Computational model uncovers linguistic universals.
problem Manual processing of linguistic typology by linguists is time-consuming and leaves key universals unexplored.
method Presented a computational model to identify known and new linguistic universals.
result The model successfully identifies known universals and uncovers new ones.
The Greenberg-Shalom hypothesis connects subgroup properties to lattice structures in Lie groups.
problem Understanding subgroup properties in Lie groups and their implications.
method Analyzing infinite discrete subgroups of semisimple Lie groups and their commensurators.
result An infinite discrete subgroup of a semisimple Lie group with a dense commensurator is a lattice in a product of some factors.
The Bers-Greenberg theorem tells that the Teichmüller space of a Riemann surface with branch points (orbifold) depends only on the genus and the number of special points, but not on the particular ramification values. On the other hand, the Maskit embedding provides a mapping from the Teichmüller space of an orbifold, …
Study answers arithmeticity question for normal subgroup of lattices.
problem Arithmeticity of discrete subgroups of semisimple Lie groups with dense commensurators.
method Examined normal subgroups of lattices in semisimple Lie groups.
result Positive answer to Greenberg-Shalom's question for lattices.
Based on the analogy between knots and primes, J. Hillman, D. Matei and M. Morishita defined the Iwasawa invariants for sequences of cyclic covers of links with an analogue of Iwasawa's class number formula of number fields. In this paper, we consider the existence of covers of links with prescribed Iwasawa invariants,…
We propose a conceptual design for a quantum blockchain. Our method involves encoding the blockchain into a temporal GHZ (Greenberger-Horne-Zeilinger) state of photons that do not simultaneously coexist. It is shown that the entanglement in time, as opposed to an entanglement in space, provides the crucial quantum adva…
The isometry group of a compact n-dimensional hyperbolic manifold is known to be finite. We show that for every n > 2, every finite group is realized as the full isometry group of some compact hyperbolic n-manifold. The cases n = 2 and n = 3 have been proven by Greenberg and Kojima, respectively. Our proof is non const…
In this paper we parametrize the Teichmüller spaces of constructible Koebe groups, that is Kleinian group that arise as covering of 2−orbifolds determined by certain normal subgroups of their fundamental groups. We also study the covering spaces of the Teichmüller spaces of those Koebe groups. Finally we prove an iso…
Proves restrictions on projective Anosov representations of hyperbolic groups.
problem Restrictions on projective Anosov representations of hyperbolic groups.
method Word hyperbolic groups and Gromov boundary analysis.
result Word hyperbolic groups with certain properties cannot admit projective Anosov representations.
The braided Ptolemy-Thompson group T∗ is an extension of the Thompson group T by the full braid group B∞ on infinitely many strands. This group is a simplified version of the acyclic extension considered by Greenberg and Sergiescu, and can be viewed as a mapping class group of a certain infinite planar s…
We begin by showing that commensurators of Zariski dense subgroups of isometry groups of symmetric spaces of non-compact type are discrete provided that the limit set on the Furstenberg boundary is not invariant under the action of a (virtual) simple factor. In particular for rank one or simple Lie groups, Zariski dens…
The paper extends Thurston's method to new variants of Mather-Thurston theorem.
problem Proving new variants of Mather-Thurston theorem for PL homeomorphisms and contactomorphisms.
method Generalizing Thurston's technique to prove new variants of Mather-Thurston theorem for PL homeomorphisms and contactomorphisms.
result The paper answers questions posed by Gelfand-Fuks and Greenberg on PL foliations and Rybicki on contactomorphisms.
Study counts and parametrizes flag components in SO0(p,q) space.
problem Counting and characterizing flag components in SO0(p,q) space.
method Parametrization and computation of Plücker coordinates.
result Anosov subgroups are virtually isomorphic to surface or free groups.
Study p-torsion growth in covers of 3-manifolds, proving Iwasawa formulas.
problem Investigate p-torsion growth in compatible systems of covers of 3-manifolds. method Establish analogues of Iwasawa's class number formula for branched covers of links.
result Prove Cuoco--Monsky type formula for branched covers of links.
Paper proposes nested MLMC for SNPE with intractable likelihoods.
problem Estimating posterior distributions from intractable likelihoods.
method Nested MLMC for loss function and gradients, with convergence results.
result Effective methods for approximating complex multimodal posteriors.
Improved MoM estimator enhances classical shadows protocol for quantum measurements.
problem Efficient estimation of expectation values with reduced measurement shots.
method Modified median-of-means estimator with optimal constants and U-statistics.
result Improved performance of modified estimator for Clifford measurements.
Novel approach to universal online learning for bounded losses, closing open problems.
problem Characterizing processes for universal online learning under non-i.i.d. conditions.
method Characterization of processes admitting strong and weak universal learning, introduction of optimistically universal learning rule.
result Introduction of a novel 1NN algorithm that is optimistically universal for bounded losses.
Universal Gaussian parity proven for 2D knots.
problem Proving universal Gaussian parity for 2D knots.
method Analyzing Gaussian parity on free 2D knots.
result Gaussian parity is universal for 2D knots.
Researchers found specific conformal groups for Einstein static universe models.
problem Understanding conformal groups of Einstein static universe models.
method Constructed explicit models for restricted conformal groups and universal covering groups.
result Determined all conformal Lorentz manifolds with maximal restricted conformal group dimension.
GCNNs gain rotation invariance with more training augmentation, making SVD-Universal more effective.
problem Improving robustness of GCNNs to adversarial attacks.
method SVD-Universal technique applied to GCNNs trained with larger rotations.
result SVD-Universal becomes more effective as GCNNs gain rotation invariance.
The study of universal links in 3-manifolds and their properties.
problem Existence and characterization of universal links in 3-manifolds.
method Analyzing branched coverings and distinguishing between universal and complement universal links.
result Closed spherical 3-manifolds are the only ones admitting universal links.
Universal MLPs with a single hidden layer can learn any function.
problem Learning on various data structures like sequences, images, sets, and graphs.
method Using group theory, the paper proves the universality of a broad class of equivariant MLPs with a single hidden layer.
result Having a hidden layer on which the group acts regularly is sufficient for universal equivariance (invariance).
Constructs universal link invariants from intersections in configuration spaces.
problem Globalise topologically all coloured Jones polynomials and ADO polynomials.
method Defines new link invariants from graded intersections in configuration spaces.
result Recover all coloured Jones polynomials and ADO polynomials for links.
We construct universal Lefschetz fibrations, defined in analogy with classical universal bundles. We also introduce the cobordism groups of Lefschetz fibrations, and we see how these groups are quotients of the singular bordism groups via the universal Lefschetz fibrations.
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…
Revives Vogel's diagrammatic technique for universal Lie algebra computations.
problem The universality of Lie algebra quantities remains open, despite many being described.
method Diagrammatic algebra based on Vogel's Λ-algebra.
result Diagrammatic technique enables truly universal computations in Lie theory.
We prove Runge-type theorems and universality results for locally univalent holomorphic and meromorphic functions. Refining a result of M. Heins, we also show that there is a universal bounded locally univalent function on the unit disk. These results are used to prove that on any hyperbolic simply connected plane doma…
Simple technique turns any adversarial attack into a universal one using few test examples.
problem Creating universal adversarial attacks with minimal data.
method Universalization technique using few adversarial test examples and spectral properties.
result Simple universalization technique achieves comparable fooling rates to state-of-the-art methods.
Universal inequalities found for Laplacian eigenvalues on convex domains.
problem Finding bounds for Laplacian eigenvalues on convex domains.
method Established two universal inequalities.
result Found new bounds for Laplacian eigenvalues.
Universal Bayes consistency proved in metric spaces.
problem Proving universal Bayes consistency in metric spaces.
method Extending a multiclass learning algorithm and proving its Bayes-consistency in all metric spaces.
result First learning algorithm universally strongly Bayes-consistent in all metric spaces.
Universal inequalities for Laplacian eigenvalues on discrete groups.
problem Proving inequalities for Laplacian eigenvalues on discrete groups.
method Analyzing Laplacian eigenvalues with Dirichlet boundary conditions on subsets of discrete groups.
result Yang-type universal inequalities for Cayley graphs of amenable groups and the d-regular tree.
New maps connect universal circles to ideal sphere for hyperbolic manifolds.
problem Understanding universal circles for Anosov foliations with branching.
method Introduced a new type of Cannon--Thurston map for leftmost universal circles.
result Fundamental group acts on leftmost universal circle with pseudo-Anosov dynamics.
This paper studies universal rates of ERM for binary classification under agnostic learning.
problem The challenge of achieving universal rates of ERM for binary classification under agnostic learning.
method The paper explores the agnostic universal rates of ERM for binary classification, revealing three possible rates: e−n, o(n−1/2), or arbitrarily slow. result The paper provides a complete characterization of which concept classes fall into each of the three categories of agnostic universal rates.
Develops a new approach to establish universality for any-dimensional machine learning models.
problem Understanding universality for models with inputs of varying sizes.
method Identifies any-dimensional functions with a unique function in an infinite-dimensional limit space, using symmetries and relations between inputs of different sizes.
result Establishes universality for several existing architectures and proposes modifications to restore it.
Softmax attention approximates complex functions and subsumes many known universal approximators.
problem Universal approximation of continuous sequence-to-sequence functions.
method Interpolation-based analysis of attention's internal mechanism, showing its ability to approximate ReLU functions.
result Softmax attention is a universal approximator for continuous sequence-to-sequence functions.
MLPs can approximate any function in context, challenging the importance of in-context universality.
problem Understanding why transformers are more effective than classical models.
method Proved MLPs with trainable activation functions are universal in context.
result Transformer success is likely due to factors other than in-context universality.
Solves open problem on universally consistent online learning with unbounded losses.
problem Open problem on universally consistent online learning with unbounded losses.
method Constructs random measurable partitions of the instance space.
result Simple memorization rule is optimistically universal for any unbounded loss.
Proves universal pairing result for 2-complexes, showing lack of positivity.
problem Detecting equivalence relations in 2-complexes.
method Analogous to Freedman et al. for manifolds, but for 2-complexes.
result Universal pairing does not detect simple homotopy equivalence vs 3-deformations for 2-complexes.
New model closes gap in understanding equivariant set functions.
problem Understanding universality of equivariant set functions.
method Proves PointNet not equivariant universal and introduces PointNetST.
result PointNetST is the simplest permutation equivariant universal model.
The paper explores universal circles for Anosov foliations and their uniqueness.
problem Exploring the uniqueness of universal circles for Anosov foliations.
method Using the flow space of an Anosov flow to parameterize the circle bundle at infinity of the foliations.
result Several constructions of a universal circle are typically distinct and not conjugate.
The paper tightens bounds on distances between Reeb graphs.
problem Certifying quasi-universality of distances between Reeb graphs.
method Establishes tight bi-Lipschitz bounds for various distances.
result Proves strict universality of the functional contortion distance for contour trees and coincides with interleaving distance for merge trees.
Improved algorithm speeds up generation of universal adversarial perturbations.
problem Slow generation of universal adversarial perturbations.
method Optimized algorithm based on orientation of perturbation vectors.
result Significantly faster generation of universal perturbations with higher fooling rates.
A universal LSTM model outperforms asset-specific models in forecasting stock volatilities.
problem Forecasting stock volatilities across different assets.
method Trained an LSTM network on a pooled dataset of liquid stocks to forecast daily realized volatilities.
result The LSTM model consistently outperforms other asset-specific parametric models in volatility forecasting.
The universal Liouville action equals the renormalized volume of a hyperbolic 3-manifold.
problem Understanding the geometric significance of the universal Liouville action.
method Analyzing the Weil-Petersson universal Teichmüller space and its relation to hyperbolic 3-manifolds.
result The gradient flow of the universal Liouville action converges to the origin, providing a bound on Weil-Petersson distance.
MAT combines meta-learning and adversarial training to defend against universal patches.
problem Defending against universal patches that fool models in various contexts.
method Meta adversarial training (MAT) integrates meta-learning with adversarial training.
result MAT increases robustness against universal patch attacks on image classification and traffic-light detection.
Study of Gödel Universe as Lie group with specific metric.
problem Characterize geodesics in the Gödel Universe.
method Geometric theory of optimal control applied to Lie groups with left-invariant Lorentz metrics.
result No closed timelike or isotropic geodesics in the Gödel Universe.
Paper finds universal speech command perturbations that fool models.
problem Existence of universal adversarial examples in speech command classification.
method Proposed a novel analytical framework for evaluating universal perturbations and a detailed distortion measurement method.
result Universal perturbations can fool speech command classification models across different models.
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…