Percolation with plasticity for neuromorphic systems

Abstract

We develop a theory of percolation with plasticity media (PWPs) rendering properties of interest for neuromorphic computing. Unlike the standard percolation, they have multiple (N ≫ 1) interfaces and exponentially large number (N!) of conductive pathways between them. These pathways consist of non-ohmic random resistors that can undergo bias induced nonvolatile modifications (plasticity). The neuromorphic properties of PWPs include: multi-valued memory, high dimensionality and nonlinearity capable of transforming input data into spatiotemporal patterns, tunably fading memory ensuring outputs that depend more on recent inputs, and no need for massive interconnects. A few conceptual examples of functionality here are random number generation, matrix-vector multiplication, and associative memory. Understanding PWP topology, statistics, and operations opens a field of its own calling upon further theoretical and experimental insights.

Numerical modeling of nonohmic percolation conduction and Poole Frenkel laws

“…Adding the displacement currents (i. e. capacitive properties) our modeling will allow to study frequency dependent and pulse percolation, of interest for deploying the percolation conduction as a base for reservoir computing. 25 Our modeling allows to introduce the algorithm of nonvolatile resistance changes in microscopic resistors of the grid (plasticity), which will extend its applicability over multi-valued memory applications.…”

Self-Organized Memristive Ensembles of Nanoparticles Below the Percolation Threshold: Switching Dynamics and Phase Field Description

“…Self-organizing networks of nanoparticles and nanowires have recently become promising systems for neuromorphic computing [ 4 , 5 , 6 ]. These networks exhibit critical behavior near metal–insulator transition, scale-free networking that can provide new brain-like information processing with potentially attractive features such as ultra-low power consumption [ 7 , 8 , 9 ]. Below the percolation threshold, networks consist of groups of particles separated by tunnel gaps; the applied voltage causes the formation of atomic scale filaments in the gaps, and observed avalanches of switching events are similar to potentiation in biological neural systems [ 10 ].…”

“…Below the percolation threshold, networks consist of groups of particles separated by tunnel gaps; the applied voltage causes the formation of atomic scale filaments in the gaps, and observed avalanches of switching events are similar to potentiation in biological neural systems [ 10 ]. In [ 9 ], such memristive nanosystems are called percolation with plasticity systems. The neuromorphic advantages of percolating nanomaterials with plasticity include multivalued memory, high dimensionality and non-linearity capable of transforming input data into spatiotemporal patterns, and no need for array interconnects [ 9 ].…”

“…In [ 9 ], such memristive nanosystems are called percolation with plasticity systems. The neuromorphic advantages of percolating nanomaterials with plasticity include multivalued memory, high dimensionality and non-linearity capable of transforming input data into spatiotemporal patterns, and no need for array interconnects [ 9 ].…”

“…In [ 16 ], a master equation is considered to analyze the networks composed of probabilistic binary memristors. The basic theory of percolation networks with plasticity is outlined in [ 9 ].…”