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The Fine-Grained Complexity of Gradient Computation for Training Large Language Models
Large language models (LLMs) have made fundamental contributions over the last a few years.
How to Capture Higher-order Correlations? Generalizing Matrix Softmax Attention to Kronecker Computation
Interestingly, the higher the order of the tensors, the lower the bound on the entries needs to be for an efficient algorithm.
Metric Transforms and Low Rank Matrices via Representation Theory of the Real Hyperrectangle
This completes the theory of Manhattan to Manhattan metric transforms initiated by Assouad in 1980.
Algorithms and Hardness for Linear Algebra on Geometric Graphs
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 $f:\mathbb{R} \rightarrow \mathbb{R}$.
