no code implementations • 7 Feb 2024 • Josh Alman, Zhao Song
Large language models (LLMs) have made fundamental contributions over the last a few years.
no code implementations • 6 Oct 2023 • Josh Alman, Zhao Song
Interestingly, the higher the order of the tensors, the lower the bound on the entries needs to be for an efficient algorithm.
no code implementations • 23 Nov 2020 • Josh Alman, Timothy Chu, Gary Miller, Shyam Narayanan, Mark Sellke, Zhao Song
This completes the theory of Manhattan to Manhattan metric transforms initiated by Assouad in 1980.
no code implementations • 4 Nov 2020 • Josh Alman, Timothy Chu, Aaron Schild, Zhao Song
We investigate whether or not it is possible to solve the following problems in $n^{1+o(1)}$ time for a $\mathsf{K}$-graph $G_P$ when $d < n^{o(1)}$: $\bullet$ Multiply a given vector by the adjacency matrix or Laplacian matrix of $G_P$ $\bullet$ Find a spectral sparsifier of $G_P$ $\bullet$ Solve a Laplacian system in $G_P$'s Laplacian matrix For each of these problems, we consider all functions of the form $\mathsf{K}(u, v) = f(\|u-v\|_2^2)$ for a function $f:\mathbb{R} \rightarrow \mathbb{R}$.