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Low-Power Silicon Spiking Neurons and Axons

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Low-Power Silicon Spiking Neurons and AxonsJohn LazzaroCS DivisionUC BerkeleyBerkeley, CA, 947 2 0AbstractThis paper presents low-power versions of two cir-cuits often used in analog VLSI models of neural sys-tems. The circuits model the spiking behavior of theaxon hillock and the pulse propagation of axons.1 IntroductionAs device dimensions decrease, die sizes increase,and wafer-sca le techniques mature, power consump-tion becomes a domina nt issue in VLSI system de-sign. A silicon neural design style that operates MOStransistors in the weak-inversion regime [7] [1] sup-ports low-power VLSI design. In this design style,popular circuits that model continuous-time dendriticprocessing operate all transistors in the weak-inver sionregime. In contrast, several popular circuits in this de-sign style, that model the spiking behavior o f the axonhillock and the pulse propagation of axons, operateseveral transistor s outside the weak-inversion regime.In many neural implementa tions , these axon circuitsdominate p ower consumption [3 ] [4] [5] [6] [2].I have designed, fabricated, and tested versions ofthese axon circuits; in these modified circui t s, all tran-sistors oper ate in the weak-inversion regime. Themodified circuits are fully functional, and show a mea -sured improvement in power consumption over theoriginal circuits. Power co nsumption decreases of afactor of 10 to 1000 have been measured, dependingon pulse width and spiking frequency.The density of the mo dified circu it s is comparableto the original circuits. The modified axon hillockcircuit adds one transistor to the original circuit; themodified model of axonal pulse propa gation adds onetransistor to each stage of delay of the original circuit.The modified circuits also add two control voltages tothe original circuits; judicious use of a process withtwo layers of polysilicon allows the addition of thesewires with a minimal increase in density.VpVoIiCCfVc5 V5 nA5 msIiVoFigure 1: Spiking neuron circuit and function,with unidirectional current input Ii, voltage pulseoutput Vo, and pulse width control voltage Vp.2 Circuit DetailsFigure 1 shows the spiking neuron circuit from [7 ],that uses a high-gain voltage amplifier with a sig-moidal nonlinearity as a gain element. The circuitconverts the unidirectional current Iiinto a s equenceof fixed-width, fixed-height voltage pulses of Vo. Dur-ing a pulse Vo= Vdd, a nd between pulses Vois a tground potential.To understand circuit op e ration, consider the cir-cuit condition after an output pulse has completed. Inthis state, Vois at ground potential, and Vcis lowerthan the switching threshold of the amplifier. The dis-charge path of the state capacitor C is closed, and thecharging path of C is open.The circuit remains in this state until the inputcurrent Iiincreases Vcto the switching thresho ld ofthe amplifier. At this point, Voswitches to Vdd. Thefeedback capacitor Cfensures the secur e switching ofthe cir cuit. The new value of Vcis above the switchingthreshold of the amplifier, and depends on the relativevalues of Cfand C.Once a pulse begins, the discharge path of the statecapacitor C is open, and the charging path of C isclosed. The c ontrol voltage Vpsets the discharge r ateof C, a nd thus the width of voltage pulse of Vo. Thecircuit remains in this state until Vcdecreases to theswitching threshold of the amplifier. At this point, Voswitches to ground po tential, and the pulse is com-plete. The voltage Vcis reset to a value below theswitching threshold of the amplifier, that depends onthe relative values of Cfand C.This circuit, as described in [7], uses two digitalinverters in series as the high-gain amplifier; Figure 2(top) shows this amplifier implementation. When usedin the spiking neuron circuit, the transistors in firstinverter of this amplifier are biased outside the weak-inversion regime. In many designs, the static c urrentconsumption of these transistors dominates the cur-rent consumption o f the chip.Figure 2 (bottom) also shows a low-power imple-mentation of a high-gain amplifier suitable for use inthe spiking neuron circuit. The contr ol voltages K1and K2limit the static current consumption of theamplifier. The response time o f the a mplifier is notsymmetric; the speed of crossing the amplifier thresh -old in a positive direction is not limited by K1andK2, but the speed of crossing the amplifier in a neg-ative direction is directly dependent on K1and K2.In many applica tions, this asymmetry allows the biascurrents of the amplifier to be set in the weak-inversionregime. The diode- c o n nected t r a n s istor acts to raisethe switching threshold of the amplifier.3 Experimental DataFigure 3 shows the static current consumption ofthe two amplifiers shown in Figure 2, as a function ofthe input voltage Vi. This figur e shows data from atest chip fabricated in the 2µm double polysilicon n-well Orbit process as supplied by MOSIS. The currentmeter used in this measurement is not able to measureVoViK1K2VoViFigure 2: Original gain stage (top circuit) and low-power gain stage (botto m circuit). K1and K2are control voltages, set to ensure all transistorsoperate in the weak-invers ion regime.0 1 2 3 4 5Vi10 nA1 µA100 µAIddoriginallow powerFigure 3: Power supply cur rent Iddfor or iginalgain stage and low-power gain stage, as a functionof Vi. Note lo g scale for current.10 KhzFrequenc y10 nA1 µA100 µA100 Hzoriginallow power1 m0.1 m10 µIddFigure 4: Power supply cur rent Iddfor or iginalspiking neuron circuit and low-power spiking neu-ron circuit, as a function of spiking frequency. La-bels next to graphs indicate pulse width of spikes,in units of seconds. Note log scale for freq uencyand current.currents b elow 5 nA. As expected, the low-power am-plifier consumes negligible current below its switchingthreshold, and a constant current above its switchingthreshold.Figure 4 shows the current consumption of the spik-ing neuron circuit of Figure 1, implemented with theoriginal amplifier and the low-power amplifier. Asexpect e d, the current consumption of the low-powercircuit is a linear function of spiking frequency, andincreases with the size of the pulse width. All datawas taken with the values of K1and K2necessary forcorrect circuit function with 10µs pulses ; the cur r entconsumption for longer pulse- w idth o per ation can bereduced by adjusting K1and K2.4 The Axonal Delay CircuitFigure 5 shows one section of the axonal delay linecircuit described in [7]. In


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