arXiv research

Study shows generative priors improve rank-one matrix recovery with optimal sample complexity.

Gradient descent with growing learning rate enables learning non-linear features in neural networks.

We consider worker skill estimation for the single-coin Dawid-Skene crowdsourcing model. In practice, skill-estimation is challenging because worker assignments are sparse and irregular due to the arbitrary and uncontrolled availability of workers. We formulate skill estimation as a rank-one correlation-matrix completi…

Gradient descent solves rank-one matrix estimation problem with detailed time evolution analysis.

Every GL(2,R)-orbit in hyperelliptic components of strata of abelian differentials in genus greater than two is either closed, dense, or contained in a locus of branched covers.

This paper sets fundamental limits for rank-one matrix estimation with varying noise levels.

The object of this paper is to study GL(2,R) orbit closures in hyperelliptic components of strata of abelian differentials. The main result is that all higher rank affine invariant submanifolds in hyperelliptic components are branched covering constructions, i.e. every translation surface in the affine invariant subman…

We present an algorithm, AROFAC2, which detects the (CP-)rank of a degree 3 tensor and calculates its factorization into rank-one components. We provide generative conditions for the algorithm to work and demonstrate on both synthetic and real world data that AROFAC2 is a potentially outperforming alternative to the go…

Paper proposes a tensor model for clustering noisy multi-view data.

We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal components simultaneously using manifold optimization techniques to enforce orth…

Study on signal-plus-noise decomposition in nonlinear spiked random matrices.

Principal components analysis (PCA) is a fundamental algorithm in data analysis. Its memory-restricted online versions are useful in many modern applications, where the data are too large to fit in memory, or when data arrive as a stream of items. In this paper, we propose ROIPCA and fROIPCA, two online PCA algorithms …

Extended Rank-One Theorem to special metric spaces.

New algorithms detect and estimate rank-one signals with prior directional information.

The paper reveals low-rank structure in neural network gradients, influenced by data and model parameters.

In this paper, we show that the simplicial volume of Q-rank one locally symmetric spaces covered by the product of R-rank one symmetric spaces is strictly positive.

Constructs explicit p-harmonic functions on specific Lie groups.

We develop a notion of rank one properly convex domains (or Hilbert geometries) in the real projective space. This is in the spirit of rank one non-positively curved Riemannian manifolds and CAT(0) spaces. We define rank one isometries for Hilbert geometries and characterize them as being equivalent to contracting elem…

The study establishes uncertainty principles on harmonic manifolds of rank one.

We explore the limit set of a particular spherical CR uniformization of a cusped hyperbolic manifold. We prove that the limit set is the closure of a countable union of $\mathbb{R}$-circles, is connected, and contains a Hopf link with three components; we also show that the fundamental group of its complement in $S^3$ …

Classifies foliations on specific symmetric spaces.

We give a positive answer to the Chavel's conjecture [J. Diff. Geom. 4 (1970), 13-20]: a simply connected rank one normal homogeneous space is symmetric if any pair of conjugate points are isotropic. It implies that all simply connected rank one normal homogeneous space with the property that the isotropy action is var…

CSD learns a common component for domain generalization, outperforming existing methods.

Improved stability for matrix recovery from rank-one measurements.

Classifies rank-one submanifolds in Euclidean space.

No Einstein hypersurfaces found in Damek-Ricci spaces.

Generalizes results on Bieri-Neumann-Strebel-Renz invariants and tropical varieties.

New insights into compact rank-one ECS manifolds, proving they are bundles over circles.

Compact rank one symmetric spaces are rigid under certain curvature conditions.

Study closed manifolds with rank one ray structures, proving completeness or covering properties.

In this paper we show that if the limit set is not small ,marked length spectrum determines geometric structure of rank one locally symmetric manifolds.

For convex domains with $C^{1,ε}$ boundary we give a precise description of the automorphism group: if an orbit of the automorphism group accumulates on at least two different closed complex faces of the boundary, then the automorphism group has finitely many components and the connected component of the identity is th…

We study the Selberg zeta and the theta function associated to bundles over even-dimensional locally symmetric spaces of rank one.

We show that cocompact lattices in rank one simple Lie groups of non-compact type distinct from SO(2m,1) (m>0) contain surface subgroups.

Researchers describe the metric structure of compact ECS manifolds.

Paper optimizes tensor deflation for non-orthogonal signals.

Study detects signals in spiked Wigner models using log likelihood ratio.

Stochastic Rank-One Bandits (Katarya et al, (2017a,b)) are a simple framework for regret minimization problems over rank-one matrices of arms. The initially proposed algorithms are proved to have logarithmic regret, but do not match the existing lower bound for this problem. We close this gap by first proving that rank…

Novel algorithm for Markov decision processes using rank-one approximation.

Rank-one measurements limit feasible sets for low-rank PSD matrices.

In this paper, based on research on rank-one isometries by W.Ballmann and M.Brin and recent research on rank-one isometries of Coxeter groups by P.Caprace and K.Fujiwara, we study a topological fractal structure of boundaries of Coxeter groups. We also show that the limit-point set is dense in a boundary of a Coxeter g…

New analysis shows how attention masks and LayerNorm prevent rank collapse in transformers.

New random walk results on rank one symmetric spaces.

We prove that a quasiisometric map between rank one symmetric spaces is within bounded distance from a unique harmonic map. In particular, this completes the proof of the Schoen-Li-Wang conjecture.

We prove that the orbits of a polar action of a compact Lie group on a compact rank one symmetric space are tautly embedded with respect to Z_2-coefficients.

The Besson-Courtois-Gallot theorem is proven for noncompact finite volume Riemannian manifolds. In particular, no bounded geometry assumptions are made. This proves the minimal entropy conjecture for nonuniform rank one lattices.

The paper analyzes tensor recovery from symmetric rank-one measurements using information theory.

Let M be a geometrically finite rank one locally symmetric manifolds. We prove that the spectrum of the Laplace operator on M is finite in a small interval which is optimal.