Abstract
A neural circuit that relies on the electrical properties of NMDA synaptic receptors is shown by numerical and theoretical analysis to be capable of realizing the winner-takes-all function, a powerful computational primitive that is often attributed to biological nervous systems. This biophysically-plausible model employs global lateral inhibition in a simple feedback arrangement. As its inputs increase, high-gain and then bi- or multi-stable equilibrium states may be assumed in which there is significant depolarization of a single neuron and hyperpolarization or very weak depolarization of other neurons in the network. The state of the winning neuron conveys analog information about its input. The winner-takes-all characteristic depends on the nonmonotonic current-voltage relation of NMDA receptor ion channels, as well as neural thresholding, and the gain and nature of the inhibitory feedback. Dynamical regimes vary with input strength. Fixed points may become unstable as the network enters a winner-takes-all regime, which can lead to entrained oscillations. Under some conditions, oscillatory behavior can be interpreted as winner-takes-all in nature. Stable winner-takes-all behavior is typically recovered as inputs increase further, but with still larger inputs, the winner-takes-all characteristic is ultimately lost. Network stability may be enhanced by biologically plausible mechanisms.
Highlights
The winner-takes-all (WTA) function is an operation that is often assumed to take place in biological nervous systems, and it has been demonstrated to be a powerful computational primitive (Maass, 2000)
The WTA characteristic in this model is conceived as resulting from strong amplification and nonlinear effects that can emerge from interactions between NMDA receptor (NMDAR) and the other ion channels in the membrane
Consideration is given to inhibitory feedback with several different characteristics: either mildly hyperpolarizing or more strongly hyperpolarizing, and having either ohmic or inward-rectifying channels
Summary
The winner-takes-all (WTA) function is an operation that is often assumed to take place in biological nervous systems, and it has been demonstrated to be a powerful computational primitive (Maass, 2000). Winner-takes-all networks have been modeled widely in the fields of computational brain science and artificial neural networks (Amari, 1972; Grossberg, 1973; Koch and Ullman, 1985; Rumelhart and Zipser, 1987; Yuille and Grzywacz, 1989; Coultrip et al, 1992; Ermentrout, 1992; Winder, 1999; Yuille and Geiger, 2003; Mao and Massaquoi, 2007; Handrich et al, 2009; Chen et al, 2013), and have been implemented in various analog electronic circuits (Lazzaro et al, 1989; Andreou et al, 1991; Deweerth and Morris, 1995; Lau and Lee, 1998; Fish and Yadid-Pecht, 2001; Indiveri, 2001; Baishnab et al, 2010) These mathematical and silicon models for the most part achieve the WTA characteristic using some sort of common inhibitory feedback in conjunction with high gain and a strong nonlinearity, often in the form of a neural thresholding operation. It is of interest due to the widespread distribution of neurons with glutamatergic synapses and lateral inhibition in many areas of the brain
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