Aim of neuromorphic engineering: o Design and construct physical models of biological neural networks that replicate:  robust computation  adaptability  learning The Memristor (memory resistor): o A passive, two-terminal electrical device first theorized by Leon Chua in [1] o Its resistance can be modified by passing current through the device. o When the current stops, the memristor remembers its state of resistance indefinitely, making it an attractive option for modeling neural synapses. [3] IntroductionResultsConclusionReferences The Brain on a Chip: Modeling Neural Plasticity Using Memristors Jack Kendall, Anthony DeAugustino - University of Florida, Gainesville FL Current very large scale integration (VLSI) neural systems: o Based on silicon transistors. o Much less efficient than biological brains in terms of: [4]  power consumption  connectivity  neural density The use of Memristors can effectively: o Model excitatory and inhibitory synapses:  pre and post spike neurons o Uses a fraction of the area required by current CMOS technology. o Requires less power during dynamic operation. [5] Figure 1: Oxygen vacancies (+) create high-conductivity regions in memristive titanium dioxide. When a voltage is applied, the oxygen vacancies drift, changing the overall resistance of the device. When the voltage is removed, the oxygen vacancies remain stationary, and the device maintains its current state. [2],[3] Figure 2: Memristor crossbar array. In the context of neuromorphic hardware, vertical electrodes represent input to an array of neurons, while horizontal electrodes represent output from a separate array of neurons. At each intersection is a memristive synapse. [3] Figure 4: Spike-timing-dependent plasticity (STDP) of A) biological synapse, and B) memristive synapse. The horizontal coordinate is the relative timing of spikes, ΔT, between pre and post-synaptic neurons, and the vertical coordinate is the change in strength of the synapse, ξ (ΔT). [5] Hebbian theory of learning: o The most successful theory of learning, “neurons that fire together, wire together.” Spike-timing-dependent-plasticity (STDP): o If a neuron consistently fires just before another, the synapse between them is strengthened. o If a neuron fires just after the other, then the synapse is weakened. o Replicated in memristive synapses by careful tuning of spike waveforms from the artificial neurons. [5] Figure 5: Actual memristive devices have voltage thresholds, below which no change in resistance will be observed. This can be exploited to produce STDP by ensuring that the threshold is only crossed when both pre and post synaptic neurons fire at approximately the same time. [5] Figure 6: In addition to modeling synapses, memristors can also model the dynamics of neural spiking. Here, the standard Hodgkin-Huxley model (a) is compared with a memristive model (b). The memristors replace the sodium and potassium conductances, G Na and G K, which are voltage and time-dependent. [6] Recent developments using memristive neural plasticity in the form of STDP learning is creating an explosion of interest and research in the technology. Areas of growth: o Discovering more material systems displaying memristive behavior, o Shifting the focus from one of characterization to one of implementation. o Researching the best way to integrate memristor arrays with CMOS circuits One thing seems clear: the road to truly powerful neuromorphic hardware is paved with memristors. Figure 7: Visualization of a memristor crossbar array (left) compared with an SEM image of a CMOS integrated array (right). The device shown is an example of resistive random-access memory (RRAM), which is expected to replace flash memory in the near future. Image courtesy of Crossbar, Inc. [1] Chua, L. (1971). Memristor - The Missing Circuit Element, CT-18(5), 507–519. [2] Strukov, D. B., Snider, G. S., Stewart, D. R., & Williams, R. S. (2008). The missing memristor found. Nature, 453(7191), 80–3. [3] Williams, R. S. (n.d.). How We Found The Missing Memristor. Spectrum, IEEE, 45(12), 28–35. [4] Sarpeshkar, R. (1998). Analog Versus Digital: Extrapolating from Electronics to Neurobiology. Neural Computation, 10(7), 1601– [5] Zamarreño-Ramos, C., Camuñas-Mesa, et al. (2011). On spike-timing- dependent-plasticity, memristive devices, and building a self-learning visual cortex. Frontiers in Neuroscience, 5(March), [6] Thomas, A. (2013). Memristor-based neural networks. Journal of Physics D: Applied Physics, 46(9), /46/9/093001