arXiv research

Proposes a model for identifying edges in low-rank dynamical networks.

Review of algorithms for linear system approximations.

Study shows dynamics of rank 1 orbifolds in flat surfaces.

We propose a method to infer stochastic low-rank RNNs from neural data.

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

A new learning-to-rank approach ensures fairness for item providers in dynamic ranking systems.

Low-rank structure emerges in neural networks during learning.

The aim of this paper is to study the spectrum of the $L^p$ Laplacian and the dynamics of the $L^p$ heat semigroup on non-compact locally symmetric spaces of higher rank. Our work here generalizes previously obtained results in the setting of locally symmetric spaces of rank one to higher rank spaces. Similarly as in t…

AdaRL improves robust RL by adaptively adjusting policy complexity.

StealthRank subtly boosts LLM rankings without detectable anomalies.

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

A new method reduces high-dimensional filtering to quadratic complexity.

We consider the problem of modeling multivariate time series with parsimonious dynamical models which can be represented as sparse dynamic Bayesian networks with few latent nodes. This structure translates into a sparse plus low rank model. In this paper, we propose a Gaussian regression approach to identify such a mod…

For real hyperbolic spaces, the dynamics of individual isometries and the geometry of the limit set of nonelementary discrete isometry groups have been studied in great detail. Most of the results were generalised to discrete isometry groups of simply connected Riemannian manifolds of pinched negative curvature. For sy…

Optimizes neural network training by dynamically updating Tucker decomposition ranks.

We study infinite covolume discrete subgroups of higher rank semisimple Lie groups, motivated by understanding basic properties of Anosov subgroups from various viewpoints (geometric, coarse geometric and dynamical). The class of Anosov subgroups constitutes a natural generalization of convex cocompact subgroups of ran…

SALT models combine ARHMM and SLDS for efficient, interpretable time-series analysis.

A method for dynamic ranking using BTL model and nearest neighbor rank centrality.

LoRA fine-tuning explained with gradient dynamics for low-rank perturbations.

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank constrained optimisation problem. This problem is non-convex and state-of-the-art algor…

We study the growth of the rank of subgroups of finite index in residually finite groups, by relating it to the notion of cost. As a by-product, we show that the `Rank vs. Heegaard genus' conjecture on hyperbolic 3-manifolds is incompatible with the `Fixed Price problem' in topological dynamics.

Riemannian gradient descent escapes some spurious critical points on low-rank matrix manifold.

AIR-Net adapts low-rank regularization dynamically for better image completion.

New approach uses compressible dynamics to train deep models efficiently.

New algorithm catches moving subspaces in bandit problems.

Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This extension is of particular interest for reduced-order modeling in various applicative …

Active learning method for neural population dynamics using optogenetics.

Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the topology of networks from time-resolved observations of their node-dynamics. The methods based on physical insights often rely on strong assumptions about the proper…

GeLoRA optimizes LoRA fine-tuning by dynamically adjusting ranks based on intrinsic dimensionality.

Proposes a nonparametric model for dynamic team rankings.

Defines foliation criterion for dense isoperiodic leaves in rank 1 affine orbifolds.

We consider dynamic pricing with many products under an evolving but low-dimensional demand model. Assuming the temporal variation in cross-elasticities exhibits low-rank structure based on fixed (latent) features of the products, we show that the revenue maximization problem reduces to an online bandit convex optimiza…

Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by incorporating temporal information and allowing for the possibility of time-varying …

Paper tackles dynamic assortment with dual contexts, improving revenue in e-commerce.

A new ranking model with dynamic covariates improves statistical analysis.

MOSAIC detects change points in dynamic networks with low-rank and sparse changes.

Rank aggregation based on pairwise comparisons over a set of items has a wide range of applications. Although considerable research has been devoted to the development of rank aggregation algorithms, one basic question is how to efficiently collect a large amount of high-quality pairwise comparisons for the ranking pur…

Paper unifies subspace identification and DMD for dynamical systems.

New method identifies network dynamics and noise structure.

Deep ReLU networks escape from the origin via saddle points with a low-rank bias.

Sparsity-based approaches have been popular in many applications in image processing and imaging. Compressed sensing exploits the sparsity of images in a transform domain or dictionary to improve image recovery from undersampled measurements. In the context of inverse problems in dynamic imaging, recent research has de…

LASER compresses recursive model activations by exploiting their low-dimensional structure.

New analysis shows how attention masks and LayerNorm prevent rank collapse in transformers.

Proposes a method to balance fairness and utility in ranking models.

We study the limiting behaviour of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that the limiting dynamics is given by a McKean-Vlasov evolution equation. Moreover, we show that in a wide range of cases the evolution of the cum…

Gradient descent promotes low-rank solutions in tensor completion.

Optimizes wide low-rank neural networks for reduced parameters and cost.

An Atlas model is a rank-based system of continuous semimartingales for which the steady-state values of the processes follow a power law, or Pareto distribution. For a power law, the log-log plot of these steady-state values versus rank is a straight line. Zipf's law is a power law for which the slope of this line is …