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Hillar C, Chan T, Taubman R, et al. Hidden Hypergraphs, Error-Correcting Codes, and Critical Learning in Hopfield Networks. Entropy (Basel). 2021;23(11)doi: 10.3390/e23111494.
Hillar, C., Chan, T., Taubman, R., & Rolnick, D. (2021). Hidden Hypergraphs, Error-Correcting Codes, and Critical Learning in Hopfield Networks. Entropy (Basel, Switzerland), 23(11), . https://doi.org/10.3390/e23111494
Hillar, Christopher, et al. "Hidden Hypergraphs, Error-Correcting Codes, and Critical Learning in Hopfield Networks." Entropy (Basel, Switzerland) vol. 23,11 (2021). doi: https://doi.org/10.3390/e23111494
Hillar C, Chan T, Taubman R, Rolnick D. Hidden Hypergraphs, Error-Correcting Codes, and Critical Learning in Hopfield Networks. Entropy (Basel). 2021 Nov 11;23(11). doi: 10.3390/e23111494. PMID: 34828192; PMCID: PMC8622935.
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Entropy (Basel). 2021 Nov 11;23(11). doi: 10.3390/e23111494.

Hidden Hypergraphs, Error-Correcting Codes, and Critical Learning in Hopfield Networks.

Entropy (Basel, Switzerland)

Christopher Hillar, Tenzin Chan, Rachel Taubman, David Rolnick

Affiliations

  1. Awecom, Inc., San Francisco, CA 94103, USA.
  2. Singapore University of Technology and Design, Singapore 487372, Singapore.
  3. School of Computer Science, McGill University, Montreal, QC H3A 0G4, Canada.

PMID: 34828192 PMCID: PMC8622935 DOI: 10.3390/e23111494

Abstract

In 1943, McCulloch and Pitts introduced a discrete recurrent neural network as a model for computation in brains. The work inspired breakthroughs such as the first computer design and the theory of finite automata. We focus on learning in Hopfield networks, a special case with symmetric weights and fixed-point attractor dynamics. Specifically, we explore minimum energy flow (MEF) as a scalable convex objective for determining network parameters. We catalog various properties of MEF, such as biological plausibility, and then compare to classical approaches in the theory of learning. Trained Hopfield networks can perform unsupervised clustering and define novel error-correcting coding schemes. They also efficiently find hidden structures (cliques) in graph theory. We extend this known connection from graphs to hypergraphs and discover

Keywords: Hopfield networks; clustering; error-correcting codes; exponential memory; hidden graph; neuroscience

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