4 citations · 11 across the 16 of their papers we have counts for
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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…
Randomized time stepping of nonlinearly parametrized solutions of evolution problems
Yijun Dong, Paul Schwerdtner, Benjamin Peherstorfer
The Dirac-Frenkel variational principle is a widely used building block for using nonlinear parametrizations in the context of model reduction and numerically solving partial diffe…
Adaptive Parallelizable Algorithms for Interpolative Decompositions via Partially Pivoted LU
Katherine J. Pearce, Chao Chen, Yijun Dong +1
Interpolative and CUR decompositions involve "natural bases" of row and column subsets, or skeletons, of a given matrix that approximately span its row and column spaces. These low…
Robust Blockwise Random Pivoting: Fast and Accurate Adaptive Interpolative Decomposition
Yijun Dong, Chao Chen, Per-Gunnar Martinsson +1
The interpolative decomposition (ID) aims to construct a low-rank approximation formed by a basis consisting of row/column skeletons in the original matrix and a corresponding inte…
Efficient Bounds and Estimates for Canonical Angles in Randomized Subspace Approximations
Yijun Dong, Per-Gunnar Martinsson, Yuji Nakatsukasa
Randomized subspace approximation with "matrix sketching" is an effective approach for constructing approximate partial singular value decompositions (SVDs) of large matrices. The…
Simpler is better: A comparative study of randomized algorithms for computing the CUR decomposition
Yijun Dong, Per-Gunnar Martinsson
The CUR decomposition is a technique for low-rank approximation that selects small subsets of the columns and rows of a given matrix to use as bases for its column and rowspaces. I…