The Eigenvalues of Mega-dimensional Matrices
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The one-dimensional integral in Equation 38 can be computed with numerical ODE solvers and the Skilling-Hutchinson trace estimator.
“One can compute the one-dimensional integral above with numerical ODE solvers and the Skilling-Hutchinson trace estimator [97,217].”
From Diffusion Models: A Comprehensive Survey of Methods and Applications (2024) · cites this paper as [217]
Cites
Maximum entropy in the problem of moments
Mead, L. R., & Papanicolaou, N. I. (1984) · Journal of Mathematical Physics · doi:10.1063/1.526446 · Cited by 585 · see citing works
Approximate solution of Fredholm integral equations by the maximum-entropy method
Mead, L. R. (1986) · Journal of Mathematical Physics · doi:10.1063/1.527267 · Cited by 121 · see citing works
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A practical Bayesian framework for backpropagation networks
MacKay, D. J. C. (1992) · Neural Computation · doi:10.1162/neco.1992.4.3.448 · Cited by 2,917 · see citing works
Score-Based Generative Modeling through Stochastic Differential Equations
Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., & Poole, B. (2020) · arXiv · doi:10.48550/arxiv.2011.13456 · Cited by 1,953 · see citing works
Diffusion Models: A Comprehensive Survey of Methods and Applications
Yang, L., Zhang, Z., Song, Y., Hong, S., Xu, R., Zhao, Y., Zhang, W., Cui, B., & Yang, M.-H. (2024) · ACM Computing Surveys · doi:10.1145/3626235 · Cited by 1,704 · see citing works
- Authors
- Skilling, J.
- Affiliations
- University of Cambridge (GB)
- Corresponding author
- Skilling, John
- ORCID
- Skilling, John
- Venue
- Maximum Entropy and Bayesian Methods
- Publisher
- Springer Netherlands
- Published
- 1989
- Pages
- 455-466
- OpenAlex
- W1552154247
- Cited by
- 66
- References
- 2
- Citations by year
- 2026: 3 · 2025: 5 · 2024: 4 · 2023: 6 · 2022: 2 · 2021: 10 · 2020: 7 · 2019: 3 · 2018: 2 · 2012: 2
- FWCI
- 12.74
- Type
- book chapter
- Language
- en
- Open access
- closed
- Locations
- Springer eBooks (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Mathematics › Statistics and Probability › Random Matrices and Applications
- Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
- Keywords
- matrix-vector multiplication, maximum entropy, determinants, Hamiltonian eigenvalues, specific heat
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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