Pattern-based computing via sequential phase transitions in hierarchical mean field neuropercolation

In this work, we describe operational principles of a pattern-based computing paradigm based on the neuropercolation model, which can be used as associative memory supporting sensory processing and pattern recognition. Neuropercolation extends the concept of phase transitions to interactive populations exhibiting frequent transients in their spatio-temporal dynamics, which can be viewed as manifestations of an asynchronous computer working with a sequence of meta-stable spatial patterns, in a bid to unravel the limitations of Turing computing principles. The model is motivated by the structural and dynamical properties of large-scale neural populations in the cerebral cortex and it implements basic building blocks of neurodynamics following the hierarchy of Freeman K-sets.The introduced mean-field approximation allows rigorous mathematical analysis of the emergent dynamics, which is the major novel contribution of this work. Specifically, we derive exact conditions for the onset of non-zero background activity, for the transition from steady state to narrow-band (limit cycle) oscillations, and for the transition from narrow-band to broad-band (chaotic) dynamics. We describe an array of connected oscillators, which exhibits transient synchronization episodes manifesting meta-stable collective states. The corresponding meta-stable spatial amplitude patterns are destabilized by inputs or spontaneously and jump to another pattern, yielding a sequence of transient patterns. These patterns are shaped by the connections between the nodes modifiable through learning. The sequence of patterns manifest the steps of the computation, which embody the meaning of the input data in the context of the system past experiences.