arXiv research

RSIC identifies multiple ranks of interest in NMF by analyzing residual sensitivity.

The symmetry-rank of a riemannian manifold is by definition the rank of its isometry group. We determine precisely which smooth closed manifolds admit a positively curved metric with maximal symmetry-rank.

New method reduces uncertainty in high-dimensional circuits by automatically determining tensor rank and adaptive sampling.

Identifies images of determinant morphism for specific co-Higgs bundles.

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.

A generalized Baumslag-Solitar (GBS) group is a finitely generated group acting on a tree with infinite cyclic edge and vertex stabilizers. We show how to determine effectively the rank (minimal cardinality of a generating set) of a GBS group; as a consequence, one can compute the rank of the mapping torus of a finite …

CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem e…

Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on least-squares data fitting and they do not possess a mechanism for tensor rank dete…

Study on complexity of random polynomials with deterministic spikes, identifying phase transitions.

Researchers study rank two theories with eight supercharges using Lefschetz pencils.

We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when neither the rank nor the noise power is known a-priori. We derive relations between th…

We determine the rank of the fundamental group of those hyperbolic 3-manifolds fibering over the circle whose monodromy is a sufficiently high power of a pseudo-Anosov map. Moreover, we show that any two generating sets with minimal cardinality are Nielsen equivalent.

Given a simple Lie group G of rank 1, we consider compact pseudo-Riemannian manifolds (M,g) of signature (p,q) on which G can act conformally. Precisely, we determine the smallest possible value for the index min(p,q) of the metric. When the index is optimal and G non-exceptional, we prove that the metric must be confo…

Truncated Singular Value Decomposition (SVD) calculates the closest rank-$k$ approximation of a given input matrix. Selecting the appropriate rank $k$ defines a critical model order choice in most applications of SVD. To obtain a principled cut-off criterion for the spectrum, we convert the underlying optimization prob…

Let G(O_S) be an S-arithmetic subgroup of a connected, absolutely almost simple linear algebraic group G over a global function field K. We show that the sum of local ranks of G determines the homological finiteness properties of G(O_S) provided the K-rank of G is 1. This shows that the general upper bound for the fini…

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

This paper develops a method to train compact neural networks with reduced memory and computational costs.

Characterizes Kähler-hyperbolicity of bounded symmetric domains based on rank and genus.

Improved tensor rank learning for CPD models using a generalized hyperbolic prior.

Researchers classify and characterize Bäcklund transformations for hyperbolic Monge-Ampère systems.

Triangulations of R^n have at least tensor rank of determinant simplices.

The trace norm is widely used in multi-task learning as it can discover low-rank structures among tasks in terms of model parameters. Nowadays, with the emerging of big datasets and the popularity of deep learning techniques, tensor trace norms have been used for deep multi-task models. However, existing tensor trace n…

We give various results and applications using the connection $(E,\nabla)$ associated with a $d$-web. Precisely, we exhibit fundamental invariants of the web related to the differential equation of first order which presents the web. They cast some new lights on the connection and its construction, both conceptually an…

We describe the set of possible vector valued side lengths of n-gons in thick Euclidean buildings of rank 2. This set is determined by a finite set of homogeneous linear inequalities, which we call the generalized triangle inequalities. These inequalities are given in terms of the combinatorics of the spherical Coxeter…

It is known that if a classical link group is a free abelian group, then its rank is at most two. It is also known that a $k$-component 2-link group ($k>1$) is not free abelian. In this paper, we give examples of $T^2$-links each of whose link groups is a free abelian group of rank three or four. Concerning the $T^2$-l…

The 2-rank of a compact Lie group $G$ is the maximal possible rank of the elementary 2-subgroup ${\mathbb Z}_{2}\times... {\mathbb Z}_{2}$ of $G$. The study of 2-ranks (and $p$-rank for any prime $p$) of compact Lie groups was initiated in 1953 by A. Borel and J.-P. Serre. Since then the 2-ranks of compact Lie groups h…

By proving precisely which singularity index lists arise from the pair of invariant foliations for a pseudo-Anosov surface homeomorphism, Masur and Smillie determined a Teichmueller flow invariant stratification of the space of quadratic differentials. In this paper we determine an analog to the theorem for $Out(F_3)$.…

Proposes a method to infer ranking properties and top-K rankings with uncertainty quantification.

Bisectors are equidistant hypersurfaces between two points and are basic objects in a metric geometry. They play an important part in understanding the action of subgroups of isometries on a metric space. In many metric geometries (spherical, Euclidean, hyperbolic, complex hyperbolic, to name a few) bisectors do not un…

We develop a general theory for the goodness-of-fit test to non-linear models. In particular, we assume that the observations are noisy samples of a submanifold defined by a \yao{sufficiently smooth non-linear map}. The observation noise is additive Gaussian. Our main result shows that the "residual" of the model fit, …

Matrix rank minimizing subject to affine constraints arises in many application areas, ranging from signal processing to machine learning. Nuclear norm is a convex relaxation for this problem which can recover the rank exactly under some restricted and theoretically interesting conditions. However, for many real-world …

Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the nuclear norm, and thus the rank may not be well approximated in practical problems. …

New tools compute index of symmetry in homogeneous fibrations.

Fix an integer m and a multi-index p = (p_1, ..., p_r) of integers p_i < m-2. The set of links of codimension > 2, with multi-index p, E(p, m), is the set of smooth isotopy classes of smooth embeddings of the disjoint union of the p_i-spheres into the m-sphere. Haefliger showed that E(p, m) is a finitely generated abel…

Physics-inspired methods optimize SVD compression of LLMs.

We study the Jacobi osculating rank of geodesics on naturally reductive homogeneous manifolds and we apply this theory to the 3-dimensional case. Here, each non-symmetric, simply connected naturally reductive 3-manifold can be given as a principal bundle over a surface of constant curvature, such that the curvature of …

This paper studies the problem of adaptively sampling from K distributions (arms) in order to identify the largest gap between any two adjacent means. We call this the MaxGap-bandit problem. This problem arises naturally in approximate ranking, noisy sorting, outlier detection, and top-arm identification in bandits. Th…

Study optimal reward schemes for inducing desired player performance in risky contests.

Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of methods have been developed for this recovery problem. However, a principled meth…

We prove that the group-homological version of the generalized Goncharov invariant of finite-volume locally rank one symmetric spaces determines their generalized Neumann-Yang invariant, which is defined using ideal fundamental cycles.

The paper addresses privacy in rank aggregation using randomized responses.

Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we aim to approximate the unknown rank based on the location of sampled entries an…

Paper identifies tensor ranks via prior predictive matching, solving system of equations.

The paper examines how gradient descent stabilizes low-rank matrix factorization in noisy conditions.

Training features used to analyse physical processes are often highly correlated and determining which ones are most important for the classification is a non-trivial tasks. For the use case of a search for a top-quark pair produced in association with a Higgs boson decaying to bottom-quarks at the LHC, we compare feat…

The problem of recovering a low $n$-rank tensor is an extension of sparse recovery problem from the low dimensional space (matrix space) to the high dimensional space (tensor space) and has many applications in computer vision and graphics such as image inpainting and video inpainting. In this paper, we consider a new …

MARS automatically selects tensor decomposition ranks, improving performance in neural network tasks.

New approach to handle ranking function variation in zero-shot NAS.