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.
Universal spaces for finite topological spaces simplify shape descriptions.
Metric spaces with certain curvature properties are universally infinitesimally Hilbertian.
Universal Gaussian parity proven for 2D knots.
The universal sl_2 invariant of bottom tangles has a universality property for the colored Jones polynomial of links. Habiro conjectured that the universal sl_2 invariant of boundary bottom tangles takes values in certain subalgebras of the completed tensor powers of the quantized enveloping algebra U_h(sl_2) of the Li…
A new model uses Toeplitz matrices to analyze time-series data transitions.
The study extends kernel universality to Riemannian symmetric spaces.
Every homomorphism from finite index subgroups of a universal lattices to mapping class groups of orientable surfaces (possibly with punctures), or to outer automorphism groups of finitely generated nonabelian free groups must have finite image. Here the universal lattice denotes the special linear group G=SL_m(Z[x1,..…
WWe define the notion of a random metric space and prove that with probability one such a space is isometricto the Urysohn universal metric space. The main technique is the study of universal and random distance matrices; we relate the properties of metric (in particulary universal) space to the properties of distance …
Deep networks have recently been shown to be vulnerable to universal perturbations: there exist very small image-agnostic perturbations that cause most natural images to be misclassified by such classifiers. In this paper, we propose the first quantitative analysis of the robustness of classifiers to universal perturba…
Unified plug-in approach for estimating symmetric properties of distributions efficiently.
Derived geometry can be defined as the universal way to adjoin finite homotopical limits to a given category of manifolds compatibly with products and glueing. The point of this paper is to show that a construction closely resembling existing approaches to derived geometry in fact produces a geometry with this universa…
We extend a recently proposed 1-nearest-neighbor based multiclass learning algorithm and prove that our modification is universally strongly Bayes-consistent in all metric spaces admitting any such learner, making it an "optimistically universal" Bayes-consistent learner. This is the first learning algorithm known to e…
Complex-valued neural networks can approximate any continuous function.
Study properties of balanced hyperbolic compact complex manifolds.
This article explores some properties of universal covers of compact Kahler manifolds, under the assumption of Caratheodory measure hyperbolicity. In particular, by comparing invariant volume forms, an inequality is established between the volume of canonical bundle of a compact Kahler manifolds and the Caratheodory me…
Simple technique turns any adversarial attack into a universal one using few test examples.
Neural networks can approximate functions uniformly across various measures.
We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, and give their ex…
Universal approximation for ODENet and ResNet with a single activation function.
Physics: Similar long-distance properties can mask vastly different short-distance metrics.
Estimating symmetric properties of a distribution, e.g. support size, coverage, entropy, distance to uniformity, are among the most fundamental problems in algorithmic statistics. While each of these properties have been studied extensively and separate optimal estimators are known for each, in striking recent work, Ac…
The study of universal links in 3-manifolds and their properties.
New high-order universal portfolios outperform standard ones.
NODEs can approximate a wide range of diffeomorphisms with strong guarantees.
Collective phenomena with universal properties have been observed in many complex systems with a large number of components. Here we present a microscopic model of the emergence of scaling behavior in such systems, where the interaction dynamics between individual components is mediated by a global variable making the …
The paper analyzes deep ReLU CNNs' approximation properties in 2D space.
In this paper, we analyze the Bollobás and Riordan polynomial for ribbon graphs with half-ribbons introduced in [Combinatorics, Probability and Computing 31, 507-549, 2022]. We prove the universality property of a multivariate version of whereas itself turns out to be universal…
In this article we present infinitely many 3-manifolds admitting infinitely many universally tight contact structures each with trivial Ozsvath-Szabo contact invariants. By known properties of these invariants the contact structures constructed here are non weakly symplectically fillable.
The Euler characteristic is the only additive topological invariant for spaces of certain sort, in particular, for manifolds with some finiteness properties. A generalization of the notion of a manifold is the notion of a V-manifold. Here we discuss a universal additive topological invariant of V-manifolds: the univers…
Study graded coverings for supermanifolds, proving their universal properties.
It is well known that spinors on oriented Riemannian manifolds cannot be defined as sections of a vector bundle associated with the frame bundle. For this reason spin and spin^c structures are often introduced. In this paper we prove that spin^c structures have a universal property among all other structures that enabl…
Unified framework proves neural networks' ability to mimic complex tasks.
PanRep learns universal node embeddings for heterogeneous graphs.
We present a simple proof for the universality of invariant and equivariant tensorized graph neural networks. Our approach considers a restricted intermediate hypothetical model named Graph Homomorphism Model to reach the universality conclusions including an open case for higher-order output. We find that our proposed…
Counterexample found for Stein property of certain solvable Lie groups.
We prove an additivity property for the normalized Seiberg-Witten invariants with respect to the universal abelian cover of those 3-manifolds, which are obtained via negative rational Dehn surgeries along connected sum of algebraic knots. Although the statement is purely topological, we use the theory of complex singul…
Sig-Splines model uses signatures and splines for time series data, achieving universality and convexity.
Narasihman and Ramanan proved that an arbitrary connection in a vector bundle over a base space B can be obtained as the pull-back (via a correctly chosen classifying map from B into the appropriate Grassmannian) of the universal connection in the universal bundle over the Grassmannian. The purpose of this paper is to …
We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994-95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there are deviations for a fe…
The aim of this paper is to introduce the concepts of homotopical smallness and closeness. These are the properties of homotopical classes of maps that are related to recent developments in homotopy theory and to the construction of universal covering spaces for non-semilocally simply connected spaces, in particular to…
The universal sl_2 invariant of string links has a universality property for the colored Jones polynomial of links, and takes values in the h-adic completed tensor powers of the quantized enveloping algebra of sl_2. In this paper, we exhibit explicit relationships between the universal sl_2 invariant and Milnor invaria…
GCNNs gain rotation invariance with more training augmentation, making SVD-Universal more effective.
We give a construction of a universal average of Lie algebra elements whose exponentiation gives (when there is an associated Lie group) a totally symmetric geometric mean of Lie group elements (sufficiently closed to the identity) with the property that in an action of the group on a space for which elements a…
It is shown that Nobeling spaces are uniquely determined by the universal extension and embedding properties.
For several instances of metric largeness like enlargeability or having hyperspherical universal covers, we construct non-large vector subspaces in the rational homology of finitely generated groups. The functorial properties of this construction imply that the corresponding largeness properties of closed manifolds dep…
UDENet and ResNet can approximate any function, with ODENet showing UAP for continuous functions.
A new generalization of Grassmannians, called ν-grassmannians, and a canonical super vector bundle over this new space, say Γ, are introduced. Then, constructing a Gauss supermap of a super vector bundle, the universal property of Γ is discussed. Finally, we generalize one of the main theorems of homotopy classificatio…
Two groups with same profinite completion have different co-Hopfian properties.