8 papers
Nyström method for symmetric indefinite matrices
Yijia Chen, Yuji Nakatsukasa, Anjali Narendran +1
The Nyström method approximates , where is a column subset ma…
Approximating Sparse Matrices and their Functions using Matrix-vector products
Taejun Park, Yuji Nakatsukasa
The computation of a matrix function is an important task in scientific computing appearing in machine learning, network analysis and the solution of partial differential eq…
Fast, High-Accuracy, Randomized Nullspace Computations for Tall Matrices
Ethan N. Epperly, Taejun Park, Yuji Nakatsukasa
In this paper, we develop RLOBPCG, an efficient method for computing a small number of singular triplets corresponding to the smallest singular values of large, tall matrices. The…
Rewarding How Models Think Pedagogically: Integrating Pedagogical Reasoning and Thinking Rewards for LLMs in Education
Unggi Lee, Jiyeong Bae, Jaehyeon Park +7
Large language models (LLMs) are increasingly deployed as intelligent tutoring systems, yet research on optimizing LLMs specifically for educational contexts remains limited. Recen…
Numerical Stability of the Nyström Method
Alberto Bucci, Yuji Nakatsukasa, Taejun Park
The Nyström method is a widely used technique for improving the scalability of kernel-based algorithms, including kernel ridge regression, spectral clustering, and Gaussian proces…
Fast Rank Adaptive CUR via a Recycled Small Sketch
Nathaniel Pritchard, Taejun Park, Yuji Nakatsukasa +1
The computation of accurate low-rank matrix approximations is central to improving the scalability of various techniques in machine learning, uncertainty quantification, and contro…