9 papers
Subzero matrix completion for sparse data analysis: large-scale learning of latent low-rank structure
Lawrence K. Saul, Ningyuan Huang, Dennis Bollweg +2
We investigate when a sparse nonnegative matrix can be recovered from a real-valued matrix of much lower rank by zeroing out its negative elements. The potential for such decomposi…
A recursive butterfly factorization with optimality guarantees
David Persson, Paul G. Beckman, Tyler Chen +2
We formalize a recursive format for representing a butterfly matrix. This new format naturally leads to a simple recursive algorithm for computing a quasi-optimal butterfly approxi…
A zero-one law for one-shot system identification
Nicolas Boullé, Diana Halikias, Samuel E. Otto +1
Can a model be identified from one experiment? We study analytic systems that are linearly parameterized by a combination of prescribed dictionary terms, such as partial differenti…
Transpose-free linear algebra
Diana Halikias, Michiel E. Hochstenbach, Alex Townsend
We study the limitations of matrix-free algorithms that access a matrix only through forward matrix-vector products (matvecs) , without access to the transpose $A…
Attention Mechanisms Through the Lens of Numerical Methods: Approximation Methods and Alternative Formulations
Michel Fabrice Serret, Alice Cortinovis, Yijun Dong +10
The attention mechanism is the computational core of modern Transformer architectures, but its quadratic complexity in the input sequence length is the bottleneck for large-scale i…
Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop
Noah Amsel, Yves Baumann, Paul Beckman +36
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the w…