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W. Bialek, C. G. Callan, Jr., and S. P. Strong, “Field theories for learning probability distributions,” Phys. Rev. Lett
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J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys
1998
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J. Erdmenger, K. T. Grosvenor, and R. Jefferson, “Information geometry in quantum field theory: lessons from simple examples,” SciPost Phys
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2001
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2003
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Then

J. J. Heckman, “Statistical Inference and String Theory,” Int. J. Mod. Phys. A
Original
2015
Later among the works it cites.
V. Balasubramanian, J. J. Heckman, and A. Maloney, “Relative Entropy and Proximity of Quantum Field Theories,” JHEP
Original
2015
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E. Malek, J. Murugan, and J. P. Shock, “The Information Metric on the moduli space of instantons with global symmetries,” Phys. Lett. B
Original
2016
Later among the works it cites.
J. J. Heckman, J. G. Bernstein, and B. Vigoda, “MCMC with Strings and Branes: The Suburban Algorithm (Extended Version),” Int. J. Mod. Phys. A
Original
2017
Later among the works it cites.
K. Hashimoto, S. Sugishita, A. Tanaka, and A. Tomiya, “Deep Learning and Holographic QCD,” Phys. Rev. D

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2022

On the Dynamics of Inference and Learning

Berman, David S., Heckman, Jonathan J., Klinger, Marc

Understand

Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set.

As more data becomes available this probability distribution becomes updated via the application of Bayes' theorem.
We present a treatment of this Bayesian updating process as a continuous dynamical system.
Statistical inference is then governed by a first order differential equation describing a trajectory or flow in the information geometry determined by a parametric family of models.

Built on

K. Hashimoto, “AdS/CFT correspondence as a deep Boltzmann machine,” Phys. Rev. D
Original
1903
Earlier work this paper cites.
C. R. Rao, “Information and accuracy attainable in the estimation of statistical parameters”,” Bulletin of the Calcutta Mathematical Society
1945
Earlier work this paper cites.
S. Kullback and R. A. Leibler, “On Information and Sufficiency,” The Annals of Mathematical Statistics
1951
Earlier work this paper cites.
M. Gell-Mann and F. E. Low, “Quantum electrodynamics at small distances,” Phys. Rev
1954
Earlier work this paper cites.
L. P. Kadanoff, “Scaling laws for Ising models near T c T_{c} ,” Physics Physique Fizika
1966
Earlier work this paper cites.
K. G. Wilson, “Renormalization group and critical phenomena. 1. Renormalization group and the Kadanoff scaling picture,” Phys. Rev. B
1971
Earlier work this paper cites.
K. G. Wilson, “Renormalization group and critical phenomena. 2. Phase space cell analysis of critical behavior,” Phys. Rev. B
1971
Earlier work this paper cites.
G. Mack, “All unitary ray representations of the conformal group SU(2,2) with positive energy,” Commun. Math. Phys
1977
Earlier work this paper cites.
J. Polchinski, “Renormalization and Effective Lagrangians,” Nucl. Phys. B
1984
Earlier work this paper cites.
Lecture Notes in Statistics. Springer-Verlag, 1985
S. Amari, Differential-Geometrical Methods in Statistics · 1985
Earlier work this paper cites.
W. Bialek, C. G. Callan, Jr., and S. P. Strong, “Field theories for learning probability distributions,” Phys. Rev. Lett
1996
Earlier work this paper cites.

Similar

Lecture Notes in Statistics. Springer-Verlag, 1996
R. Neal, Bayesian Learning for Neural Networks · 1996
Cited alongside, same era.
Butterworth-Heinemann, 1996
R. K. Pathria, Statistical Mechanics · 1996
Cited alongside, same era.
J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys
1998
Cited alongside, same era.
J. Erdmenger, K. T. Grosvenor, and R. Jefferson, “Information geometry in quantum field theory: lessons from simple examples,” SciPost Phys
Original
2001
Cited alongside, same era.
Y. Gal, V. Jejjala, D. K. Mayorga Pena, and C. Mishra, “Baryons from Mesons: A Machine Learning Perspective,” arXiv:2003.10445 [hep-ph]
Original
2003
Cited alongside, same era.

Then

J. J. Heckman, “Statistical Inference and String Theory,” Int. J. Mod. Phys. A
Original
2015
Later among the works it cites.
V. Balasubramanian, J. J. Heckman, and A. Maloney, “Relative Entropy and Proximity of Quantum Field Theories,” JHEP
Original
2015
Later among the works it cites.
E. Malek, J. Murugan, and J. P. Shock, “The Information Metric on the moduli space of instantons with global symmetries,” Phys. Lett. B
Original
2016
Later among the works it cites.
J. J. Heckman, J. G. Bernstein, and B. Vigoda, “MCMC with Strings and Branes: The Suburban Algorithm (Extended Version),” Int. J. Mod. Phys. A
Original
2017
Later among the works it cites.
K. Hashimoto, S. Sugishita, A. Tanaka, and A. Tomiya, “Deep Learning and Holographic QCD,” Phys. Rev. D

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

The MIT Press, 2006

C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning · 2006

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J. Halverson, A. Maiti, and K. Stoner, “Neural Networks and Quantum Field Theory,” Mach. Learn. Sci. Tech

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2008

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H. Dimov, I. N. Iliev, M. Radomirov, R. C. Rashkov, and T. Vetsov, “Holographic Fisher information metric in Schrödinger spacetime,” Eur. Phys. J. Plus

Original

2009

Cited alongside, same era.

U. Miyamoto and S. Yahikozawa, “Information metric from a linear sigma model,” Phys. Rev. E

Original

2012

Cited alongside, same era.

V. Balasubramanian, J. J. Heckman, E. Lipeles, and A. P. Turner, “Statistical Coupling Constants from Hidden Sector Entanglement,” Phys. Rev. D

Original

2012

Cited alongside, same era.

D. P. Kingma and J. Ba, “Adam: A Method for Stochastic Optimization,” arXiv e-prints

Original

2014

Cited alongside, same era.

T. Bayes, Rev., “An essay toward solving a problem in the doctrine of chances,” Phil. Trans. Roy. Soc. Lond

Cited in the paper.

Original

2018

Later among the works it cites.

P. Mehta, M. Bukov, C.-H. Wang, A. G. R. Day, C. Richardson, C. K. Fisher, and D. J. Schwab, “A high-bias, low-variance introduction to Machine Learning for physicists,” Phys. Rept

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2019

Later among the works it cites.

D. Bachtis, G. Aarts, and B. Lucini, “Quantum field-theoretic machine learning,” Phys. Rev. D

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2021

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10, 2021

Original

D. Bachtis, G. Aarts, and B. Lucini, “Quantum field theories, Markov random fields and machine learning,” in 32nd IUPAP Conference on Computational Physics · 2021

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A. Tsuchiya and K. Yamashiro, “A geometrical representation of the quantum information metric in the gauge/gravity correspondence,” Phys. Lett. B

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2022

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D. Bachtis, G. Aarts, F. Di Renzo, and B. Lucini, “Inverse Renormalization Group in Quantum Field Theory,” Phys. Rev. Lett

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2022

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