order normal form for perturbed Hamiltonians $H_ε=H_0 +εH_1 +\frac{ε^2}{2} H_2$, relative to the periodic flow of the unperturbed Hamiltonian $H_0$. The formalism presented here is global, and can be easily implemented in any CAS. We illustrate it by means of two examples: the H…

We present a geometric proof of the averaging theorem for perturbed dynamical systems on a Riemannian manifold, in the case where the flow of the unperturbed vector field is periodic and the $\mathbb{S}^{1}$-action associated to this vector field is not necessarily trivial. We generalize the averaging procedure \cite{A…

Two non-Morse-Bott Chern-Simons functions on homology 3-spheres.

Researchers found infinite links with specific bridge positions.

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…

We outline a detection method for adversarial inputs to deep neural networks. By viewing neural network computations as graphs upon which information flows from input space to out- put distribution, we compare the differences in graphs induced by different inputs. Specifically, by applying persistent homology to these …

We propose an algorithm to enhance certified robustness of a deep model ensemble by optimally weighting each base model. Unlike previous works on using ensembles to empirically improve robustness, our algorithm is based on optimizing a guaranteed robustness certificate of neural networks. Our proposed ensemble framewor…

We consider a classifier whose test set is exposed to various perturbations that are not present in the training set. These test samples still contain enough features to map them to the same class as their unperturbed counterpart. Current architectures exhibit rapid degradation of accuracy when trained on standard data…

Noise Injection probes deep learning dynamics during training phases.

Classifiers such as deep neural networks have been shown to be vulnerable against adversarial perturbations on problems with high-dimensional input space. While adversarial training improves the robustness of image classifiers against such adversarial perturbations, it leaves them sensitive to perturbations on a non-ne…

We construct a determinant of the Laplacian for infinite-area surfaces which are hyperbolic near infinity and without cusps. In the case of a convex co-compact hyperbolic metric, the determinant can be related to the Selberg zeta function and thus shown to be an entire function of order two with zeros at the eigenvalue…

A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed.The perturbation parameter is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion method, the dynamics of variables given by the forward SDEs is treated exactly. …

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…

Adversarial attacks on deep neural networks traditionally rely on a constrained optimization paradigm, where an optimization procedure is used to obtain a single adversarial perturbation for a given input example. In this work we frame the problem as learning a distribution of adversarial perturbations, enabling us to …

Geometrically transforms nonconservative dynamics to linearize Kepler and Manev systems.

Adversarial perturbations fool deepfake detectors with high accuracy.

Several data analysis techniques employ similarity relationships between data points to uncover the intrinsic dimension and geometric structure of the underlying data-generating mechanism. In this paper we work under the model assumption that the data is made of random perturbations of feature vectors lying on a low-di…

In recent years, deep neural network approaches have been widely adopted for machine learning tasks, including classification. However, they were shown to be vulnerable to adversarial perturbations: carefully crafted small perturbations can cause misclassification of legitimate images. We propose Defense-GAN, a new fra…

This work precisely characterizes and improves the tradeoff between robustness and accuracy in linear regression.

More data can widen the gap between robust and standard models against adversarial attacks.

Improves deep learning robustness by enforcing local and global compactness.

Study how nodal domains change on surfaces under perturbations.

This paper provides both a detailed study of color-dependence of link homologies, as realized in physics as certain spaces of BPS states, and a broad study of the behavior of BPS states in general. We consider how the spectrum of BPS states varies as continuous parameters of a theory are perturbed. This question can be…

Clustering algorithms are used in a large number of applications and play an important role in modern machine learning-- yet, adversarial attacks on clustering algorithms seem to be broadly overlooked unlike supervised learning. In this paper, we seek to bridge this gap by proposing a black-box adversarial attack for c…

Deep neural networks are known to be vulnerable to adversarial attacks. Current methods of defense from such attacks are based on either implicit or explicit regularization, e.g., adversarial training. Randomized smoothing, the averaging of the classifier outputs over a random distribution centered in the sample, has b…

The study uses response theory to understand RNNs processing input signals.

New regularizer for machine learning using private data.

Study shows different behaviors of noncompact hypersurfaces under mean curvature flow.

Adversarial attacks add perturbations to the input features with the intent of changing the classification produced by a machine learning system. Small perturbations can yield adversarial examples which are misclassified despite being virtually indistinguishable from the unperturbed input. Classifiers trained with stan…

Framework predicts nonlinear system responses using GFDT and generative models.

Reinforcement Learning optimizes low-thrust interplanetary trajectories under disturbances.

In adversarial attacks to machine-learning classifiers, small perturbations are added to input that is correctly classified. The perturbations yield adversarial examples, which are virtually indistinguishable from the unperturbed input, and yet are misclassified. In standard neural networks used for deep learning, atta…

The paper analyzes adversarial training effects on classification accuracy.

More training data can hurt the generalization of adversarially robust models.

LGAC enhances heat transfer in turbulent boundary layers using slot jets.

Empirical study on SGD hyperparameters and adversarial robustness.

The paper analyzes how quantization affects the Fisher Information Matrix's dominant eigenvalue.