Ising model: Difference between revisions

Revision as of 10:25, 23 September 2024

Revision as of 09:50, 13 October 2024

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===Neuroscience===

The activity of [[neuron]]s in the brain can be modelled statistically. Each neuron at any time is either active + or inactive&nbsp;−. The active neurons are those that send an [[action potential]] down the axon in any given time window, and the inactive ones are those that do not. Because the neural activity at any one time is modelled by independent bits, [[J.John J. Hopfield|Hopfield]] suggested in 1982 that a dynamical Ising model would provide a [[Hopfield net|first approximation]] to a neural network which is capable of [[learning]].<ref>{{Citation| author= J. J. Hopfield| title = Neural networks and physical systems with emergent collective computational abilities| journal = Proceedings of the National Academy of Sciences of the USA| volume= 79 | pages= 2554–2558| year= 1982| doi = 10.1073/pnas.79.8.2554| pmid = 6953413| issue= 8| pmc= 346238| postscript= .|bibcode = 1982PNAS...79.2554H | doi-access = free}}</ref> This learning [[recurrent neural network]] was published by [[Shun'ichi Amari]] in 1972.<ref name="Amari1972">{{cite journal |last1=Amari |first1=Shun-Ichi |title=Learning patterns and pattern sequences by self-organizing nets of threshold elements|journal= IEEE Transactions |date=1972 |volume=C |issue=21 |pages=1197–1206 }}</ref><ref name=DLhistory>{{cite arXiv|last=Schmidhuber|first=Juergen|date=2022|title=Annotated History of Modern AI and Deep Learning |class=cs.NE|eprint=2212.11279}}</ref>

Following the general approach of Jaynes,<ref>{{Citation| author=Jaynes, E. T.| title= Information Theory and Statistical Mechanics | journal= Physical Review| volume = 106 | pages= 620–630 | year= 1957| doi=10.1103/PhysRev.106.620| postscript=.|bibcode = 1957PhRv..106..620J| issue=4 | s2cid= 17870175 }}</ref><ref>{{Citation| author= Jaynes, Edwin T.| title = Information Theory and Statistical Mechanics II |journal = Physical Review |volume =108 | pages = 171–190 | year = 1957| doi= 10.1103/PhysRev.108.171| postscript= .|bibcode = 1957PhRv..108..171J| issue= 2 }}</ref> a later interpretation of Schneidman, Berry, Segev and Bialek,<ref>{{Citation|author1=Elad Schneidman |author2=Michael J. Berry |author3=Ronen Segev |author4=William Bialek | title= Weak pairwise correlations imply strongly correlated network states in a neural population| journal=Nature| volume= 440 | pages= 1007–1012| year=2006| doi= 10.1038/nature04701| pmid= 16625187| issue= 7087| pmc= 1785327| postscript= .|arxiv = q-bio/0512013 |bibcode = 2006Natur.440.1007S |title-link=neural population }}</ref>