arXiv research

This paper protects rankings from differential privacy breaches.

Right inverse found for Cartan differential in rank-1 symmetric spaces.

Paper introduces differentiable sorting and ranking with $O(n \log n)$ time complexity.

Differentiable sorting and rank normalization are incompatible, with specific conditions for admissibility.

Optimal privacy-preserving ranking from noisy comparisons.

Any nonpositively curved symmetric space admits a topological compactification, namely the Hadamard compactification. For rank one spaces, this topological compactification can be endowed with a differentiable structure such that the action of the isometry group is differentiable. Moreover, the restriction of the actio…

Geometric families of low-rank covariances improve flexibility and tractability in high dimensions.

New method finds efficient low-rank neural networks during training.

Paper develops DP methods for low-rank matrix estimation with near-optimal performance.

Monotonic differentiable sorting networks improve upon previous methods.

Rank-based metrics are some of the most widely used criteria for performance evaluation of computer vision models. Despite years of effort, direct optimization for these metrics remains a challenge due to their non-differentiable and non-decomposable nature. We present an efficient, theoretically sound, and general met…

CoLoRA models predict PDE solutions quickly and accurately with minimal data.

Diffsurv extends differentiable sorting to handle censored time-to-event data.

This paper improves entropy bounds for ranking time-series complexity.

We provide a novel proof that the set of directions that admit a saddle connection on a meromorphic quadratic differential with at least one pole of order at least two is closed, which generalizes a result of Bridgeland and Smith, and Gaiotto, Moore, and Neitzke. Secondly, we show that this set has finite Cantor-Bendix…

Study the distribution for low-rank matrix learning, improving inference methods.

Several tasks in machine learning are evaluated using non-differentiable metrics such as mean average precision or Spearman correlation. However, their non-differentiability prevents from using them as objective functions in a learning framework. Surrogate and relaxation methods exist but tend to be specific to a given…

Study on affine surfaces with specific algebraic properties.

Researchers classify differential operators between 3-sphere and 2-sphere bundles.

PILNO uses neural operators to solve PDEs efficiently on point clouds.

LR-EDNN reduces PDE solver complexity by limiting network weights to low-rank subspace.

Efficiently samples complex distributions using tensor train format.

In translation surfaces of finite area (corresponding to holomorphic differentials), directions of saddle connections are dense in the unit circle. On the contrary, saddle connections are fewer in translation surfaces with poles (corresponding to meromorphic differentials). The Cantor-Bendixson rank of their set of dir…

Study differential operators and their solutions on manifolds, proving upper bounds and curvature.

Link prediction (LP) algorithms propose to each node a ranked list of nodes that are currently non-neighbors, as the most likely candidates for future linkage. Owing to increasing concerns about privacy, users (nodes) may prefer to keep some of their connections protected or private. Motivated by this observation, our …

We describe Veech groups of flat surfaces arising from irrational angled polygonal billiards or irreducible stable abelian differentials. For irrational polygonal billiards, we prove that these groups are non-discrete subgroups of SO(2,R) and we calculate their rank.

The study characterizes wobbly rank-2 bundles on Riemann surfaces using spectral curves.

A JAX toolbox solves optimal transport problems for point clouds and histograms.

The paper mostly collects material on generic rank of $A$--modules with respect to differential geometric applications. Our research was motivated by geometry of $A$--structures. In particular, we discuss the case where $A$ is an unitary associative algebra not necessary with inversion. Some of the examples are studied…

The paper solves a 25-year-old problem about maximal growth distributions on manifolds.

DP-GD achieves dimension-independent convergence for unconstrained private GLMs.

In this paper, we introduce a novel and robust approach to Quantized Matrix Completion (QMC). First, we propose a rank minimization problem with constraints induced by quantization bounds. Next, we form an unconstrained optimization problem by regularizing the rank function with Huber loss. Huber loss is leveraged to c…

In this present paper, we study geometric structures of rank two prolongations of implicit second-order partial differential equations (PDEs) for two independent and one dependent variables and characterize the type of these PDEs by the topology of fibers of the rank two prolongations. Moreover, by using properties of …

We consider a problem of equivalence of generic pairs $(X,V)$ on a manifold $M$, where $V$ is a distribution of rank $m$ and $X$ 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 extend the validity of a Gromov's dimension comparison estimate for topological hypersurfaces to sufficiently large classes of rectifiable sets, arising from Sobolev mappings. Our tools are a suitably weak exterior differentiation for pullback differential forms and a new low rank property for Sobolev mappings.

Paper extends multivariate rank tests for robust subspace detection.

These are lecture notes of a course on symmetry group analysis of differential equations, based mainly on P. J. Olver's book 'Applications of Lie Groups to Differential Equations'. The course starts out with an introduction to the theory of local transformation groups, based on the Stefan-Sussman theory on the integrab…

Listwise learning-to-rank methods form a powerful class of ranking algorithms that are widely adopted in applications such as information retrieval. These algorithms learn to rank a set of items by optimizing a loss that is a function of the entire set -- as a surrogate to a typically non-differentiable ranking metric.…

We establish a "low rank property" for Sobolev mappings that pointwise solve a first order nonlinear system of PDEs, whose smooth solutions have the so-called "contact property". As a consequence, Sobolev mappings from an open set of the plane, taking values in the first Heisenberg group and that have almost everywhere…

Geometric structures on surfaces relate to 2-plane distributions in 5D.

It is established that the existence of non-isotropic vector field which Jacobi operator of maximal rank is an obstacle for the existence of non-trivial second-order symmetric parallel tensor field. In turns out that presence of such obstacle follows that manifold as pseudo-Riemannian manifold is locally non-reducible.…

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…

New method differentiates square-root Kalman filters robustly.

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

Differentially private graph learning via bounded sensitivity PPR.

High resolution magnetic resonance (MR) images are desired for accurate diagnostics. In practice, image resolution is restricted by factors like hardware, cost and processing constraints. Recently, deep learning methods have been shown to produce compelling state of the art results for image super-resolution. Paying pa…

An isomorphism of symplectically tame smooth pseudocomplex structures on the complex projective plane which is a homeomorphism and differentiable of full rank at two points is smooth.

Study on harmonic metrics for rank 3 Higgs bundles in Hitchin section.