5 accepted papers
Computing the polar decomposition and the related matrix sign function has been a well-studied problem in numerical analysis for decades. Recently, it has emerged as an important subroutine within the Muon algorithm for training deep neural networks. However, the requirements of this application di…
It is understood that different neural network architectures are suited to different tasks, but is there always a single best architecture for a given task? We compare the expressive power of transformers, RNNs, and transformers with chain of thought tokens on a simple and natural class of tasks we…
The core component of attention is the scoring function, which transforms the inputs into low-dimensional queries and keys and takes the dot product of each pair. While the low-dimensional projection improves efficiency, it causes information loss for certain tasks that have intrinsically high-dimen…
Attention-based mechanisms are widely used in machine learning, most prominently in transformers. However, hyperparameters such as the number of attention heads and the attention rank (i.e., the query/key dimension) are set nearly the same way in all realizations of this architecture, without theore…
Approximating the action of a matrix function $f(\vec{A})$ on a vector $\vec{b}$ is an increasingly important primitive in machine learning, data science, and statistics, with applications such as sampling high dimensional Gaussians, Gaussian process regression and Bayesian inference, principle comp…