Analogue integrated circuit design for sustained neurons in a
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Analogue integrated-circuit design for sustained neurons in a fly Eqn. 2 can be shown to be identical to eqn. 1 by rearranging its G.B. Zhang, G. Bayramoglu, J. Liu and H. Ogmen terms and by letting z, = V,, a = Vale,p = Zap/Va y = &/e. and An analogue integratedcircuit design of a fly’s sustained neurons The output of the second multiplier MUL2 is proportional to the is presented. Circuit simulation of the design shows that the excitatory input to the ith cell. Inhibitory inputs from adjacent output exhibits non-associative learning in agreement with spatial locations are subtracted from this excitatory input by using electrophysiologicalstudies of these neurons. The output is shown inverter and adder circuits (not shown in Fig. I) to produce the to encode the contrast of the input. output of the sustained cell at the ith location. Introduction: The fly offers an excellent prototype for biomimetic vision processors and navigation systems, due to its robust opto- motor behaviour and its relatively simple nervous system. 2‘6 1 peak Recently, several neuromorphic vision sensors based on the fly’s visual system have been built and tested [I]. Neurophysiological studies [2, 31 suggest that the fly optomotor system receives inputs from sustained neurons located in the first optic ganglion, the lam- ina. Existing neuromorphic vision sensors have not yet incorpo- rated a model for these neurons into their design and do not capture the full functionality of the fly optomotor system. We present here an analogue integrated-circuit design for these sus- tained neurons. The design can be used as an ‘early visual proces- sor’ with spatio-temporal adaptation properties. The proposed 2.0 circuit can also be integrated as a front end to opto-motor naviga- tion systems. 1.9 J I 0 0.05 0.10 0.15 0.20 0.25 0.30 t f f VED VED time, ms 1449/21 Fig. 2 Response of sustained unit to step input with onset and rise times of 0.1 and 0.01 ms, respectively Inputs Z and J were 2 and 20 pA, respectively flu: 2.5 1 T vc output GND a b 2.3 > 1449/1( a- C Q Fig. 1 Model and circuit design for sustained units ?? a Model b Circuit design . 21 Circuit design: Our design is based on a neural network model for the fly’s sustained neurons  whose activities had been recorded in the chiasm between the lamina and the second optic ganglion, 1.9 I 1 the medulla [5, 61. The model is shown in Fig. la. The luminance 10-1 100 101 signal at the spatial position i is denoted by 4. A baseline signal I Weber contrast is added to J, to represent the spatially uniform background lumi- nance, as well as the internal signal that sets a baseline neural activity when the external signal is zero (the dark current). The Fig. 3 Peak and plateau values o response against Weber contrast f ’ (defined as J/I) suinmed signal is transmitted via synapses whose gain zichanges as a function of the input, following 0 peak 0 plateau dzi -=4 dt P - .i) - ?%(I+ J i ) Results: We designed and simulated the circuits with Cadence where t is time, and a,p and y are parameters related to the syn- Analog Artist and SPICE in TSMC 0.35 pn process. Fig. 2 shows aptic transmission process [4, 71. These Variable-gain synapses are the output waveform obtained for a step input. Following the depicted by hatched rectangular shapes in Fig. la. The output of onset of the step, the output initially rises to approximately 2.5V this stage is given by the product of the input and the synaptic and rapidly decays to a plateau value of 2.3 V. This output wave- gain, i.e. z,(Z + JJ, and provides the excitatory drive (depicted by form illustrates the non-associative learning property of sustained semicircularhatched synaptic symbols) for the sustained neuron at neurons. Non-associative learning consists of sensitisation and the spatial location i. The sustained neuron also receives inhibitory habituation. Sensitisation corresponds to an increased response to inputs (depicted by semicircular open synaptic symbols) from novel stimulus, which in our simulations is observed as an over- adjacent spatial locations. shoot response to stimulus onset. Habituation corresponds to a Key elements of the circuit design for the sustained neuron are decreased response to sustained stimuli, which in our simulations shown in Fig. lb. Two modified Gilbert multipliers (MULI and is observed as a decay of the response. Similar output waveforms MUL2) are the main components of the circuit. Let the voltage had been reported in neurophysiological studies [5, 61 and model across the capacitor C be denoted by V,. Using the symbols simulations . Non-associative learning in our model leads to defined in Fig. 1, this voltage can be written as adaptive and nonlinear encoding of the input luminance, a crucial ELECTRONICS LETTERS 5th July 2001 c Vol. 37 N 3. 14 867 aspect of early vision processing. We studied the dependence of CMOS current-mode exponential-control the output on the amplitude of the input in a series of simulations, variable-gain amplifier which showed that the peak and the plateau values of the response are nonlinear monotonic increasing functions of J and nonlinear C.-C. Chang, M.-L. Lin and %-I. Liu monotonic decreasing functions of I. Together, these results sug- gest that the circuit encodes the contrast rather than the absolute A CMOS current-mode exponential-control variable-gain amplitude of the input. Fig. 3 shows that the peak and the pla- amplifier is presented. It consists of a first-order current-mode teau values of the response are approximately linear functions of pseudo-exponential circuit and a current-mode multiplier. Based Weber contrast on a logarithmic scale. Fig. 4 shows that the peak on the Taylor’s series expansion, the pseudo-exponential circuit and the plateau values of the response are approximately linear can be realised by MOSFETs in saturation. The proposed circuit functions of Michelson contrast on a linear scale, in particular has been fabricated in a 0.5 pm N-well CMOS process with a gain when contrast is above 0.3. control range of 15dB. The experimental results confitm the feasibility of the proposed varidble-gain amplifier. 2’6 1 / Introduction: A multiplier with an input signal and an exponential input can realise a variable-gain amplifier (VGA). Traditionally, 2.4 - the exponential input circuit is implemented in bipolar technology due to the exponential characteristics. It could not be realised > directly by MOSFETs in saturation due to square-law characteris- ai 6 2.2 - tics. Thus, several pseudo-exponential functions [l - 61 have been Q explored. In this Letter, a CMOS current-mode VGA,which con- 2 sists of a pseudo-exponential circuit and a current-mode multi- plier. is presented. The pseudo-exponential circuit is based ton the 2.0 - approximated Taylor’s series. The proposed circuits have been fabricated in a 0.5 pn N-well CMOS process and the experimental results are given to demonstrate this proposed VGA. 1.84 0 ‘ ‘ - 0.2 . . . 0.4 . ’ ’ 0.6 . ’ ‘ 0.8 ’ ‘ ‘ 1.o Michelson contrast 1449/41 Fig. 4 Peak and plateau values of response against Michelson contrast (defined as J/(J f 21)) 0 peak 0 plateau a b 1052/11 I 1 Fig. 1 First-order pseudo-exponential circuit and current-mode mur‘tiplier Conclusion: Simulations of the proposed design have shown that a Exponential circuit the circuit exhibits non-associative learning and encodes the con- b Multiplier trast rather than the absolute amplitude of the input. These prop- erties result from temporal and spatial adaptation achieved through variable-gain synapses and lateral inhibition, respectively. 0 IEE 2001 8 May 2001 Electronics Letters Online No: 20010631 D 01: IO. 1049/el:20010631 G.B. Zhang and J. Liu (Department of Electrical Engineering, The Fig. 2 Photograph showing pseudo-exponential circuit ana’ multijdier ,University of Texas at Dallas, PO Box 830688, EC33, Richardson, T X 75083-0688, USA) Circuit implementation: The proposed VGA consists of a current- G. Bayramoglu and H. Ogmen (Department of Electrical & Computer mode multiplier and a current-mode first-order pseudo-exponen- Engineering, University of Houston. Houston, T.Y 77204-4005, USA) tial circuit. The pseudo-exponential circuit is shown in Fig. l a E-mail: firstname.lastname@example.org [2, 61, the PMOS and NMOS transistors being in saturati” and having the same transconductance parameters, K. The drain cur- rents of A41 and M 2 can be given as References INDIVERI,G., and DOUGLAS, R.: ‘Neuromorphic vision sensors’, Science, 2000, 288, pp. 1189-1190 and COOMBE, P.E., SRINIVASAN,M.v., and GUY, R.G.: ‘Are the large monopolar cells of the insect lamina on the optomotor pathway’, J . Comp. Physiol. A , 1989, 166, pp. 23-35 OGMEN, H., and GAGNE, s : ‘Neural network architectures for where G = V,, V,, - I VTpl VTn. ~ - Furthermore, according to the motion perception and elementary motion detection in the fly approximation of the Taylor’s series expansion (i.e. 2b2 . visual system’, Neural Netw., 1990, 3, pp. 487-505 b2 + for I(a/b)xl < l), the output current, , (= ZM3 + Z,, Z ,, OGMEN, H., and GAGNE, s : ‘Neural models for sustained and on-off = I,,, + ZM5),can be expressed as units of insect lamina’, Biol. Cybernetics, 1990, 63, pp. 51-60 ARNETT. D.w.: ‘Spatial and temporal integration properties of units in the first optic ganglion of dipterans’, J. Neurophysiol., 1972, 35, pp. 429444 JANSONIUS, N.M., and VAN HATEREN, J.H.: ‘On spiking units in the first optic chiasm of the blowfly 111. The sustaining unit’, J. Comp. The error of the pseudo-exponential function is within 5% if Physiol. A , 1993, 173, pp. 187-192 4 . 5 7 5 5 IcTRIKGZ 5 0.815 and the output dynamic range can be CARPENTER, G.A , and GROSSBERG, s.: ‘Adaptation and transmitter 15dB. Inversely, taking the output current, I y , from the two gating in vertebrate photoreceptors’, J. Theoretical Neurobiol., PMOS transistors, M7 and MS, a negative exponential factor 868 1981, 1, pp. 1-42 function can be obtained as ELECTRONICS LETTERS 5th July2001 Vol. 37 No. 74 .