Synchronicity and coherence in artificial neural networks
Sheng-Yuan Lin · Scholarly Commons (University of Pennsylvania) · 1994
This dissertation describes a new model and a new approach to study the dynamics of artificial neural networks. In traditional artificial neural network research, the formal neuron model is adopted, which takes the average frequency of the action potential pulses as the only relevant information. There is evidence that the time information does play an important role in neural computation, and that biological neural networks exhibit very complex dynamics. The complexity of neural dynamics include phase-locking, quasi-periodic firing, chaotic firing, and bifurcations due to change in the parameters of the neurons. A new neuron model called the Programmable Unijunction Oscillator Neuron (PUTON) capable of providing the complexities mentioned above is developed. The PUTON is structurally simple, has low power consumption, and can be described by simple mathematics. The complexity of the PUTON when driven by a periodic (sinusoidal) signal is demonstrated via bifurcation diagrams and several metrics of the dynamics. Analog electronic circuits implementation of the PUTON are developed, and opto-electronical realization are demonstrated. A novel method to characterize the dynamics of the PUTON is developed. The method focuses on the phase information of the pulses fired by the neurons. The phase is measured relative to the periodic driving signal. The continuous time dynamics of the PUTON when driven by a periodic signal is transformed to a discrete one-dimensional map. Mathematical analyses are used to prove that the system can exhibit chaotic dynamics under certain conditions. The characteristics of the model neurons studied are obtained in great detail. The results of experiments and simulations are presented and shown to be in excellent agreement. A network of 32 PUTONs coupling through a Synapse Chip provided by the JPL is built to demonstrate phase-locking in a pulsed neural network. Methods of characterizing the performance of such a network are explored. The phase-locking capability of the network suggests potential for solving optimization problems like the TSP rapidly. The research work presented in this dissertation provides the foundation for a new generation of neural network hardware, in which complexity, bifurcation and chaos on the neuron level may be exploited to achieve higher-level functions.