arXiv research

DM2L tackles missing labels in multi-label learning by modeling local and global rank structures.

The paper proposes using low rank assumption to improve causal structure learning in DAGs.

Study the rank of Nijenhuis tensor on parallelizable almost complex manifolds.

Paper introduces a novel framework for recognizing dynamic ranking structures in preference-based data.

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

Research reveals deep networks often learn low-rank structures, leading to more efficient training and fine-tuning.

Derives smooth homogeneous structures for low-rank tensors.

New methods rank players using covariates and comparisons, outperforming existing algorithms.

We prove the $C^{1}$ regularity for a class of abnormal length-minimizers in rank $2$ sub-Riemannian structures. As a consequence of our result, all length-minimizers for rank $2$ sub-Riemannian structures of step up to $4$ are of class $C^{1}$.

We prove that there does not exist any real hypersurface in complex Grassmannians of rank two with semi-parallel structure Jacobi operator. With this result, the nonexistence of real hypersurface in complex Grassmannians of rank two with recurrent structure Jacobi operator is proved.

Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as smoothness, sparsity, or probabilistic independence about these underlying distri…

The paper addresses calibration in label ranking, a structured prediction task.

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

Analyzes the structure and rank of neural network Hessians.

Algorithm recovers multiple low-rank matrices from unlabeled data.

We introduce a new framework for optimal transport using Schatten-p regularization to recover low-rank structures.

We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming that the underlying matrix has low rank, or is well-approximated by a low rank matr…

Generalizes Dolbeault cohomology computation to Levi-flat CR structures on compact Lie groups.

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

We propose to solve a label ranking problem as a structured output regression task. We adopt a least square surrogate loss approach that solves a supervised learning problem in two steps: the regression step in a well-chosen feature space and the pre-image step. We use specific feature maps/embeddings for ranking data,…

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

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…

In recent years, a class of dictionaries have been proposed for multidimensional (tensor) data representation that exploit the structure of tensor data by imposing a Kronecker structure on the dictionary underlying the data. In this work, a novel algorithm called "STARK" is provided to learn Kronecker structured dictio…

A new kernel for ranked data tackles computational challenges.

New spectral methods improve matrix estimation in RL with low-rank structure.

Estimates low-rank distributional matrices from incomplete samples.

Reduced-rank method improves least-squares regression under output regularity.

Paper improves MVSC using tensor low-rank modeling.

The paper tackles pure exploration in multi-armed bandits with low rank structure using oblivious sampling.

New method for summarizing ranking distributions using consensus ranking distributions.

Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation methods, such as Tucker or CP decomposition, result in degraded model accuracy becau…

The paper defines a new connection on sub-Riemannian manifolds and explores conditions for almost quasi-Sasakian manifolds to be Einstein.

Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from sparse PCA, the dominant eigenvectors are allowed to be dense but are assumed to have a low-rank structure when matricized appropriately. Such a…

Proposes GTTN for discovering all low-rank structures in deep multi-task learning.

We use group homology to define invariants in algebraic K-theory and in an analogue of the Bloch group for Q-rank one lattices and for some other geometric structures. We also show that the Bloch invariants of CR structures and of flag structures can be recovered by a fundamental class construction.

Study on almost complex structures with maximal Nijenhuis tensor rank and cohomological properties.

Paper classifies structures on 5D manifolds with specific rank and conditions.

Affine maps reveal higher rank structures in certain spaces.

We show that generalized broken fibrations in arbitrary dimensions admit rank-2 Poisson structures compatible with the fibration structure. After extending the notion of wrinkled fibration to dimension 6 we prove that these wrinkled fibrations also admit compatible rank-2 Poisson structures. In the cases with indefinit…

New method interprets ranked data on permutahedron graph.

Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric $A$ as $L^TL$, the problem can be cast as looking for a linear map between two …

Sasakian structures found on tangent sphere bundles of certain symmetric spaces.

We present old and recent results on rank problems and linearizability of geodesic planar webs.

New invariant real rank identifies constant real Lie algebroids.

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

Bayesian model improves image completion accuracy by automatically learning low rank structure.

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…

Many latent (factorized) models have been proposed for recommendation tasks like collaborative filtering and for ranking tasks like document or image retrieval and annotation. Common to all those methods is that during inference the items are scored independently by their similarity to the query in the latent embedding…