A framework maps Boltzmann-weighted lattice configurations to correlated random matrix ensembles via real-space to momentum-space variance profiles, deriving spectral moments and resolvent densities benchmarked on Ising and Edwards-Anderson models.
arXiv preprint 2306.12418 (2023)
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Nyström's method always yields higher-accuracy leading eigenvalues than Rayleigh-Ritz for positive semi-definite matrices given a subspace approximation, with improvements that can be arbitrarily large.
CSULoRA decomposes LoRA updates into fully aligned, partially aligned, and off-subspace components and solves a closed-form penalized minimum-change problem to preserve safe parts while attenuating unsafe directions.
Accelerates the power method for extracting top principal components using fast sketching and regularized spectral approximation for stronger low-rank guarantees.
The filter echo generalizes diffusion echoes for visualizing nonlinear filters beyond adaptive smoothing and adds a compression method that cuts storage needs by a factor of 20 to 100.
Randomized subspace iteration improves low-rank approximation quality over randomized SVD for pretrained models by using power iterations to enhance spectral separation, preserving predictive accuracy better under aggressive compression.
Direct SVD solves coupled decompositions; randomized versions with novel balanced subspace selection improve efficiency and apply to face recognition.
citing papers explorer
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Random Matrix Spectra from Boltzmann-Weighted Lattice Ensembles
A framework maps Boltzmann-weighted lattice configurations to correlated random matrix ensembles via real-space to momentum-space variance profiles, deriving spectral moments and resolvent densities benchmarked on Ising and Edwards-Anderson models.
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Finding accurate eigenvalues and eigenvectors of positive semi-definite matrices given a subspace
Nyström's method always yields higher-accuracy leading eigenvalues than Rayleigh-Ritz for positive semi-definite matrices given a subspace approximation, with improvements that can be arbitrarily large.
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CSULoRA: Closest Safe Update Low-Rank Adaptation
CSULoRA decomposes LoRA updates into fully aligned, partially aligned, and off-subspace components and solves a closed-form penalized minimum-change problem to preserve safe parts while attenuating unsafe directions.
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Accelerating Power Method with Fast Sketching for Stronger Low-Rank Approximation
Accelerates the power method for extracting top principal components using fast sketching and regularized spectral approximation for stronger low-rank guarantees.
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The Filter Echo: A General Tool for Filter Visualisation
The filter echo generalizes diffusion echoes for visualizing nonlinear filters beyond adaptive smoothing and adds a compression method that cuts storage needs by a factor of 20 to 100.
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Low-Rank Compression of Pretrained Models via Randomized Subspace Iteration
Randomized subspace iteration improves low-rank approximation quality over randomized SVD for pretrained models by using power iterations to enhance spectral separation, preserving predictive accuracy better under aggressive compression.
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Randomized coupled decompositions
Direct SVD solves coupled decompositions; randomized versions with novel balanced subspace selection improve efficiency and apply to face recognition.
- Fast and accurate conditioning for large-scale and online Gaussian process prediction problems