Neurons... in a nutshell A quick tutorial. Silicon Neurons. Neurons of the world. Equivalent Circuit. E ex (Na +,...) Glutammate. V mem. C mem.

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1 Neurons... in a nutshell quick tutorial Silicon Neurons CNS WS7/8 Class Giacomo Indiveri Institute of Neuroinformatics University ETH Zurich Zurich, December 7 Complexity Real Neurons Conductance based models Integrate and fire models Rate based models Sigmoidal units Linear threshold units Neurons of the world Equivalent Circuit Glutammate E ex (Na,...) GB E inh (K, Cl,...) G l Dendritic tree Soma xon If excitatory input currents are relatively small, the neuron behaves exactly like a first order lowpass filter.

2 Spike generating mechanism ction potentials of the world E Na g Na g K G l E K If the membrane voltage increases above a certain threshold, a spikegenerating mechanism is activated and an action potential is initiated. Spike properties The FI curve Refractory Period Pulse Width I in =I 1 I in =I 2 > I 1 Spike Frequency (F) Refractory Period Input Current (I)

3 Hardware implementations of spiking neurons Conductancebased models of spiking neurons The first artificial neuron model was proposed in the 1943 by McCulloch and Pitts. Hardware implementations of this model date almost back to the same period. Hardware implementations of spiking neurons are relatively new. One of the most influential circuits that implements an integrate and fire (I&F) model of a neuron was the xonhillock Circuit, proposed by Carver Mead in the late 198s. In 1991 Misha Mahowald and Rodney Douglas proposed a conductancebased silicon neuron and showed that it had properties remarkably similar to those of real cortical neurons. Conductance based SiNeurons Conductance based SiNeurons Silicon neuron s measurements Sodium Current Sodium 1V V τna V thr I Naoff E Na Vm [Ca] G Naoff I Naon I Na V τk V thr V thr K G Naon G I K IK Passive Leak E V leak mem C G mem leak Passive Vm [Ca] Vm Potassium Potassium Current E K E K [Ca] I ms

4 Neurons... in a nutshell quick tutorial The xonhillock Circuit Positive Feedback Input current Membrane voltage Complexity Real Neurons Conductance based models Integrate and fire models Rate based models Sigmoidal units Linear threshold units Reset Output voltage The xonhillock Circuit Capacitive Divider voltage Given the change V 2, what is V 1? C2 time Q = C 1 V 1 C 2 (V 1 V 2 ) = constant C 1 V 1 C 2 ( V 1 V 2 ) = V1 Q C1 V2 Slope = V 1 = C 2 C1 C2 V 2

5 Positive Feedback xonhillock Circuit Dynamics C fb voltage Iin C m C fb voltage t H t L time C m time I r Positive Feedback = C fb C m C fb V dd t L = C fb C m = C fb V dd I in I in t H = C fb C m I r I in = C fb I r I in V dd Frequency I in Pulse width 1/I r for I r I in Gain Power Dissipation How to make voltage gain The xonhillock circuit is very compact and allows for implementations of dense arrays of silicon neurons BUT it has a major drawback: power consumption During the time when an inverter switches, a large amount of current flows from V dd to Gnd. What s bad about this?

6 Gain more elaborate I&F circuit C fb V pb nother way to make gain I inj C m Vthr V thresh V b C r This circuit is lowpower, has an explicit voltage threshold, and models the refractory period of real spikes. V thr sets the spiking voltage threshold sets the refractory period length sets the pulse width I&F circuit output n ultra lowpower I&F circuit daptation Positive Feedback V thr =2.V =.V 3 =.4V =.36V =.32V I in V adap (V) 2 1. V w =.6V Firing rate (Hz) V sf V spk 1. =.4V Time (s) Input current intensity (arbitrary units) Leak V lk C adap V alk Spiking Threshold V rf Refractory Period

7 Subthreshold behavior and positive feedback n ultra lowpower I&F spike 2. V inj M21 I inj M V adap M16 M6 M7 I fb M3 V o1 M8 M13 V spk M14 I fb = I 1 e κ V in U T 2 V lk M I leak M19 I adap V ca M18 M17 M12 I reset V sf d dt = I inj I leak I fb I adap M1 M2 V in M4 M M9 M1 M11 V o2 I adap = I e κ Vca U T (1 e Vmem U T ) V ca = V ca C p C p C a Membrane potential (V) d dt = I net I 1 e κ2 Vsf Vmem κ2 U T U e T I e κ Vca U T e κ Cp Vmem CpCa U T Time (s) n ultra lowpower array of I&F circuits Si Neuron on ClassChip Rev.1 Neurons M3 M (in) 29 (adap) M4 M7 M11 M14 M18 Vspk 34 (spike) M1 Vmem M9 M12 M M19 36 Cmem 4 Vin Vrst (Vmem) M1 M13 M16 (thr) 27 Neurons M2 Vca (adaplk) 39 M M8 (ref) M Time (s) Time (s)

8 daptation circuits pplications V gs M21 I inj I leak I adap V adap M M16 M6 26 M7 (in) I fb M1 I reset 36 M2 (Vmem) V sf V in M3 M1 M4 M V o1 29 (adap) M8 Vmem M9 Cmem M1 M3 M13 M14 M4 V o2 M6 V spk M7 4 (thr) M9 Vin M1 M11 M12 M13 M14 M M16 Vrst M18 Vspk Basic research M19 34 (spike) Neuromorphic Sensors Multichip sensoractuator systems Computation? M11 27 M17 M2 Vca (ref) V lk M M19 V ca M18 M17 M12 (adaplk) 39 M M8 Next week Silicon Synapses and then... Longterm (analog) storage and multichip systems