MyJournals Home  

RSS FeedsEntropy, Vol. 19, Pages 299: Critical Behavior in Physics and Probabilistic Formal Languages (Entropy)

 
 

23 june 2017 16:15:30

 
Entropy, Vol. 19, Pages 299: Critical Behavior in Physics and Probabilistic Formal Languages (Entropy)
 


We show that the mutual information between two symbols, as a function of the number of symbols between the two, decays exponentially in any probabilistic regular grammar, but can decay like a power law for a context-free grammar. This result about formal languages is closely related to a well-known result in classical statistical mechanics that there are no phase transitions in dimensions fewer than two. It is also related to the emergence of power law correlations in turbulence and cosmological inflation through recursive generative processes. We elucidate these physics connections and comment on potential applications of our results to machine learning tasks like training artificial recurrent neural networks. Along the way, we introduce a useful quantity, which we dub the rational mutual information, and discuss generalizations of our claims involving more complicated Bayesian networks.


 
155 viewsCategory: Informatics, Physics
 
Entropy, Vol. 19, Pages 298: The Legendre Transform in Non-Additive Thermodynamics and Complexity (Entropy)
Entropy, Vol. 19, Pages 300: Test of the Pauli Exclusion Principle in the VIP-2 Underground Experiment (Entropy)
 
 
blog comments powered by Disqus


MyJournals.org
The latest issues of all your favorite science journals on one page

Username:
Password:

Register | Retrieve

Search:

Physics


Copyright © 2008 - 2024 Indigonet Services B.V.. Contact: Tim Hulsen. Read here our privacy notice.
Other websites of Indigonet Services B.V.: Nieuws Vacatures News Tweets Nachrichten