arXiv research

The paper analyzes how low-rank layers in neural networks improve generalization.

Paper introduces GAMs for interpretable learning-to-rank models.

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

We solve linear equations with tensors of any rank.

This paper compares rank aggregation methods for partial label ranking.

This work transfers fairness notions from binary classification to learning to rank.

The paper addresses privacy in rank aggregation using randomized responses.

We consider the problem of learning over non-stationary ranking streams. The rankings can be interpreted as the preferences of a population and the non-stationarity means that the distribution of preferences changes over time. Our goal is to learn, in an online manner, the current distribution of rankings. The bottlene…

The paper establishes theoretical foundations for low-rank knowledge distillation in LLMs.

This paper protects rankings from differential privacy breaches.

Weight Decay induces low-rank weight matrices in neural networks, improving generalization.

Learning to rank is a supervised learning problem where the output space is the space of rankings but the supervision space is the space of relevance scores. We make theoretical contributions to the learning to rank problem both in the online and batch settings. First, we propose a perceptron-like algorithm for learnin…

New bound for neural networks with full-rank weights, independent of network width.

Matrices of (approximate) low rank are pervasive in data science, appearing in recommender systems, movie preferences, topic models, medical records, and genomics. While there is a vast literature on how to exploit low rank structure in these datasets, there is less attention on explaining why the low rank structure ap…

Partial convexification improves tractability of low-rank spectral optimization problems.

In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint. We first establish that a class of special rank minimization problems has closed-form solutions. Using this result, we then propose penalty decomposition methods for general rank minimization pro…

Researchers show mixtures of ranking models are generally identifiable.

GANs improve missing data imputation for ranking tasks.

In domains like bioinformatics, information retrieval and social network analysis, one can find learning tasks where the goal consists of inferring a ranking of objects, conditioned on a particular target object. We present a general kernel framework for learning conditional rankings from various types of relational da…

We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only if it is linearizable and its curvature vanishes. This result leads to the direct web-theoretical proof of the Poincaré's theorem: a planar 4-web of maximum rank is lineari…

Researchers describe the metric structure of compact ECS manifolds.

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

The paper tackles learning true rankings from noisy, incomplete data.

We say that a Riemannian manifold M has rank at least k if every geodesic in M admits at least k parallel Jacobi fields. The Rank Rigidity Theorem of Ballmann and Burns-Spatzier, later generalized by Eberlein-Heber, states that a complete, irreducible, simply connected Riemannian manifold M of rank at least 2 (the high…

Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a non-linear link function used within factorization. In particular, by applying the round …

Whitehead doubles have matching meridional rank and bridge number.

We study the problem of learning to rank from multiple information sources. Though multi-view learning and learning to rank have been studied extensively leading to a wide range of applications, multi-view learning to rank as a synergy of both topics has received little attention. The aim of the paper is to propose a c…

The paper improves transformer generalization bounds using rank-dependent covering number bounds.

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 …

Develops a method to infer partial rankings from sparse comparisons.

Suppose that $X_1, \ldots , X_n$ are continuous semimartingales that are reversible and have nondegenerate crossings. Then the corresponding rank processes can be represented by generalized Stratonovich integrals, and this representation can be used to decompose the relative log-return of portfolios generated by functi…

Language models exhibit low-rank structure, which can be used for generation.

For random elements in free groups, we find a rank and set of subgroups.

IRMAE learns compact latent spaces by minimizing rank.

Unified framework for statistical inference of low-rank tensors.

Study ranking in generalized linear bandits with position and item dependencies.

New insights into risk aversion for complex decision models.

Compact RCD(K,N) spaces with maximal rank are homeomorphic to infranilmanifolds.

New methods recover best rank-r approximations from few entries.

Study on rank-one ECS manifolds, focusing on dilational type.

Paper develops methods for non-quadratic loss low-rank matrix recovery.

In a recent work \cite{BG}, given a collection of continuous semimartingales, authors derive a semimartingale decomposition from the corresponding ranked processes in the case that the ranked processes can meet more than two original processes at the same time. This has led to a more general decomposition of ranked pro…

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

Label ranking aims to learn a mapping from instances to rankings over a finite number of predefined labels. Random forest is a powerful and one of the most successful general-purpose machine learning algorithms of modern times. In this paper, we present a powerful random forest label ranking method which uses random de…

The paper disproves a generalized toral rank conjecture with various counter-examples.

Supervised linear feature extraction can be achieved by fitting a reduced rank multivariate model. This paper studies rank penalized and rank constrained vector generalized linear models. From the perspective of thresholding rules, we build a framework for fitting singular value penalized models and use it for feature …

We prove that any action of a higher rank lattice on a Gromov-hyperbolic space is elementary. More precisely, it is either elliptic or parabolic. This is a large generalization of the fact that any action of a higher rank lattice on a tree has a fixed point. A consequence is that any quasi-action of a higher rank latti…

Improved GoF statistics using entropy-regularized optimal transport for multivariate rank.