1. HYBRID COMPUTATION WITH SPIKES Rahul Sarpeshkar Robert J. Shillman Associate Professor MIT Electrical Engineering and Computer Science Banbury Sejnowski talk 5/18/04 Supported by the Swartz Foundation and NSF

2. SUMMARY 1.I show how analog processing instead of traditional A-D-then-DSP processing can result in huge wins in energy efficiency, for example, in a bionic ear processor for the deaf that is soon to go commercial and that is likely to be unbeatable even at the end of Moore’s law. 2. Analog is more efficient than digital at low precision and vice versa. Hybrid computation can be more efficient than either because it is based on a better tradeoff between robustness and efficiency in computational systems compared with the analog and digital extremes. 3.Spike count is digital, interspike intervals are analog, so spikes are natural for hybrid computing. I show how spikes can be used to create ‘carries’ and create a distributed representation of a real number. 4.I describe the architecture of an HSM, a Hybrid State Machine built with spikes, which generalizes the notion of Finite State Machines (FSMs) in digital computation to the hybrid domain. 5. One of these HSMs, a two-spiking-neuron HSM, is among the world’s most energy- efficient A/D converters and is the first time-based converter that achieves linear scaling in conversion time with bit precision instead of exponential. It works by converting spike-time information to spike-count information in a recursive fashion with an underlying clock providing synchrony. 6.Every spike matters in these computations but there can be some redundancy for error correction. 7.A synthetic engineering approach that exploits the analog and digital aspects of spikes for efficient computation may provide new ideas for how spikes could be used in neurobiology and complement traditional analytic approaches.

3. 1 2 3 6 7 4 55 The charge from the electrode stimulation pulses is conducted to the spiral ganglion cell and activation occurs. THE BIONIC EAR

4. ULTRA-LOW-POWER ANALOG PROCESSOR FOR BIONIC EARS (COCHLEAR IMPLANTS) AND SPEECH RECOGNITION

6. NOISE IN ANALOG DEVICES AND SYSTEMS

9. HOW MUCH ANALOG DO YOU DO BEFORE YOU GO DIGITAL?

11. Example: Is the number of input pulses greater than 2 11 -1?

12. “Analog” DSP:A Hybrid Multiplier We let Q=I*T do the elementary multiplication Kirhchoff’s current law does addition Spiking neuron circuits perform carries in ripple-carry fashion. Precision can be adapted with speed

13. FINITE STATE MACHINEHYBRID STATE MACHINE (HSM) THE HYBRID STATE MACHINE (HSM) 1.“Spike” = Pulse or Digital Event. 2.Each discrete state in the HSM is like a ‘behavior’ in which a rapidly reconfigurable analog dynamical system changes its parameters or topology.

14. An HSM for Successive Approximation A/D Conversion

15. SPIKING A-TO-D CONVERTER 1. Among the world’s most energy-efficient converters. The first time- based converter that achieves a linear scaling in conversion time with bit precision instead of exponential scaling. 2. Underlying Clock provides synchrony for operation. 3. Spike-time and spike-count (1 or 0) codes toggle back and forth between each neuron. Thus, count and time codes are simultaneously present. 4. The count code (s) may be viewed as performing successively more precise digital signal restoration on the original analog input timing signal. 5. Every spike matters in the computation. 6. Can build similar HSMs for pattern recognition, learning, and analog memory.

16. SUMMARY 1.I show how analog processing instead of traditional A-D-then-DSP processing can result in huge wins in energy efficiency, for example, in a bionic ear processor for the deaf that is soon to go commercial and that is likely to be unbeatable even at the end of Moore’s law. 2. Analog is more efficient than digital at low precision and vice versa. Hybrid computation can be more efficient than either because it is based on a better tradeoff between robustness and efficiency in computational systems compared with the analog and digital extremes. 3.Spike count is digital, interspike intervals are analog, so spikes are natural for hybrid computing. I show how spikes can be used to create ‘carries’ and create a distributed representation of a real number. 4.I describe the architecture of an HSM, a Hybrid State Machine built with spikes, which generalizes the notion of Finite State Machines (FSMs) in digital computation to the hybrid domain. 5. One of these HSMs, a two-spiking-neuron HSM, is among the world’s most energy-efficient A/D converters and is the first time-based converter that achieves linear scaling in conversion time with bit precision instead of exponential scaling. It works by converting spike-time information to spike-count information in a recursive fashion with an underlying clock providing synchrony. 6.Every spike matters but there can be some spike redundancy for error correction. 7.A synthetic engineering approach that exploits the analog and digital aspects of spikes for efficient computation may provide new ideas for how spikes could be used in neurobiology and complement traditional analytic approaches.