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Mathematical equivalence between statistical mechanics and machine learning theory has been known since the 20th century, and research based on this equivalence has provided novel methodologies in both theoretical physics and statistical learning theory.
C. Shannon, A mathematical theory of communication, The Bell system technical journal
1948
Earlier work this paper cites.
E. Hewitt and L. Savage, Symmetric measures on cartesian products, Transactions of the American Mathematical Society
1955
Earlier work this paper cites.
L. Brillouin, Science and Information theory
1956
Earlier work this paper cites.
E. Jaynes, Information theory and statistical mechanics, Physical review
1957
Earlier work this paper cites.
R. Landauer, Irreversibility and heat generation in the computing process, IBM journal of research and development
1961
Earlier work this paper cites.
H. Araki, Von neumann algebras of local observables for free scalar field, Journal of Mathematical Physics
1964
Earlier work this paper cites.
H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero: I, Annals of Mathematics
1964
Earlier work this paper cites.
I. Gel’fand and G. Shilov, Generalized functions
1964
Earlier work this paper cites.
I. Good, Speculations concerning the first ultraintelligent machine, Advances in computers
1966
Earlier work this paper cites.
H. Araki and E. Woods, A classification of factors, Publications of the Research Institute for Mathematical Sciences, Kyoto University. Ser. A
1968
Earlier work this paper cites.
M. Atiyah, Resolution of singularities and division of distributions, Communications on pure and applied mathematics
1970
Earlier work this paper cites.
J. Bernstein, Modules over a ring of differential operators. study of the fundamental solutions of equations with constant coefficients, Funktsional’nyi Analiz i ego Prilozheniya
1971
Earlier work this paper cites.
M. Sato and T. Shintani, On zeta functions associated with prehomogeneous vector spaces, Proceedings of the National Academy of Sciences
1972
Earlier work this paper cites.
C. Bennett, Logical reversibility of computation, IBM journal of Research and Development
1973
Earlier work this paper cites.
H. Araki, On the equivalence of the kms condition and the variational principle for quantum lattice systems, Communications in Mathematical Physics
1974
Earlier work this paper cites.
H. Akaike, A new look at the statistical model identification, IEEE Transactions on Automatic Control
1974
Earlier work this paper cites.
S. Edwards and P. Anderson, Theory of spin glasses, Journal of Physics F: Metal Physics
1975
Earlier work this paper cites.
D. Sherrington and S. Kirkpatrick, Solvable model of a spin-glass, Physical review letters
1975
Earlier work this paper cites.
G. Box, Science and statistics, Journal of the American Statistical Association
1976
Earlier work this paper cites.
M. Kashiwara, B-functions and holonomic systems, Inventiones mathematicae
1976
Earlier work this paper cites.
G. Schwarz, Estimating the dimension of a model, The annals of statistics
1978
Earlier work this paper cites.
G. Parisi, The order parameter for spin glasses: a function on the interval 0-1, Journal of Physics A: Mathematical and General
1980
Earlier work this paper cites.
J. Hopfield, Neural networks and physical systems with emergent collective computational abilities., Proceedings of the national academy of sciences
1982
Earlier work this paper cites.
J. Hartigan, A failure of likelihood asymptotics for normal mixtures, Proceedings of the Barkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, 1985
1985
Earlier work this paper cites.
M. Mézard, G. Parisi and M. Virasoro, Spin glass theory and beyond: An Introduction to the Replica Method and Its Applications
1987
Earlier work this paper cites.
E. Levin, N. Tishby and S. Solla, A statistical approach to learning and generalization in layered neural networks, Proceedings of the IEEE
1990
Earlier work this paper cites.
S. Amari, N. Fujita and S. Shinomoto, Four types of leaning curves, Neural Computation
1992
Earlier work this paper cites.
A. Gelfand, D. Dey and H. Chang, Model determination using predictive distributions with implementation via sampling-based methods, Bayesian statistics
1992
Earlier work this paper cites.
K. Hagiwara, N. Toda and S. Usui, On the problem of applying aic to determine the structure of a layered feedforward neural network, Proceedings of 1993 International Conference on Neural Networks (IJCNN-93-Nagoya, Japan)
1993
Cited alongside, same era.
S. Amari and N. Murata, Statistical theory of learning curves under entropic loss criterion, Neural Computation
1993
Cited alongside, same era.
N. Murata, S. Yoshizawa and S. Amari, Network information criterion-determining the number of hidden units for an artificial neural network model, IEEE transactions on neural networks
1994
Cited alongside, same era.
K. Fukumizu, A regularity condition of the information matrix of a multilayer perceptron network, Neural networks
1996
Cited alongside, same era.
J. Kollár, Singularities of pairs, Proceedings of Symposia in Pure Mathematics
1997
A. Gelman, J. Hwang and A. Vehtari, Understanding predictive information criteria for bayesian models, Statistics and computing
2014
Later among the works it cites.
K. Binmore, On the foundations of decision theory, Homo Oeconomicus
2017
Later among the works it cites.
N. Hayashi and S. Watanabe, Upper bound of bayesian generalization error in non-negative matrix factorization, Neurocomputing
2017
Later among the works it cites.
M. Drton and M. Plummer, A bayesian information criterion for singular models, Journal of the Royal Statistical Society Series B: Statistical Methodology
2017
Later among the works it cites.
A. Vehtari, A. Gelman and J. Gabry, Practical bayesian model evaluation using leave-one-out cross-validation and waic, Statistics and computing
2017
Later among the works it cites.
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Cited alongside, same era.
M. Peruggia, On the variability of case-deletion importance sampling weights in the bayesian linear model, Journal of the American Statistical Association
1997
Cited alongside, same era.
M. Talagrand, Replica symmetry breaking and exponential inequalities for the sherrington-kirkpatrick model, The Annals of Probability
2000
Cited alongside, same era.
S. Watanabe, Algebraic information geometry for learning machines with singularities, Advances in neural information processing systems
2000
Cited alongside, same era.
S. Watanabe, Learning efficiency of redundant neural networks in bayesian estimation, IEEE Transactions on Neural Networks
2001
Cited alongside, same era.
S. Watanabe, Algebraic geometrical methods for hierarchical learning machines, Neural Networks
2001
Cited alongside, same era.
D. Spiegelhalter, N. Best, B. Carlin and A. D. Linde, Bayesian measures of model complexity and fit, Journal of the royal statistical society: Series b (statistical methodology)
2002
Cited alongside, same era.
A. Vehtari and J. Lampinen, Bayesian model assessment and comparison using cross-validation predictive densities, Neural computation
2002
Cited alongside, same era.
S. Watanabe, Mathematical theory of Bayesian statistics
2018
Later among the works it cites.
S. Nakajima, K. Watanabe and M. Sugiyama, Variational Bayesian learning theory
2019
Later among the works it cites.
2019
Later among the works it cites.
R. McElreath, Statistical rethinking: A Bayesian course with examples in R and Stan
2020
Later among the works it cites.
N. Hayashi, The exact asymptotic form of bayesian generalization error in latent dirichlet allocation, Neural Networks
2021
Later among the works it cites.
S. Watanabe, Waic and wbic for mixture models, Behaviormetrika
2021
Later among the works it cites.
S. Watanabe, Information criteria and cross validation for bayesian inference in regular and singular cases, Japanese Journal of Statistics and Data Science
2021
Later among the works it cites.
N. Kariya and S. Watanabe, Asymptotic analysis of singular likelihood ratio of normal mixture by bayesian learning theory for testing homogeneity, Communications in Statistics-Theory and Methods
2022
Later among the works it cites.
S. Watanabe, Mathematical theory of bayesian statistics for unknown information source, Philosophical Transactions of the Royal Society A
2022
Later among the works it cites.
S. Wei, D. Murfet, M. Gong, H. Li, J. Gell-Redman and T. Quella, Deep learning is singular, and that’s good, IEEE Transactions on Neural Networks and Learning Systems
2022
Later among the works it cites.
S. Nagayasu and S. Watanbe, Asymptotic behavior of free energy when optimal probability distribution is not unique, Neurocomputing
2022
Later among the works it cites.
2022
Later among the works it cites.
Y. Iba and K. Yano, Posterior covariance information criterion for weighted inference, Neural computation
2023
Later among the works it cites.
A. Okuno and K. Yano, A generalization gap estimation for overparameterized models via the langevin functional variance, Journal of Computational and Graphical Statistics
2023
Later among the works it cites.
2023
Later among the works it cites.
M. Aoyagi, Consideration on the learning efficiency of multiple-layered neural networks with linear units, Neural Networks
2024
Closest in time.
S. Nagayasu and S. Watanabe, Free energy of bayesian convolutional neural network with skip connection, Proceedings of Asian Conference on Machine Learning
2024
Closest in time.
2024
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L. Bereska and E. Gavves, Mechanistic interpretability for ai safety–a review, arXiv preprint
2024
Closest in time.
2024
Closest in time.
2024
Closest in time.
G. Wang, J. Hoogland, S. van Wingerden, Z. Furman and D. Murfet, Differentiation and specialization of attention heads via the refined local learning coefficient, The Thirteenth International Conference on Learning Representations
2025
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