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The Brain on a Chip:
Modeling Neural Plasticity Using Memristors
• 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 1971. [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]
• 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 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]
• 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
Figure 2: Memristor crossbar array. In the context of
technology.
neuromorphic hardware, vertical electrodes represent
o Requires less power during dynamic operation. [5]
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 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, GNa and GK, which are
voltage and time-dependent. [6]
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]
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.
References
Conclusion
Results
Introduction
Jack Kendall, Anthony DeAugustino - University of Florida, Gainesville FL
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.
http://doi.org/10.1038/nature06932
[3] Williams, R. S. (n.d.). How We Found The Missing Memristor. Spectrum, IEEE,
45(12), 28–35. http://doi.org/10.1109/MSPEC.2008.4687366
[4] Sarpeshkar, R. (1998). Analog Versus Digital: Extrapolating from Electronics to
Neurobiology. Neural Computation, 10(7), 1601–1638.
http://doi.org/10.1162/089976698300017052
[5] Zamarreño-Ramos, C., Camuñas-Mesa, et al. (2011). On spike-timingdependent-plasticity, memristive devices, and building a self-learning visual
cortex. Frontiers in Neuroscience, 5(March), 26.
http://doi.org/10.3389/fnins.2011.00026
[6] Thomas, A. (2013). Memristor-based neural networks. Journal of Physics D:
Applied Physics, 46(9), 093001. http://doi.org/10.1088/00223727/46/9/093001