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Analog Neural Networks

September 19, 2022

Computing machines existed before the electronic analog computers of the early 20th century and the digital computers of the late 20th century and beyond. As evidenced by the attempt of Charles Babbage (1791-1871) in the creation of his Analytical Engine in the early 19th century, mechanical systems were one means of computation available to earlier generations. One interesting mechanical computing device was the wheel-on-disk integrator, invented by B.H. Hermann in 1814.[1]

Disk integrator

Two versions of the mechanical disk integrator. Left, wheel-on-disk integrator, invented by B.H. Hermann in 1814 and used by Vannevar Bush (1890-1974) in the MIT differential analyzer.[2] Right, a ball-on-disk version invented by Hannibal Ford (1877–1955) in 1919.[3] The mechanical principal is that the wheel or ball will spin faster at the outer edge of the disk. (Created by the author using Inkscape. Also uploaded to Wikimedia Commons. Click for larger image.)

The wheel-on-disk integrator was used by Vannevar Bush (1890-1974) in the MIT differential analyzer. Differential analyzers were impressive enough to be included in two science fiction films; namely, Earth vs. the Flying Saucers (1956, Fred F. Sears, Director)[4] and When Worlds Collide (1951, Rudolph Maté, Director)[5]. As electronics developed, especially stable operational amplifiers such as the Philbrick K2-W, analog computation was transferred from the mechanical to the electronic realm. An operational amplifier integrator is shown in the figure.

Operational amplifier integrator

An operational amplifier integrator.

In operation, the capacitor is discharged to make the output voltage zero at time zero. Having the same value resistor in the non-inverting input eliminates drifting caused by input bias currents.

(Created using Inkscape.)

I'm a member of the baby boomer generation; so, digital computing wasn't part of my undergraduate physics education. Instead, I had several laboratory exercises in analog computation, one of which was the calculation of the trajectory of projectiles launched on Jupiter and on Earth. The results of the calculation, as displayed on an x-y chart recorder, were as you would expect from the 2.4 times difference in surface gravity between the planets.

Deep neural networks are the present darlings of computer science, having enabled such things as speech recognition and its companion technology, natural language processing, image recognition, and e-commerce recommender systems. These are presently implemented using considerable computer hardware and at a substantial energy cost. It's estimated that global data centers presently consume about 200 terawatt-hours annually, which is the electrical usage of 16 million United States households (11,000 kilowatt hours each per year). Is there a better way?

Feral Network

A decade ago, I created this Feral Network graphic as a counterpoint to neural networks.

Feel free to use this image for non-commercial purposes, such as a personal coffee mug or T-shirt.

(Created by the author using Inkscape. Click for larger image.)

The human brain does wonderful things using an energy budget of only twenty watts (Architects once estimated an auditorium's cooling requirement by considering that each person is the equivalent of a 75 watt incandescent light bulb. Our rampant rotundness has scaled this up to 100 watts). Neurons and synapses in the human brain operate through chemical action mediated by action potentials of about 100 millivolts that allow millisecond processing.[6]

Artificial solid state neurons are not limited by such a voltage constraint, and they can be fabricated at the nanoscale at a size that's a thousand times smaller than their biological counterparts.[6] Researchers at the MIT-IBM Watson AI Lab of the Massachusetts Institute of Technology (Cambridge, Massachusetts) have developed prototype nanoscale high voltage protonic programmable resistors that are 10,000 times faster than biological synapses, and these could form the basis for an analog neural network.[6-7] Such resistors would be a key building block for an analog deep learning neural network, just as transistors are for the digital version.[7]

The energy-efficient shuttling and intercalation of protons causing the resistance modulation are on a nanosecond timescale at room temperature.[6] The resistors are compatible with standard silicon processing, and they have symmetric, linear, and reversible modulation characteristics with a twenty-fold dynamic range of conductance states, thereby exceeding all performance characteristics of their biological counterparts.[6]

Says senior author of the paper describing this research, Bilge Yildiz, a professor of Materials Science and Engineering at MIT,
"The working mechanism of the device is electrochemical insertion of the smallest ion, the proton, into an insulating oxide to modulate its electronic conductivity. Because we are working with very thin devices, we could accelerate the motion of this ion by using a strong electric field, and push these ionic devices to the nanosecond operation regime."[7]

Details of the MIT artificial synapse

Details of the MIT artificial synapse. Left and center are proton-loaded structures of tungsten trioxide (WO3), a candidate synapse material investigated by the MIT research team in a 2020 study.[8] On the right is an artificial synapse in which ions of hydrogen (protons, shown as H+) can migrate back and forth between a hydrogen reservoir material (R) and tungsten trioxide (A) by passing through an electrolyte layer (E). The movement of the ions is controlled by the polarity and voltage applied through gold electrodes (S and D), and this changes the electrical resistance of the device. (Left image and right image courtesy of MIT and distributed under the Creative Commons Attribution Non-Commercial No Derivatives license. Click for larger image.)

The artificial synapses operate at voltages a hundred times higher than those for biological synapse, and this enables faster ionic conduction.[7] Lead author and MIT postdoctoral researcher, Murat Onen, explains that this increase in speed will lead to an advancement in neural networks. "Once you have an analog processor, you will no longer be training networks everyone else is working on. You will be training networks with unprecedented complexities that no one else can afford to, and therefore vastly outperform them all. In other words, this is not a faster car, this is a spacecraft."[7]

Phosphorus-doped silica, inorganic phosphosilicate glass, is one material that the MIT team has used for the resistors, and this enables ultrafast proton movement through a multitude of nanometer-sized pores that provide paths for proton diffusion at high voltages and has been found to be robust for millions of cycles.[7] Other studied materials are intercalation compounds similar to those found in lithium-ion batteries.[8] One of these is tungsten trioxide (WO3), as shown in the figure above.[8] Just after finishing this article, I noticed that the ever educational Sabine Hossenfelder (b. 1976) posted a YouTube video relevant to this topic.[9]


  1. A. Ben Clymer, "The Mechanical Analog Computers of Hannibal Ford and William Newell," IEEE Annals of the History of Computing, vol. 15, no. 2 (1993), pp. 19-34, https://doi.org/10.1109/85.207741. Avaiable as PDF file here.
  2. V. Bush and H. Hazen, "The differential analyzer: a new machine for solving differential equations," Journal of the Franklin Institute, vol. 212, no. 4 (October, 1931), pp. 447-488https://doi.org/10.1016/S0016-0032(31)90616-9. Avaiable as PDF file here.
  3. H.C. Ford, "Mechanical movement," U.S. Patent No. 1,317,915, October 7, 1919 (via Google Patents.
  4. Earth vs. the Flying Saucers (1956, Fred F. Sears, Director)
  5. When Worlds Collide (1951, Rudolph Maté, Director)
  6. Murat Onen, Nicolas Emond, Baoming Wang, Difei Zhang, Frances M. Ros, Ju Li, Bilge Yildiz and Jesús A. del Alamo, "Nanosecond protonic programmable resistors for analog deep learning," Science, vol. 377, no. 6605 (July 28, 2022), pp. 539-543, DOI: 10.1126/science.abp8064.
  7. Adam Zewe, "New hardware offers faster computation for artificial intelligence, with much less energy," MIT Press Release, July 28, 2022.
  8. David L. Chandler, "Engineers design a device that operates like a brain synapse," MIT Press Release, June 19, 2020 .
  9. Sabine Hossenfelder, "What's the difference between a brain and a computer?" YouTube Video, July 30, 2022.

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