5 citations · 5 across the 2 of their papers we have counts for
5 papers
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…
Quasi-optimal hierarchically semi-separable matrix approximation
Noah Amsel, Tyler Chen, Feyza Duman Keles +4
We present a randomized algorithm for producing a quasi-optimal hierarchically semi-separable (HSS) approximation to an matrix using only matrix-vector products wit…
Arbitrary-Depth Universal Approximation Theorems for Operator Neural Networks
Annan Yu, Chloé Becquey, Diana Halikias +2
The standard Universal Approximation Theorem for operator neural networks (NNs) holds for arbitrary width and bounded depth. Here, we prove that operator NNs of bounded width and a…
Discrete variants of Brunn-Minkowski type inequalities
Diana Halikias, Bo'az Klartag, Boaz A. Slomka
We present an alternative, short proof of a recent discrete version of the Brunn-Minkowski inequality due to Lehec and the second named author. Our proof also yields the four funct…
A Cheeger inequality for graphs based on a reflection principle
Edward Gelernt, Diana Halikias, Charles Kenney +1
Given a graph with a designated set of boundary vertices, we define a new notion of a Neumann Laplace operator on a graph using a reflection principle. We show that the first eigen…