A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Analytic torsion matches Ray-Singer for specific nilmanifolds.
Analytic torsion defined for rank 2 distributions on 5-manifolds.
There are two different approaches to exhibit submaximal symmetric rank 2 distributions in 5D via Monge equations. In this note we establish precise relations between these models, find auto-equivalences of one family, and treat two special equations.
The paper designs tests for comparing ranked preference data and finds significant differences.
In 1910 E. Cartan constructed the canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions on a 5-dimensional manifold. We solve the analogous problems for rank 2 distributions on an n-dimensional manifold for arbitrary n greater than 5. Our method is a kind of symplectification…
The paper analyzes tensor recovery from symmetric rank-one measurements using information theory.
We demonstrate how the novel approach to the local geometry of structures of nonholonomic nature, originated by Andrei Agrachev, works in the following two situations: rank 2 distributions of maximal class in R^n with non-zero generalized Wilczynski invariants and rank 2 distributions of maximal class in R^n with addit…
We consider the question whether an orientable 5-manifold can be equipped with a rank two distribution of Cartan type and what 2-plane bundles can be realized. We obtain a complete answer for open manifolds. In the closed case, we settle the topological part of this problem and present partial results concerning its ge…
New gossip algorithms improve robustness of rank-based statistics in decentralized systems.
New methods provide stable ranking without assumptions on data distributions.
RCPO uses ranked choice modeling for better LLM alignment.
To certain types of generic distributions (subbundles in a tangent bundle) one can associate canonical Cartan connections. Many of these constructions fall into the class of parabolic geometries. The aim of this article is to show how strong restrictions on the possibles sizes of automorphism groups of such distributio…
Efficiently reduces tensor ranks using mean-field approximation.
Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of objects scales factorially in . One recent way that has been used to reduce storage complexity has been to exploit probabilistic independence, but as we argue, full independence assumptions impo…
In this paper we derive the maximum entropy characteristics of a particular rank order distribution, namely the discrete generalized beta distribution, which has recently been observed to be extremely useful in modelling many several rank-size distributions from different context in Arts and Sciences, as a two-paramete…
For a generic distribution of rank two on a manifold of dimension five, we introduce the notion of a generalized contact form. To such a form we associate a generalized Reeb field and a partial connection. From these data, we explicitly constructed a pseudo--Riemannian metric on of split signature. We prove tha…
Framework for optimizing search engine rankings using observational data.
Novel method for efficient low-rank matrix estimation and bandit algorithms.
Study symplectification of rank 2 distributions and their connections.
Paper develops inference methods for low-rank tensors without debiasing.
We consider the problem of search through comparisons, where a user is presented with two candidate objects and reveals which is closer to her intended target. We study adaptive strategies for finding the target, that require knowledge of rank relationships but not actual distances between objects. We propose a new str…
Improves CRRR for better mobility analysis with DCTM.
Enhances labels from unlabeled data using sample correlations.
We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical counterparts, our method promotes couplings with low transport rank, a new struct…
We give a description of Nurowski's conformal structure for some examples of bracket-generating rank 2 distributions in dimension 5, aka -distributions, namely the An-Nurowski circle twistor distribution for pairs of surfaces of constant Gauss curvature rolling without slipping or twisting over each other. In …
New method for summarizing ranking distributions using consensus ranking distributions.
Estimates low-rank distributional matrices from incomplete samples.
New insights into compact rank-one ECS manifolds, proving they are bundles over circles.
Rank-statistic method approximates -divergences without density-ratio estimation.
Analytic proof for minimal rank Sard conjecture.
New method tests independence using ROC analysis and bipartite ranking.
New method for robust PCA with exponential family distributions.
Recently, the \textit{Tensor Nuclear Norm~(TNN)} regularization based on t-SVD has been widely used in various low tubal-rank tensor recovery tasks. However, these models usually require smooth change of data along the third dimension to ensure their low rank structures. In this paper, we propose a new definition of da…
This paper investigates the rank distribution, cumulative probability, and probability density of price returns for the stocks traded in the KSE and the KOSDAQ market. This research demonstrates that the rank distribution is consistent approximately with the Zipf's law with exponent (KSE) and -1.31 (KOSDAQ),…
We construct canonical frames and find all maximally symmetric models for a natural generic class of corank 2 distributions on manifolds of odd dimension greater or equal to 7. This class of distributions is characterized by the following two conditions: the pencil of 2-forms associated with the corresponding Pfaffian …
New ranking system balances fairness and user utility.
The paper presents two schemes for sampling matrices from specific distributions on a manifold.
Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points plays an important role. Up to now, these two problems have always been conside…
A novel regularizer of the PARAFAC decomposition factors capturing the tensor's rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor completion method incorporates prior information to enhance its smoothing and predictio…
Convex PCA improves Euclidean PCA for convex data subsets.
New method for initializing low-rank neural networks improves performance.
We consider a problem of equivalence of generic pairs on a manifold , where is a distribution of rank and is a distribution of rank one. We construct a canonical bundle with a canonical frame. We prove that two pairs are equivalent if and only if the corresponding frames are diffeomorphic. As a p…
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 …
Paper studies model stealing for low-rank language models.
The notion of curvature discussed in this paper is a far going generalization of the Riemannian sectional curvature. It was first introduced by Agrachev, Barilari and Rizzi in arXiv:1306.5318, and it is defined for a wide class of optimal control problems: a unified framework including geometric structures such as Riem…
The paper improves recommendation systems by ensuring their outputs are reliable.
Proves Sard conjecture for specific distributions, controlling divergence of vector fields.
The paper improves spectral ranking methods for diverse comparison graphs.