What is a memristor? The resistor with memory behind neuromorphic and bio-hybrid chips

A memristor, short for memory resistor, is a two-terminal circuit element whose resistance depends on the current that has passed through it and persists without power. Leon Chua proposed the memristor in 1971; HP Labs linked it to a physical device in 2008. Because its conductance changes with use, a memristor can act as an artificial synapse.

Key takeaways

• Chua (1971, IEEE Transactions on Circuit Theory) described the memristor as a missing fourth basic circuit element, relating charge and magnetic flux.
• Strukov and colleagues at HP Labs (2008, Nature) reported a titanium dioxide device that behaved as a memristor.
• Memristors store information as resistance and can compute where data is stored, a key idea in neuromorphic computing.
• Memristive devices have reproduced synapse-like learning, including spike-timing-dependent plasticity (Jo et al., 2010).
• Serb et al. (2020) used memristive synapses to connect silicon neurons with a living rat hippocampal neuron.

How does a memristor work? #

Classical circuit theory has three passive two-terminal elements, each linking two of the four basic electrical quantities: voltage, current, charge and magnetic flux.

Chua noticed that one pairing, flux and charge, had no element, and argued on grounds of symmetry that a fourth element should exist. Its defining feature is that its resistance (called memristance) is not fixed but depends on how much charge has passed through it. Chua and Kang (1976, Proceedings of the IEEE) generalized the idea to a broader class of “memristive devices and systems.”

The pinched hysteresis loop #

The fingerprint of a memristor is its current-voltage curve. Drive it with an alternating voltage and the curve traces a loop that is pinched at the origin: when voltage is zero, current is zero, but the path going up differs from the path coming down. That gap is memory. The device’s present behavior depends on what happened before.

What did HP Labs find in 2008? #

For decades, the memristor was a theoretical curiosity. In 2008, Strukov, Snider, Stewart and Williams at HP Labs reported in Nature that a thin film of titanium dioxide between two electrodes behaved as a memristor. Their model treated the film as two regions, one with oxygen vacancies that conduct well and one without. Applied voltage moves the boundary between them, changing the overall resistance, and the boundary stays put when the voltage is removed.

Not everyone accepts that such devices are memristors in Chua’s strict sense. Vongehr and Meng (2015, Scientific Reports) argued that the missing memristor “has not been found.” For this reason many researchers use the broader term “memristive device” for resistive switching components.

Why do memristors matter for neuromorphic computing? #

Conventional computers keep memory and processing apart and spend much of their energy moving data between them. Memristors offer a different arrangement in which storage and computation share the same device.

Synapses in silicon #

A biological synapse has a strength that changes with activity and persists, which is the basis of synaptic plasticity and learning. A memristor has a conductance that changes with applied pulses and persists. The parallel is direct:

• Weight storage. Conductance plays the role of synaptic weight.
• Potentiation and depression. Pulses of one polarity raise conductance; the other polarity lowers it, echoing long-term potentiation and depression.
• Timing-dependent learning. Jo et al. (2010, Nano Letters) reported a nanoscale memristor device that showed spike-timing-dependent plasticity.
• Non-volatility. The weight survives without power.

Computing in memory #

Arrange memristors in a crossbar, a grid of rows and columns with a device at each crossing, and the array can multiply a vector by a matrix in one step. Input voltages on the rows, multiplied by each device’s conductance and summed as currents along each column, follow Ohm’s and Kirchhoff’s laws. This is the core operation of neural networks. Prezioso et al. (2015, Nature) trained a small integrated neural network built from metal-oxide memristors in a crossbar to classify simple patterns, an early demonstration of training directly in memristive hardware.

Memristors can also act as physical reservoirs. Tanaka et al. (2019, Neural Networks) review memristive devices among the substrates used for physical reservoir computing, where the device’s history-dependent dynamics supply the fading memory a reservoir needs. That connects memristors to echo state networks and to spiking neural networks implemented in hardware.

How is a memristive neural network built and trained? #

A typical memristive network follows a sequence that mirrors software neural networks, with the weights held in physical devices.

1. Map weights to conductances. Each synaptic weight is assigned to one device, or to a pair of devices so that negative weights can be represented as a difference.
2. Apply inputs as voltages. Input values are encoded as voltage levels or pulse lengths on the crossbar rows.
3. Read outputs as currents. Column currents give the weighted sums, which pass to neuron circuits.
4. Update weights with pulses. Training sends programming pulses that nudge conductances up or down, either following a rule computed off-chip or a local rule such as spike-timing-dependent plasticity.
5. Verify and correct. Because devices are imprecise, systems often read back conductances and reprogram them.

The appeal is that steps 2 and 3 happen in place, without fetching weights from a separate memory, which is the source of much of the energy cost in conventional hardware.

How can memristors connect living neurons to chips? #

The same properties that make memristors synapse-like make them candidates for linking biology and electronics. Serb and colleagues reported in Scientific Reports (2020) a set of “memristive links between brain and silicon spiking neurons.” According to the paper:

1. A memristor paired with a titanium oxide microelectrode connected a silicon neuron to a neuron of the rat hippocampus, delivering weighted stimuli that produced responses resembling excitatory postsynaptic potentials.
2. A reverse link, from the biological neuron back to silicon, used a microelectrode-memristor pair.
3. In a three-neuron brain-silicon network, the memristive synapses underwent long-term potentiation or depression driven by neuronal firing rates.

This is a small system, but it shows a path toward adaptive interfaces in which the connection between tissue and electronics learns rather than staying fixed. That matters for brain-computer interfaces and for bio-silicon hybrid computing, where living neurons on a microelectrode array exchange signals with electronic circuits.

Memristors versus living synapses #

What are the limitations of memristors? #

• Variability. Devices differ from one another and from cycle to cycle.
• Drift. Stored resistance can change over time.
• Limited precision. Many devices hold only a modest number of reliable levels.
• Endurance. Repeated switching can wear devices out.
• Array effects. Crossbars suffer from sneak currents and wire resistance at scale.

Living neurons offer an alternative route to adaptive, energy-efficient computing, one where the synapses are real. We compare the two paths in our article on biocomputing versus silicon energy efficiency. At Organoid Programming we are building the software layer for the living side of that comparison.

Conclusion #

A memristor is a resistor with memory: its resistance depends on the charge that has passed through it and persists without power. Predicted by Chua in 1971 and linked to devices in 2008, memristors now underpin research into in-memory and neuromorphic computing, and early experiments show memristive synapses can even link silicon to living neurons, bringing electronics a step closer to biocomputing.

Frequently asked questions

What is a memristor in simple terms?

A memristor is an electronic component that remembers how much current has passed through it. Push current one way and its resistance goes down; push it the other way and resistance goes up. When the power is switched off, it keeps its last resistance. That memory makes it useful for storing data and for mimicking synapses, whose strength also changes with use.

Who invented the memristor?

Leon Chua proposed the memristor theoretically in 1971 in IEEE Transactions on Circuit Theory, describing it as a missing fourth basic circuit element alongside the resistor, capacitor and inductor. In 2008, Strukov, Snider, Stewart and Williams at HP Labs reported in Nature that a titanium dioxide thin-film device behaved as a memristor, in a paper titled The missing memristor found.

Why are memristors compared to synapses?

A biological synapse has a strength that changes with activity and persists afterward, which is how networks of neurons learn. A memristor has a conductance that changes with the voltage pulses applied to it and persists afterward. Jo and colleagues reported in Nano Letters in 2010 a nanoscale memristor that showed spike-timing-dependent plasticity, a learning rule seen in real synapses.

Is a memristor the same as RRAM?

They overlap heavily. Resistive random-access memory (RRAM) uses devices whose resistance switches between states when voltage is applied, and many such devices are described as memristors or memristive devices. Whether every resistive switching device is a memristor in Chua’s strict mathematical sense has been debated, so researchers often use the broader term memristive device.

How are memristors used with living neurons?

Memristors can serve as adaptive links between biological and electronic neurons. Serb and colleagues reported in Scientific Reports in 2020 a network in which memristive synapses connected silicon spiking neurons to a neuron of the rat hippocampus, in both directions, and the memristive connections underwent long-term potentiation or depression driven by neuronal firing rates.

What are the main challenges with memristors?

Memristive devices vary from one to another and from one switching cycle to the next, and their resistance can drift over time. Many have only a limited number of reliable states and finite endurance. Large crossbar arrays also suffer from sneak currents and wire resistance. These issues make it hard to build large, precise analog computing systems from them.

Sources

1. Chua (1971). Memristor: the missing circuit element. IEEE Transactions on Circuit Theory.
2. Chua & Kang (1976). Memristive devices and systems. Proceedings of the IEEE.
3. Strukov, Snider, Stewart & Williams (2008). The missing memristor found. Nature.
4. Jo et al. (2010). Nanoscale memristor device as synapse in neuromorphic systems. Nano Letters.
5. Prezioso et al. (2015). Training and operation of an integrated neuromorphic network based on metal-oxide memristors. Nature.
6. Serb et al. (2020). Memristive synapses connect brain and silicon spiking neurons. Scientific Reports.
7. Vongehr & Meng (2015). The missing memristor has not been found. Scientific Reports.
8. Tanaka et al. (2019). Recent advances in physical reservoir computing: a review. Neural Networks.