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As a result, a neural network in which all of the neurons are firing or not firing is similar to a magnetic material in which all of the spins are all pointing up or down.

Spin Glasses and Complexity

When we create a memory, it is stored in our brain as a pattern of neural activity encoded by the strength of the synapses. These synapses can be either excitatory — they favour the transmission of information — or inhibitory — they inhibit transmission — and vary in connection strength.

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When the memory is triggered, the neurons fire or stay silent in a pattern configured by these synaptic connections. Mathematical models of the recall of learned memories are based around simulations of binary neurons linked by connections of varying strengths.

In such neurological models, memories are introduced in the same way as in real brains — as a pattern of binary activity encoded by connections and inhibitions of varying strengths. In these models, disordered states that resemble spin glasses emerge when the number of stored patterns and the network size the number of stored memories approaches infinity.

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They are essentially a frustrated state of frozen neural activity. Previous models, however, do not accurately represent the balance of synapse configurations that have been found in brains. Instead the models had generally assumed an equal balance of excitatory and inhibitory synapses with similar strengths. So you have a kind of balance that retains the heterogeneity in the brain within an optimal range.

Volume I: Basic Examples

They also demonstrated mathematically that these states are not linked to memory retrieval. If you compute the same measure for a spin glass you will have zero. Browse all. Buyer's Guide Jobs Sign in Register. Lik Wee Lee , Adam P.

Spin Glasses

Analytic and algorithmic solution of random satisfiability problems. Monte Carlo simulations of spin glasses at low temperatures Helmut G. Katzgraber , Matteo Palassini , Allison P.

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Nature of the spin glass state. Matteo Palassini , Adam P.

Spin and link overlaps in three-dimensional spin glasses. Florent Krzakala , Olivier C. Related Papers.

Spin glass - Wikipedia

By clicking accept or continuing to use the site, you agree to the terms outlined in our Privacy Policy , Terms of Service , and Dataset License. The methodology developed in the study of these models led to further important tools and ideas that found applications in different branches of computer science, including combinatorial optimization theory, machine learning and signal processing.

Fundamental concepts appeared relating average algorithmic complexity of optimization and inference problems with phase transitions in spin glass models. In the last two decades this connection flourished and spin glass theory was used for algorithmic development and analysis in many applications including error correcting codes, clustering of graphs and data, compressed sensing, training of neural networks, reconstruction of interaction networks from biological data, to name a few.