arXiv research

Abstract result on correlations of pairs in exponentially growing discrete subsets.

We prove that the size of the super summit set of a braid can grow exponentially with the canonical length of the braid, even for pseudo-Anosov braids.

The study shows exponential distortion in virtually special groups containing free subgroups.

Suppose that $Γ_0\subset\mathbb R^{n+1}$ is a closed countably $n$-rectifiable set whose complement $\mathbb R^{n+1}\setminus Γ_0$ consists of more than one connected component. Assume that the $n$-dimensional Hausdorff measure of $Γ_0$ is finite or grows at most exponentially near infinity. Under these assumptions, we…

The Tits alternative for Out(F_n) is reduced to the case where all elements in the subgroup under consideration grow polynomially.

Study shows torsion grows subexponentially in book of I-bundles but can grow exponentially in non-regular covers.

It is well-known that neural networks are universal approximators, but that deeper networks tend in practice to be more powerful than shallower ones. We shed light on this by proving that the total number of neurons $m$ required to approximate natural classes of multivariate polynomials of $n$ variables grows only line…

Minimal graphs over simply connected domains grow at most exponentially.

New knot homology invariant grows exponentially with color.

New hyperbolic manifolds show exponential homology torsion growth.

This paper uses Reinforcement Learning to select features from a large dataset.

Paper proposes a method to identify negative transfers in multitask learning using surrogate models.

In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We prove that the sparse estimator from such a method can retain all of the importa…

The paper defines conditions for a free-by-free group to be hyperbolic.

A new method for exponentially weighted moving models using approximations.

We show that if a f.g. group $G$ has a non-elementary WPD action on a hyperbolic metric space $X$, then the number of $G$-conjugacy classes of $X$-loxodromic elements of $G$ coming from a ball of radius $R$ in the Cayley graph of $G$ grows exponentially in $R$. As an application we prove that for $N\ge 3$ the number of…

Random quotients of hyperbolic cubulated groups remain cubulated.

New rank 3 distributions with exponentially growing symmetries.

Accelerated gradient method's stability deteriorates exponentially with steps.

For d=2n+1 a positive odd integer, we consider sequences of arithmetic subgroups of SO_0(d,1) and Spin(d,1) yielding corresponding hyperbolic manifolds of finite volume and show that, under appropriate and natural assumptions, the torsion of the associated cohomology groups grows exponentially.

We prove that almost all geodesics on a noncompact locally symmetric space of finite volume grow with a logarithmic speed -- the higher rank generalization of a theorem of D. Sullivan (1982). More generally, under certain conditions on a sequence of subsets $A_n$ of a homogeneous space $G/Γ$ ($G$ a semisimple Lie group…

Improved sample efficiency in preference-based RL with multiple comparisons.

We show that there is a family of pseudo-Anosov braids independently parameterized by the braid index and the (canonical) length whose smallest conjugacy invariant sets grow exponentially in the braid index and linearly in the length and conclude that the conjugacy problem remains exponential in the braid index under t…

Given a simply connected, closed four manifold, we associate to it a simply connected, closed, spin five manifold. This leads to several consequences : the stable and unstable homotopy groups of such a four manifold is determined by its second Betti number, and the ranks of the homotopy groups can be explicitly calcula…

Ancient solutions on a strip are constant if polynomial, and have finite-dimensional space for slower growth.

When does the amount of torsion in the homology of an arithmetic group grow exponentially with the covolume? We give many examples where this is so, and conjecture precise conditions.

New algorithm reduces super-arm selection complexity exponentially.

New hyperbolic graph constructed from projections of free splitting graph.

We give bounds on the number of non-simple closed curves on a negatively curved surface, given upper bounds on both length and self-intersection number. In particular, it was previously known that the number of all closed curves of length at most $L$ grows exponentially in $L$. We get exponentially tighter bounds given…

This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation are established. The estimators that achieve the optimal rates are constructed …

We show that the number of isometry classes of cusped hyperbolic $3$-manifolds that bound geometrically grows at least super-exponentially with their volume, both in the arithmetic and non-arithmetic settings.

Groups on CAT(0) cube complexes grow exponentially uniformly.

In this paper we prove that for suitable sequences of congruence subgroups of Bianchi groups, including the standard exhaustive sequences of a congruence subgroup, and even symmetric powers of the standard representation of Sl_2(C) the size of the torsion part in the first homology grows exponentially. This extends res…

Compound interest as well as inflation grows exponentially with time, whereas other means to repay debt grow polynomially. For this and other, mostly political, reasons, debt without inflation is unsustainable. We suggest a discontinuous way to eliminate debt by nullifying it. This scenario is preferable to current cen…

This paper analyzes VAE approximation errors in conditional exponential families.

Study on immersions with flat normal bundle in curved spaces.

The study of private inference has been sparked by growing concern regarding the analysis of data when it stems from sensitive sources. We present the first method for private Bayesian inference in exponential families that properly accounts for noise introduced by the privacy mechanism. It is efficient because it work…

We show that a smooth unknotted curve in R^3 satisfies an isoperimetric inequality that bounds the area of an embedded disk spanning the curve in terms of two parameters: the length L of the curve and the thickness r (maximal radius of an embedded tubular neighborhood) of the curve. For fixed length, the expression giv…

We analyze a controlled price formation experiment in the laboratory that shows evidence for bubbles. We calibrate two models that demonstrate with high statistical significance that these laboratory bubbles have a tendency to grow faster than exponential due to positive feedback. We show that the positive feedback ope…

Exponential family extensions of principal component analysis (EPCA) have received a considerable amount of attention in recent years, demonstrating the growing need for basic modeling tools that do not assume the squared loss or Gaussian distribution. We extend the EPCA model toolbox by presenting the first exponentia…

This paper refines bounds on random walk speed in Teichmüller space.

The volume conjecture and its generalizations say that the colored Jones polynomial corresponding to the N-dimensional irreducible representation of sl(2;C) of a (hyperbolic) knot evaluated at exp(c/N) grows exponentially with respect to N if one fixes a complex number c near 2*Pi*I. On the other hand if the absolute v…

EPC curriculum improves MARL performance as agent population grows.

With the rapidly growing scales of statistical problems, subset based communication-free parallel MCMC methods are a promising future for large scale Bayesian analysis. In this article, we propose a new Weierstrass sampler for parallel MCMC based on independent subsets. The new sampler approximates the full data poster…

Study shows exponential growth of knot polynomial tied to Chern-Simons invariant.

This paper proves exponential mixing for frame flows on hyperbolic manifolds with cusps.

ReLU networks don't exponentially distort curve lengths as previously thought.

Expressive efficiency refers to the relation between two architectures A and B, whereby any function realized by B could be replicated by A, but there exists functions realized by A, which cannot be replicated by B unless its size grows significantly larger. For example, it is known that deep networks are exponentially…