[Paper Review] Method of increasing the information capacity of associative memory of oscillator neural networks using high-order synchronization effect

Andrei Velichko, Maksim Belyaev+2 more|arXiv (Cornell University)|May 14, 2018

Nonlinear Dynamics and Pattern Formation25 references3 citations

TL;DR

This paper proposes a novel method to significantly increase the information capacity of oscillator neural networks (ONNs) by exploiting high-order synchronization in thermally coupled VO₂-switches. Using computational modeling of two- and three-oscillator systems, the authors demonstrate that synchronization order—defined as the ratio of harmonics at a common frequency—enables up to ~650 distinct synchronous states (Ns) in three-oscillator schemes and ~260 in two-oscillator systems, with optimal coupling strength maximizing capacity and noise reducing it.

ABSTRACT

Computational modelling of two- and three-oscillator schemes with thermally coupled $VO_2$-switches is used to demonstrate a novel method of pattern storage and recognition in an impulse oscillator neural network (ONN) based on the high-order synchronization effect. The method ensures high information capacity of associative memory, i.e. a large number of synchronous states $N_s$. Each state in the system is characterized by the synchronization order determined as the ratio of harmonics number at the common synchronization frequency. The modelling demonstrates attainment of $N_s$ of several orders both for a three-oscillator scheme $N_s$~650 and for a two-oscillator scheme $N_s$~260. A number of regularities are obtained, in particular, an optimal strength of oscillator coupling is revealed when $N_s$ has a maximum. A general tendency toward information capacity decrease is shown when the coupling strength and switch inner noise amplitude increase. An algorithm of pattern storage and test vector recognition is suggested. It is also shown that the coordinate number in each vector should be one less than the switch number to reduce recognition ambiguity. The demonstrated method of associative memory realization is a general one and it may be applied in ONNs with various mechanisms and oscillator coupling topology.

Motivation & Objective

• To develop a method for increasing the information capacity of associative memory in oscillator neural networks.
• To investigate the role of high-order synchronization in enabling multiple stable synchronous states.
• To identify optimal coupling strength and noise levels that maximize memory capacity.
• To propose a practical algorithm for pattern storage and recognition in ONNs.

Proposed method

• Computational modeling of two- and three-oscillator neural networks using thermally coupled VO₂-switches.
• Defining synchronization order as the ratio of harmonics at the common synchronization frequency to characterize distinct synchronous states.
• Using numerical simulations to analyze the number of stable synchronous states (Ns) under varying coupling strengths and noise amplitudes.
• Introducing an algorithm for storing and recognizing test vectors based on the number of oscillators and their synchronization patterns.
• Setting the number of vector coordinates to one less than the number of switches to reduce recognition ambiguity.
• Analyzing the system's behavior across different coupling topologies and mechanisms to ensure general applicability.

Experimental results

Research questions

• RQ1 How does high-order synchronization in VO₂-switched oscillator networks enable a large number of distinct synchronous states?
• RQ2 What is the optimal coupling strength that maximizes the number of stable synchronous states (Ns)?
• RQ3 How do increasing coupling strength and internal noise affect the information capacity of the associative memory?
• RQ4 What is the relationship between the number of oscillators and the maximum achievable Ns in such systems?
• RQ5 Can a general algorithm be designed for pattern storage and recognition that minimizes ambiguity in vector recognition?

Key findings

• The three-oscillator scheme achieved up to approximately 650 distinct synchronous states (Ns ~ 650), demonstrating high information capacity.
• The two-oscillator scheme achieved up to approximately 260 distinct synchronous states (Ns ~ 260), confirming scalability.
• An optimal coupling strength was identified at which the number of synchronous states (Ns) reaches a maximum.
• Increasing coupling strength beyond the optimal value leads to a decrease in Ns, indicating a trade-off.
• Higher internal noise amplitude reduces the number of stable synchronous states, degrading memory capacity.
• Reducing recognition ambiguity is achieved by setting the number of vector coordinates to one less than the number of switches.