arXiv research

New research determines the optimal sample complexity for multiclass and list learning.

This work characterizes when a hypothesis class can be k-list learned.

New bounds show agnostic multiclass learning depends on two dimensions: Natarajan and Daniely-Shalev-Shwartz.

Learnable multiclass hypothesis classes don't always have a sample compression scheme of fixed size.

Adaptive sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. A sequential adaptive sampling-and-refinement procedure called Distilled Sensing (DS) is proposed and analyzed. DS is a form of multi-stage experimental design and testing. Because of the adaptive nature of the…

Tyler's M-estimator's phase transition at DS-SNR = 1 is resolved.

Optimal sample complexity for autoregressive chain-of-thought learning proven.

Sharp sample complexity for multiclass PAC learning with bandit feedback.

New Sauer inequality improves multiclass hypothesis class bounds.

Unsupervised dimension selection is an important problem that seeks to reduce dimensionality of data, while preserving the most useful characteristics. While dimensionality reduction is commonly utilized to construct low-dimensional embeddings, they produce feature spaces that are hard to interpret. Further, in applica…

The Homogeneity Conjecture explores if constant displacement isometries imply homogeneous spaces.

Multiple classifier systems focus on the combination of classifiers to obtain better performance than a single robust one. These systems unfold three major phases: pool generation, selection and integration. One of the most promising MCS approaches is Dynamic Selection (DS), which relies on finding the most competent c…

Characterizes statistical complexity of realizable regression in PAC and online learning.

DS-UI improves DNN uncertainty inference by combining a DNN classifier with MoGMM.

In this note we study globally homogeneous Riemannian quotients $Γ\backslash (M,ds^2)$ of homogeneous Riemannian manifolds $(M,ds^2)$. The Homogeneity Conjecture is that $Γ\backslash (M,ds^2)$ is (globally) homogeneous if and only if $(M,ds^2)$ is homogeneous and every $γ\in Γ$ is of constant displacement on $(M,ds^2)$…

Proofs centerless unimodular contact Lie algebras.

In this paper, we present a scalable distributed implementation of the Sampled Limited-memory Symmetric Rank-1 (S-LSR1) algorithm. First, we show that a naive distributed implementation of S-LSR1 requires multiple rounds of expensive communications at every iteration and thus is inefficient. We then propose DS-LSR1, a …

Improved bound on the product of first Laplacian eigenvalue and area for genus three surfaces.

Study examines deformations of Kerr-(A)dS near horizon geometry.

DGDS uses documents to center conversations, promising broader AI understanding.

In this article we first show that any finite cover of the moduli space of closed Riemann surfaces of genus $g$ with $g\geq 2$ does not admit any Riemannian metric $ds^2$ of nonnegative scalar curvature such that $ds^2 \succ ds_{T}^2$ where $ds_{T}^2$ is the Teichmüller metric. Our second result is the proof that any c…

Density sketches summarize data distributions for accurate sampling and estimation.

Geodesic orbit spaces and their families are studied in pseudo-Riemannian manifolds.

DS-Sync improves distributed DNN training efficiency by 94% with minimal accuracy loss.

The $H^1(ds)$-gradient flow shrinks circles with radius $r_0$ to a point.

New algorithms improve submodular minimization via DC programming.

A main theoretical interest in biology and physics is to identify the nonlinear dynamical system (DS) that generated observed time series. Recurrent Neural Networks (RNNs) are, in principle, powerful enough to approximate any underlying DS, but in their vanilla form suffer from the exploding vs. vanishing gradients pro…

Study verifies Homogeneity Conjecture for three odd-dimensional spheres in positive curvature.

DS-GDA solves nonconvex-nonconcave problems without regularity conditions.

DS-TS adapts to abrupt and smooth changes in bandit problems.

Dantzig Selector (DS) is widely used in compressed sensing and sparse learning for feature selection and sparse signal recovery. Since the DS formulation is essentially a linear programming optimization, many existing linear programming solvers can be simply applied for scaling up. The DS formulation can be explained a…

In this paper we consider the Martin compactification, associated with the operator $\mathcal{L} = Δ-1$, of a complete non-compact surface $(Σ^2, ds^2)$ with negative curvature. In particular, we investigate positive eigenfunctions with eigenvalue one of the Laplace operator $Δ$ of $(Σ^2, ds^2)$ and prove a uniqueness …

In dynamic selection (DS) techniques, only the most competent classifiers, for the classification of a specific test sample are selected to predict the sample's class labels. The more important step in DES techniques is estimating the competence of the base classifiers for the classification of each specific test sampl…

MOB-dS uses permutation to correct for dependency in discrete survival data.

Quasiclassical generalized Weierstrass representation (GWR) for highly corrugated surfaces with slow modulation in the four-dimensional Euclidean space is proposed. Integrable deformations of such surfaces are described by the dispersionless Davey-Stewartson hierarchy. Quasiclassical GWRs for other four-dimensional spa…

All inextendible null geodesics in four dimensional de Sitter space dS^4 are complete and globally achronal. This achronality is related to the fact that all observer horizons in dS^4 are eternal, i.e. extend from future infinity scri^+ all the way back to past infinity scri^-. We show that the property of having a nul…

Let $X$be a complex hyperelliptic curve of genus two equipped with the canonical metric $ds^2$. We study mean field equations on complex hyperelliptic curves and show that the Gaussian curvature function of $(X,ds^2)$ determines an explicit solution to a mean field equation.

We discuss several aspects of the relation between asymptotically AdS and asymptotically dS spacetimes including: the continuation between these types of spaces, the global stability of asymptotically dS spaces and the structure of limits within this class, holographic renormalization, and the maximal mass conjecture o…

We show that for a smooth closed curve $γ$ on a compact Riemannian surface without boundary, the inner product of two eigenfunctions $e_λ$ and $e_μ$ restricted to $γ$, $|\int e_λ\overline{e_μ}\,ds|$, is bounded by $\min\{λ^\frac12,μ^\frac12\}$. Furthermore, given $0<c<1$, if $0<μ<cλ$, we prove that $\int e_λ\overline{e…

The global symmetry algebras of partially-massless (PM) higher-spin (HS) fields in (A)dS$_{d+1}$ are studied. The algebras involving PM generators up to depth $2\,(\ell-1)$ are defined as the maximal symmetries of free conformal scalar field with $2\,\ell$ order wave equation in $d$ dimensions. We review the constructi…

Paper analyzes robustness of data-selective Volterra NLMS algorithm.

Our aim is to determine the lower central series (LCS) and derived series (DS) for the braid groups of the sphere and of the finitely-punctured sphere. We show that for all n (resp. all n\geq 5), the LCS (resp. DS) of the n-string braid group B\_n(S^2) is constant from the commutator subgroup onwards, and that Γ\_2(B\_…

New binary classification techniques help multiclass classification by aggregating proper learners.

Scaling multinomial logistic regression to datasets with very large number of data points and classes is challenging. This is primarily because one needs to compute the log-partition function on every data point. This makes distributing the computation hard. In this paper, we present a distributed stochastic gradient d…

While crowdsourcing has become an important means to label data, there is great interest in estimating the ground truth from unreliable labels produced by crowdworkers. The Dawid and Skene (DS) model is one of the most well-known models in the study of crowdsourcing. Despite its practical popularity, theoretical error …

In this work, we introduce a deep-structured conditional random field (DS-CRF) model for the purpose of state-based object silhouette tracking. The proposed DS-CRF model consists of a series of state layers, where each state layer spatially characterizes the object silhouette at a particular point in time. The interact…

The study improves the upper bound for the first eigenvalue of Laplacian on compact surfaces of large genus.

We focus on kernel methods for set-valued inputs and their application to Bayesian set optimization, notably combinatorial optimization. We investigate two classes of set kernels that both rely on Reproducing Kernel Hilbert Space embeddings, namely the ``Double Sum'' (DS) kernels recently considered in Bayesian set opt…