Contraction Properties of VLSI Cooperative Competitive Neural Networks of Spiking Neurons

Part of Advances in Neural Information Processing Systems 20 (NIPS 2007)

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Emre Neftci, Elisabetta Chicca, Giacomo Indiveri, Jean-jeacques Slotine, Rodney Douglas


A non–linear dynamic system is called contracting if initial conditions are for- gotten exponentially fast, so that all trajectories converge to a single trajectory. We use contraction theory to derive an upper bound for the strength of recurrent connections that guarantees contraction for complex neural networks. Specifi- cally, we apply this theory to a special class of recurrent networks, often called Cooperative Competitive Networks (CCNs), which are an abstract representation of the cooperative-competitive connectivity observed in cortex. This specific type of network is believed to play a major role in shaping cortical responses and se- lecting the relevant signal among distractors and noise. In this paper, we analyze contraction of combined CCNs of linear threshold units and verify the results of our analysis in a hybrid analog/digital VLSI CCN comprising spiking neurons and dynamic synapses.