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.
New method certifies joint adversarial robustness of model ensembles.
Two triples of triangles having pairwise disjoint outlines in 3-space are called combinatorially isotopic if one triple can be obtained from the other by a continuous motion during which the outlines of the triangles remain pairwise disjoint. We conjecture that it can be algorithmically checked if an (ordered or unorde…
We estimate from below the number of lines meeting each of given 4 disjoint smooth closed curves in a given cyclic order in the real projective 3-space and in a given linear order in the Euclidean 3-space. Similarly, we estimate the number of circles meeting in a given cyclic order given 6 disjoint smooth closed curves…
New theorem on embedding Moebius bands in 3D space.
We note a simple algebraic proof of Frolkina's result that does not contain uncountably many pairwise disjoint copies of the Möbius band, and of a similar result in higher dimensions.
Despite the remarkable performance of deep neural networks on various computer vision tasks, they are known to be susceptible to adversarial perturbations, which makes it challenging to deploy them in real-world safety-critical applications. In this paper, we conjecture that the leading cause of adversarial vulnerabili…
We show that many algebraic actions of higher-rank abelian groups on zero-dimensional groups are mutually disjoint. The proofs exploit differences in the entropy geometry arising from subdynamics and a form of Abramov--Rokhlin formula for half-space entropies.
The following problem was proposed in 2010 by S. Lando. Let and be two unions of the same number of disjoint circles in a sphere. Do there always exist two spheres in 3-space such that their intersection is transversal and is a union of disjoint circles that is situated as in one sphere and as in the ot…
We are concerned with the vulnerability of computer vision models to distributional shifts. We formulate a combinatorial optimization problem that allows evaluating the regions in the image space where a given model is more vulnerable, in terms of image transformations applied to the input, and face it with standard se…
Study on planar graph braid groups' second homology.
Avoids noncompact hypersurfaces from touching in evolving flows.
We provide a self-contained treatment of set-theoretic subsolutions to flow by mean curvature, or, more generally, to flow by mean curvature plus an ambient vector field. The ambient space can be any smooth Riemannian manifold. Most importantly, we show that if two such set-theoretic subsolutions are initially disjoint…
Study reveals how high-dimensional models are vulnerable to consistent adversarial attacks.
Infinite volume found in the thick part of -Hitchin-Riemann moduli space.
The study bounds the excess of disjoint nonorientable surfaces in a 4-manifold.
Improved estimation of concentration using half-spaces for adversarial vulnerability.
A Heegaard splitting of a closed, orientable three-manifold satisfies the disjoint curve property if the splitting surface contains an essential simple closed curve and each handlebody contains an essential disk disjoint from this curve [Thompson, 1999]. A splitting is full if it does not have the disjoint curve proper…
A manifold is T-embedded into an affine space if its tangent spaces at distinct points are disjoint. We prove that an n-dimensional disc cannot be T-embedded into 2n-dimensional space.
We study the space of "link maps": the space of maps of a disjoint union of compact, closed manifolds P_1, . . ., P_k into a manifold N whose images are pairwise disjoint. We apply the manifold calculus of functors developed by Goodwillie and Weiss to study the difference between it and its linear and quadratic approxi…
For links with vanishing pairwise linking numbers, the link components bound pairwise disjoint surfaces in . In this paper, we describe the set of genera of such surfaces in terms of the -function, which is a link invariant from Heegaard Floer homology. In particular, we use the -function to give lower bou…
The detection of software vulnerabilities (or vulnerabilities for short) is an important problem that has yet to be tackled, as manifested by the many vulnerabilities reported on a daily basis. This calls for machine learning methods for vulnerability detection. Deep learning is attractive for this purpose because it a…
Many deep learning models are vulnerable to the adversarial attack, i.e., imperceptible but intentionally-designed perturbations to the input can cause incorrect output of the networks. In this paper, using information geometry, we provide a reasonable explanation for the vulnerability of deep learning models. By consi…
Determining the space of free discrete two generator groups of Möbius transformations is an old and difficult problem. In this paper we show how to construct large balls of full dimension in this space. To do this, we begin with a marked discrete group of non-separating disjoint circle type. Such a group determines thr…
Solves Plateau-Douglas problem for singular configurations in general metric spaces.
2D complexes can be almost-embedded in 4D space without self-intersections.
The paper provides a converse to linking theorems for graphs in 3-space and higher dimensions.
Each year, thousands of software vulnerabilities are discovered and reported to the public. Unpatched known vulnerabilities are a significant security risk. It is imperative that software vendors quickly provide patches once vulnerabilities are known and users quickly install those patches as soon as they are available…
Approximates cycles in planar and bounded-genus graphs.
We show that any two disjoint crooked planes in R^3 are leaves of a crooked foliation. This answers a question asked by Charette and Kim.
This paper is devoted to dualization of paracompactness to the coarse category via the concept of -disjointness. Property A of G.Yu can be seen as a coarse variant of amenability via partitions of unity and leads to a dualization of paracompactness via partitions of unity. On the other hand, finite decomposition com…
We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note …
Despite achieving impressive performance, state-of-the-art classifiers remain highly vulnerable to small, imperceptible, adversarial perturbations. This vulnerability has proven empirically to be very intricate to address. In this paper, we study the phenomenon of adversarial perturbations under the assumption that the…
Decomposes ultrametric spaces into scaled simplices.
We present a new property, the Disjoint Path Concordances Property, of an ENR homology manifold X which precisely characterizes when X times R has the Disjoint Disks Property. As a consequence, X times R is a manifold if and only if X is resolvable and it possesses this Disjoint Path Concordances Property.
A membership inference attack (MIA) against a machine-learning model enables an attacker to determine whether a given data record was part of the model's training data or not. In this paper, we provide an in-depth study of the phenomenon of disparate vulnerability against MIAs: unequal success rate of MIAs against diff…
A new classification method using disjoint centroids and normalized distance.
This work examines how adversarial vulnerability changes with the dimensionality of the subspace of perturbations.
Deep neural networks (DNNs) are found to be vulnerable against adversarial examples, which are carefully crafted inputs with a small magnitude of perturbation aiming to induce arbitrarily incorrect predictions. Recent studies show that adversarial examples can pose a threat to real-world security-critical applications:…
NTK neural networks are robust to adversarial attacks in nonparametric regression.
We identify the space of left-invariant oriented complex structures on the complex Heisenberg group, and prove that it has the homotopy type of the disjoint union of a point and a 2-sphere.
Symplectic embeddings of balls into specific manifolds are studied, with restrictions and obstructions identified.
Uniform bounds found for Sierpinski carpet hyperbolic components.
Increasing numbers of software vulnerabilities are discovered every year whether they are reported publicly or discovered internally in proprietary code. These vulnerabilities can pose serious risk of exploit and result in system compromise, information leaks, or denial of service. We leveraged the wealth of C and C++ …
Over the past few years, neural networks were proven vulnerable to adversarial images: targeted but imperceptible image perturbations lead to drastically different predictions. We show that adversarial vulnerability increases with the gradients of the training objective when viewed as a function of the inputs. Surprisi…
We show that any number of disjointly embedded 2-spheres in 4-space can be pulled apart by a link homotopy, ie, by a motion in which the 2-spheres stay disjoint but are allowed to self-intersect.
Characteristic classes of oriented vector bundles can be identified with cohomology classes of the disjoint union of classifying spaces BSO_n of special orthogonal groups SO_n with n=0,1,... A characteristic class is stable if it extends to a cohomology class of a homotopy colimit BSO of classifying spaces BSO_n. Simil…
New research shows that the dimension gap between intrinsic and ambient dimensions affects adversarial vulnerability of machine learning models.
Three disjoint rays in euclidean 3-space form Borromean rays provided their union is knotted, but the union of any two components is unknotted. We construct infinitely many Borromean rays, uncountably many of which are pairwise inequivalent. We obtain uncountably many Borromean hyperplanes.