Related papers: Vector Fitting for Matrix-valued Rational Approxim…
Mapping UV theories onto low energy effective descriptions is a procedure known as matching. The last decade has seen tremendous progress in the development of new tools for efficiently performing matching calculations, by relying on…
This study identifies that visual-related functional decoding is distributed across different decoder layers in Multimodal Large Language Models (MLLMs). Typically, each function, such as counting, grounding, or OCR recognition, narrows…
Rank minimization can be converted into tractable surrogate problems, such as Nuclear Norm Minimization (NNM) and Weighted NNM (WNNM). The problems related to NNM, or WNNM, can be solved iteratively by applying a closed-form proximal…
Many large MDPs can be represented compactly using a dynamic Bayesian network. Although the structure of the value function does not retain the structure of the process, recent work has shown that value functions in factored MDPs can often…
Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…
Fitting distances to tree metrics and ultrametrics are two widely used methods in hierarchical clustering, primarily explored within the context of numerical taxonomy. Given a positive distance function…
Over the past decade, various matrix completion algorithms have been developed. Thresholded singular value decomposition (SVD) is a popular technique in implementing many of them. A sizable number of studies have shown its theoretical and…
Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…
Many past works aim to improve visual reasoning in models by supervising feature importance (estimated by model explanation techniques) with human annotations such as highlights of important image regions. However, recent work has shown…
In this paper, we address the problem of convergence of sequential variational inference filter (VIF) through the application of a robust variational objective and Hinf-norm based correction for a linear Gaussian system. As the dimension of…
Steering vectors (SVs) offer a lightweight way to control large language models (LLMs) at inference time by shifting hidden activations, providing a practical middle ground between prompting and fine-tuning. Yet SVs can be unreliable in…
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…
Bi-level optimization model is able to capture a wide range of complex learning tasks with practical interest. Due to the witnessed efficiency in solving bi-level programs, gradient-based methods have gained popularity in the machine…
We consider the approximation of manifold-valued functions by embedding the manifold into a higher dimensional space, applying a vector-valued approximation operator and projecting the resulting vector back to the manifold. It is well known…
Determining the number of factors is essential to factor analysis. In this paper, we propose {an efficient cross validation (CV)} method to determine the number of factors in approximate factor models. The method applies CV twice, first…
We present an approximation scheme for support vector machine models that use an RBF kernel. A second-order Maclaurin series approximation is used for exponentials of inner products between support vectors and test instances. The…
Approximating a manifold-valued function from samples of input-output pairs consists of modeling the relationship between an input from a vector space and an output on a Riemannian manifold. We propose a function approximation method that…
Functional approximation as a high-order continuous representation provides a more accurate value and gradient query compared to the traditional discrete volume representation. Volume visualization directly rendered from functional…
The valence force field (VFF) model is a concise physical interpretation of the atomic interaction in terms of the bond and angle variations in the explicit quadratic functional form, while the machine learning (ML) method is a flexible…
Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data,…