Abstract
A major puzzle in neural networks is understanding the information encoding principles that implement the functions of the brain systems. Population coding in neurons and plastic changes in synapses are two important subjects in attempts to explore such principles. This forms the basis of modern theory of neuroscience concerning self-organization and associative memory. Here we wish to suggest an information storage scheme based on the dynamics of evolutionary neural networks, essentially reflecting the meta-complication of the dynamical changes of neurons as well as plastic changes of synapses. The information storage scheme may lead to the development of a complete description of all the equilibrium states (fixed points) of Hopfield networks, a space-filling network that weaves the intricate structure of Hamming star-convexity, and a plasticity regime that encodes information based on algorithmic Hebbian synaptic plasticity.
Highlights
The study of memory includes two important components: the storage component of memory and the systems component of memory 1, 2
In respect of the underlying combinatorial space-filling structure of Hopfield networks, we establish an exact formula for describing all the equilibrium states of Hopfield networks with ultra-low thresholds
It provides a basis for the building of a primitive Hopfield network whose equilibrium states contain the prototypes
Summary
The study of memory includes two important components: the storage component of memory and the systems component of memory 1, 2. Fixed Point Theory and Applications an Ising model used in statistical physics 12–15 , and the study of constrained optimization problems such as the famous traveling salesman problem 16 Since it was initiated by Kohonen and Anderson in 1972, associative memory has remained widely open in neural networks 17–21. A mathematical proof asserts that the ongoing changes of the evolutionary network’s nodal-and-coupling dynamics will eventually come to rest at equilibrium states 31 This result reflects, in a deep mathematical sense, that plastic changes in the coupling dynamics may appear as a mechanism for associative memory. It provides a clear map that all the domains of attraction in Hopfield networks are star-convexity-like and that the phase space can be filled with those star-convexity-like domains It applies to frame a primitive Hopfield network that might consolidate an insight of exploring a plasticity regime in the information storage scheme
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