Temporal considerations and coherence in neural networks
Mostafa H. Eldefrawy · ScholarlyCommons (University of Pennsylvania) · 1994
We investigated novel artificial model neurons with similar capabilities to the biological neuron's various firing modalities. Such neurons can encode their stimulus particularly when it is periodic in the form of phase-locked firing, bursting, and chaotic firing, which could underlie certain forms of neural computations. Model neurons were investigated, and the integrate-and-fire model neuron was then adopted for investigation and implementation because of its structural simplicity, and complex rich firing modalities, under periodic stimulus. Periodic stimulus is thought to emerge via coherent neural activities or the firing of synchronized coupled neuron populations (networks), which are then received and processed by the neuron via its synapto-dendritic processes. The periodically driven integrate-and-fire model neuron was implemented as a simple relaxation oscillator circuit utilizing the S-shaped nonlinearity of a glow-lamp that represented the biological neuron's excitable membrane characteristics. This model neuron's firing modalities under sinusoidal stimulus was then characterized using: first, instantaneous frequency measurements and numerical simulations, where for the first time such measurements were performed using a sophisticated "Frequency and Interval Time Analyzer", which showed the neuron to exhibit phase-locking, bursting, and erratic firing behavior and enabled representing its behavior in the form of bifurcation diagrams. Second, concepts and tools from the theory of nonlinear dynamics were used to predict the neuron's behavior via phase transition maps (PTMs) that were analytically derived and numerically computed because of the transcendental nature of the PTM equations. A new modified integrate-and-fire neuron was then developed which resulted in an analytical closed form expression for the PTM that turned out to be the well studied "circle map" which is known to exhibit chaos for certain ranges of its parameter space. This is significant because, first, since the circle map expression provides instant description of the neuron's behavior for any chosen set of the neuron's and driving signal's parameters, a big saving in computing resources compared to the numerically produced phase transition maps is achieved. Second, now it is possible to implement the circle map in Silicon using a simple circuit that is also able to generate chaos, which could be useful for annealing applications. The collective computing capabilities of the brain are thought to be due to coherent firing or synchronization of distant neurons, suggesting that synchronization underlies feature linking abilities in the visual cortex. Thus, we studied synchronization in arrays of coupled integrate-and-fire neurons, using hardware experimentation as well as computer modeling and numerical simulation. Synchronization in coupled integrate-and-fire neurons was then explored in solving the travelling salesman problem, a well known NP-complete optimization problem, resulting in the development of a heuristic "random deletions" algorithm that outperformed other known heuristic optimization techniques, as applied to the traveling salesman problem. The algorithm seems to use chaos to randomly search the solution space in order to achieve annealing and find an optimum solution. We found three auditory perception tasks to be suitable for possible implementation using this model neuron. This work suggests that artificial neural networks employing functionally complex processing elements like the integrate-and-fire bifurcating neuron studied here, could provide functional capabilities in neural networks that are beyond the capabilities of present day neural networks, especially in the performance of higher level functions like feature binding, cognition, and efficient solution of optimization problems. (Abstract shortened by UMI.)