J. Lazzaro, S. Ryckebusch, M.A. Mahowald, C. A. Mead
We have designed, fabricated, and tested a series of compact CMOS integrated circuits that realize the winner-take-all function. These analog, continuous-time circuits use only O(n) of interconnect to perform this function. We have also modified the winner-take-all circuit, realizing a circuit that computes local nonlinear inhibition.
Two general types of inhibition mediate activity in neural systems: subtractive in(cid:173) hibition, which sets a zero level for the computation, and multiplicative (nonlinear) inhibition, which regulates the gain of the computation. We report a physical real(cid:173) ization of general nonlinear inhibition in its extreme form, known as winner-take-all.
We have designed and fabricated a series of compact, completely functional CMOS integrated circuits that realize the winner-take-all function, using the full analog nature of the medium. This circuit has been used successfully as a component in several VLSI sensory systems that perform auditory localization (Lazzaro and Mead, in press) and visual stereopsis (Mahowald and Delbruck, 1988). Winner(cid:173) take-all circuits with over 170 inputs function correctly in these sensory systems.
We have also modified this global winner-take-all circuit, realizing a circuit that computes local nonlinear inhibition. The circuit allows multiple winners in the net(cid:173) work, and is well suited for use in systems that represent a feature space topograph(cid:173) ically and that process several features in parallel. We have designed, fabricated, and tested a CMOS integrated circuit that computes locally the winner-take-all function of spatially ordered input.
Lazzaro, Ryckebusch, Mahowald and Mead
THE WINNER-TAKE-ALL CmCUIT
Figure 1 is a schematic diagram of the winner-take-all circuit. A single wire, asso(cid:173) ciated with the potential Vc, computes the inhibition for the entire circuit; for an n neuron circuit, this wire is O(n) long. To compute the global inhibition, each neuron k contributes a current onto this common wire, using transistor T2 a.' To apply this global inhibition locally, each neuron responds to the common wire volt(cid:173) age Vc, using transistor Tla.' This computation is continuous in time; no clocks are used. The circuit exhibits no hysteresis, and operates with a time constant related to the size of the largest input. The output representation of the circuit is not binary; the winning output encodes the logarithm of its associated input.
Figure 1. Schematic diagram of the winner-take-all circuit. Each neuron receives a unidirectional current input 11;; the output voltages VI •.. VB represent the result of the winner-take-all computation. If II; = max(II ••• IB ), then VI; is a logarithmic function of 11;; if Ii <: 11;, then Vi ~ O.
A static and dynamic ana.lysis of the two-neuron circuit illustrates these system properties. Figure 2 shows a schematic diagram of a two-neuron winner-take-all circuit. To understand the beha.vior of the circuit, we first consider the input condition II = 12 = 1m. Transistors TIl ~d T12 have identical potentials at gate and source, and are both sinking 1m; thus, the drain potentials VI and V2 must be equal. Transistors T21 and T22 have identical source, drain, and gate potentials, and therefore must sink the identical current ICI = IC2 = Ic/2. In the subthreshold region of operation, the equation 1m = 10 exp(Vc/Vo) describes transistors Til and T12 , where 10 is a fabrication parameter, and Vo = kT/qlt. Likewise, the equation Ic/2 = 10 exp((Vm - Vel/Volt where Vm = VI = V2, describes transistors T21 and T22 . Solving for Vm(Im, Ie) yields
Vm = Voln(~:) + Voln(:;).