Synchronized Interactions in Spiked Neuronal Networks

Abstract

The study of artificial neural networks has originally been inspired by neurophysiology and cognitive science. It has resulted in a rich and diverse methodology and in numerous applications to machine intelligence, computer vision, pattern recognition and other applications. The random neural network (RNN) is a probabilistic model which was inspired by the spiking behaviour of neurons, and which has an elegant mathematical treatment which provides both its steady-state behaviour and offers efficient learning algorithms for recurrent networks. Second order interactions, where more than one neuron jointly act upon other cells, have been observed in nature; they generalise the binary (excitatory-inhibitory) interaction between pairs of cells and give rise to synchronous firing by many cells. In this paper we develop an extension of the RNN to the case of synchronous interactions which are based on at two cells that jointly excite a third cell; this local behaviour is in fact sufficient to create synchronous firing by large ensembles of cells. We describe the system state and derive its stationary solution as well as a O(N 3) gradient descent learning algorithm for a recurrent network with N cells when both standard excitatory-inhibitory interactions, as well as synchronous firing, are present. * This research was undertaken as part of the ALADDIN (Autonomous Learning Agents for Decentralised Data and Information Systems) project and is jointly funded by a BAE Systems and EPSRC (UK Engineering and Physical Research Council) strategic partnership under Grant No. EP/C548051/1.

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“…Here, the RNN was used to design fast decision algorithms based on learning a wide range of problem instances (Gelenbe and Timotheou [143]), and then using it for rapidly selecting the best match to the current need.…”

Erol Gelenbe: A Career in Multi-Disciplinary Probability Models

“…His team studied fast decision algorithms based on learning a wide range of problem instances and their optimal rescuer and rescue vehicle allocations [38,158,159], and selecting in real-time the allocation that best matches the current observed emergency situation. They also studied low-cost, light-weight and disruption tolerant techniques that can offer robust communications in emergency environments [173], and many of these methods actually span both the military and the civilian domain [36,171,172,186,203].…”

Managing Emergencies Optimally Using a Random Neural Network-Based Algorithm

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