$250 prize for checking Jake Cannell's Brain Efficiency

I support this and will match the $250 prize.

Here are the central background ideas/claims:

1.) Computers are built out of components which are also just simpler computers, which bottoms out at the limits of miniaturization in minimal molecular sized (few nm) computational elements (cellular automata/tiles). Further shrinkage is believed impossible in practice due to various constraints (overcoming these constraints if even possible would require very exotic far future tech).

2.) At this scale the landauer bound represents the ambient temperature dependent noise (which can also manifest as a noise voltage). Reliable computation at speed is only possible using non-trivial multiples of this base energy, for the simple reasons described by landauer and elaborated on in the other refs in my article.

3.) Components can be classified as computing tiles or interconnect tiles, but the latter is simply a computer which computes the identity but moves the input to an output in some spatial direction. Interconnect tiles can be irreversible or reversible, but the latter has enormous tradeoffs in size (ie optical) and or speed or other variables and is thus not used by brains or GPUs/CPUs.

4.) Fully reversible computers are possible in theory but have enormous negative tradeoffs in size/speed due to 1.) the need to avoid erasing bits throughout intermediate computations, 2.) the lack of immediate error correction (achieved automatically in dissipative interconnect by erasing at each cycle) leading to error build up which must be corrected/erased (costing energy), 3.) high sensitivity to noise/disturbance due to 2

And the brain vs computer claims:

5.) The brain is near the pareto frontier for practical 10W computers, and makes reasonably good tradeoffs between size, speed, heat and energy as a computational platform for intelligence

6.) Computers are approaching the same pareto frontier (although currently in a different region of design space) - shrinkage is nearing its end

I certainly don’t expect any prize for this, but…

why there has been so little discussion about his analysis since if true it seems to be quite important

…I can at least address this part from my perspective.

Some of the energy-efficiency discussion (particularly interconnect losses) seems wrong to me, but it seems not to be a crux for anything, so I don’t care to spend time looking into it and arguing about it. If a silicon-chip AGI server were 1000× the power consumption of a human brain, with comparable performance, its electricity costs would still be well below my local minimum wage [LW(p) · GW(p)]. So who cares? And the world will run out of GPUs long before it runs out of the electricity needed to run them. And making more chips (or brains-in-vats or whatever) is a far harder problem than making enough solar cells to power them, and that remains true even if we substantially sacrifice energy-efficiency for e.g. higher speed.

If we (or an AI) master synthetic biology and can make brains-in-vats, tended and fed by teleoperated robots, then we (or the AI) can make whole warehouses of millions of them, each far larger (and hence smarter) than would be practical in humans who had to schlep their brains around the savannah, and they can have far better cooling systems (liquid-cooled with 1°C liquid coolant coming out of the HVAC system, rather than blood-temperature which is only slightly cooler than the brain), and each can have an ethernet/radio connection to a distant teleoperated robot body, etc. This all works even when I’m assuming “merely brain efficiency”. It doesn’t seem important to me whether it’s possible to do even better than that.

Likewise, the post argues that existing fabs are pumping out the equivalent of 5 million (5000 maybe? See thread below.) brains per year, which to me seems like plenty for AI takeover—cf. the conquistadors [LW · GW], or Hitler / Stalin taking over a noticeable fraction of humanity with a mere 1 brain each. Again, maybe there’s room for improvement in chip tech / efficiency compared to today, or maybe not, it doesn’t really seem to matter IMO.

Another thing is: Jacob & I agree that “the cortex/cerebellum/BG/thalamus system is a generic universal learning system”, but he argues that this system isn’t doing anything fundamentally different from the MACs and ReLUs and gradient descent that we know and love from deep learning, and I think he’s wrong, but I don’t want to talk about it for infohazard reasons. Obviously, you have no reason to believe me. Oh well. We’ll find out sooner or later. (I will point out this paper arguing that correlations between DNN-learned-model-activations and brain-voxel-activations is weaker evidence than it seems. The paper is mostly about vision but also has an LLM discussion in Section 5.) Anyway, there are a zillion important model differences that are all downstream of that core disagreement, e.g. how many GPUs it will take for human-level capabilities, how soon and how gradually-vs-suddenly we’ll get human-level capabilities, etc. And hence I have a hard time discussing those too ¯\_(ツ)_/¯

Jacob & I have numerous other AI-risk-relevant disagreements too, but they didn’t come up in the “Brain Efficiency” post.

I'm confused at how somebody ends up calculating that a brain - where each synaptic spike is transmitted by ~10,000 neurotransmitter molecules (according to a quick online check), which then get pumped back out of the membrane and taken back up by the synapse; and the impulse is then shepherded along cellular channels via thousands of ions flooding through a membrane to depolarize it and then getting pumped back out using ATP, all of which are thermodynamically irreversible operations individually - could possibly be within three orders of magnitude of max thermodynamic efficiency at 300 Kelvin.  I have skimmed "Brain Efficiency" though not checked any numbers, and not seen anything inside it which seems to address this sanity check.

(Copied with some minor edits from here [LW(p) · GW(p)].)

Jacob's argument in the Density and Temperature [LW · GW] section of his Brain Efficiency post basically just fails.

Jacob is using a temperature formula for blackbody radiators, which is basically irrelevant to temperature of realistic compute substrate - brains, chips, and probably future compute substrates are all cooled by conduction through direct contact with something cooler (blood for the brain, heatsink/air for a chip). The obvious law to use instead would just be the standard thermal conduction law: heat flow per unit area proportional to temperature gradient.

Jacob's analysis in that section also fails to adjust for how, by his own model in the previous section, power consumption scales linearly with system size (and also scales linearly with temperature).

Put all that together, and a more sensible formula would be:

$\frac{q}{A}=\frac{C_1{T}_{S}R}{R^2}=\frac{C_2(T_S-T_E)}{R}$

... where:

• $R$ is radius of the system
• $A$ is surface area of thermal contact
• $q$ is heat flow out of system
• $T_S$ is system temperature
• $T_E$ is environment temperature (e.g. blood or heat sink temperature)
• $C_1,C_2$ are constants with respect to system size and temperature

(Of course a spherical approximation is not great, but we're mostly interested in change as all the dimensions scale linearly, so the geometry shouldn't matter for our purposes.)

First key observation: all the $R$'s cancel out. If we scale down by a factor of 2, the power consumption is halved (since every wire is half as long), the area is quartered (so power density over the surface is doubled), and the temperature gradient is doubled since the surface is half as thick. So, overall, equilibrium temperature stays the same as the system scales down.

So in fact scaling down is plausibly free, for purposes of heat management. (Though I'm not highly confident that would work in practice. In particular, I'm least confident about the temperature gradient scaling with inverse system size, in practice.)

On top of that, we could of course just use a colder environment, i.e. pump liquid nitrogen or even liquid helium over the thing. According to this meta-analysis, the average temperature delta between e.g. brain and blood is at most ~2.5 C, so even liquid nitrogen would be enough to achieve ~100x larger temperature delta if the system were at the same temperature as the brain; we don't even need to go to liquid helium for that.

In terms of scaling, our above formula says that $T_S$ will scale proportionally to $T_E$. Halve the environment temperature, halve the system temperature. And that result I do expect to be pretty robust (for systems near Jacob's interconnect Landauer limit), since it just relies on temperature scaling of the Landauer limit plus heat flow being proportional to temperature delta.

I would contribute $75 to the prize. : ) 

I think Jake is right that the brain is very energy efficient (disclaimer: I'm currently employed by Jake and respect his ideas highly.)  I'm pretty sure though that the question about energy efficiency misses the point. There are other ways to optimize the brain, such as improving axonal transmission speed from the current range 0.5 - 10 meters/sec to more like the speed of electricity through wires ~250,000,000 meters per second. Or adding abilities the mammalian brain does not have, such as the ability to add new long range neurons connecting distal parts of the brain. We can reconfigure the long range neurons we have, but not add new ones. So basically, I come down on the other side of his conclusion in his recent post. I think rapid recursive self-improvement through software changes is indeed possible, and a risk we should watch out for.

I made some long comments below about why I think the whole Synapses [LW(p) · GW(p)] section is making an implicit type error that invalidates most of the analysis. In particular, claims like this:

Thus the brain is likely doing on order ${10}^{14}$ to ${10}^{15}$ low-medium precision multiply-adds per second.

Are incorrect or at least very misleading, because they're implicitly comparing "synaptic computation" to "flop/s", but "synaptic computation" is not a performance metric of the system as a whole.

My most recent comment is here [LW(p) · GW(p)], which I think mostly stands on its own. This thread starts here [LW(p) · GW(p)], and an earlier, related thread starts here [LW(p) · GW(p)].

If others agree that my basic objection in these threads is valid, but find the presentation in the most recent comment is still confusing, I might expand it into a full post.

It's been years since I looked into it and I don't think I have access to my old notes, so I don't plan to make a full entry. In short, I think the claim of "brains operate at near-maximum thermodynamic efficiency" is true. (I don't know where Eliezer got 6 OoM but I think it's wrong, or about some nonobvious metric [edit: like the number of generations used to optimize].)

I should also reiterate that I don't think it's relevant to AI doom arguments [LW(p) · GW(p)]. I am not worried about a computer that can do what I can do with 10W; I am worried about a computer that can do more than what I can do with 10 kW (or 10 MW or so on).

[EDIT: I found one of the documents that I thought had this and it didn't, and I briefly attempted to run the calculation again; I think 10^6 cost reduction is plausible for some estimates of how much computation the brain is using, but not others.]

This comment is about interconnect losses, based on things I learned from attending a small conference on energy-efficient electronics at UC Berkeley in 2013. I can’t immediately find my notes or the handouts so am going off memory.

Eli Yablonovitch kicked off the conference with the big picture. It’s all about interconnect losses, he said. The formula is ½CV² from charging and discharging the (unintentional / stray) "capacitor" in which one "plate" is the interconnect wire and the other "plate" is any other conductive stuff in its vicinity.

There doesn’t seem to be any plan for how to dramatically reduce the stray capacitance C, he said, so we really just need to get V lower (or of course switch to optical interconnects—see this comment of mine [LW(p) · GW(p)], referring to a project whose earlier stages was the topic of one of the conference talks).

The challenge is that conventional transistors need V to be much higher than kT/e, where e is the electron charge, because the V is forming an electrostatic barrier that is supposed to block electrons, even when those electrons might be randomly thermally excited sometimes. The relevant technical term here is “subthreshold swing”. There is a natural (temperature-dependent) limit to subthreshold swing in normal transistors, based on thermal excitation over the barrier—the “thermionic limit” of 60mV/decade at room temperature. He might have said that actual transistors still had room for improvement before hitting that thermionic limit, but anyway the focus of the conference was to do much better than the thermionic limit.

There were a bunch of talks covering different possible approaches. All seemed sound in principle, none seemed ready for primetime, and I haven’t checked what if anything has come of them since 2013.

• You can "increase q" and thereby decrease kT/q. Wait, what? Recall, the electrostatic barrier is qV, where q is the electric charge of the thing climbing the barrier. In a transistor, the thing climbing the barrier is a single individual electron. But one of the presenters was trying to develop mechanical (!) (NEMS) contacts that would switch a connection on and off the old-fashioned way—by actual physical contact between two conductors. The trick is that a mechanical cantilever could easily have a charge of 10e or 100e, and therefore a quite low voltage could actuate it without thermal noise being an issue. Obviously they were having a heck of a time with reliability, stiction and so on, but they suggested that there were no fundamental barriers.
• You can have step-up / step-down voltage converters (I hesitate to use the word “transformers”) between the switches/transistors and the interconnects. I.e., we can send a high-current-at-low-voltage through the wires, then step it up to a low-current-at-high-voltage when it arrives at a transistor gate. Doesn't violate any laws of physics, but how do we do that at nanometer scale? I recall two talks in this category. One involved a stack of two nanofabricated mechanically-coupled piezoelectric blocks of different sizes, in a larger mechanical box. The other involved a ferroelectic layer, which under certain circumstances could act like a capacitor in series whose capacitance was negative. (For the latter, I vaguely recall that I started out skeptical but looked into it and decided that the theory was sound.)
• You can just lower the temperature while redesigning the chip to have a lower-than-ambient (e.g. liquid nitrogen) operating voltage, hence lowering kT/e. I think Eli said that the math did in fact work out—the energy costs of cooling below ambient could be more than paid back. (I think it doesn’t help “in the ideal limit”, but I think he said it would help with actual chips, or something.)
• You can use a different kind of switch that doesn’t involve electrons being thermally excited over a barrier. I recall one talk in this category. It concerned quantum tunneling transistors (a cousin of “backwards diodes”, I think). I recall that their preliminary experimental results did not show subthreshold swing better than the thermionic limit. I think I wasn’t convinced that their approach could beat the thermionic limit even in theory. I believe they weren’t quite sure either. They said “how sharp is the semiconductor band edge” was a basic physics question that, to their dismay, theoretical physicists seemed to have never looked into.

Anyway, that’s my understanding of interconnect losses.

Jacob’s discussion of interconnect losses is quite different, and doesn’t even mention ½CV². There was some elaboration in this thread [LW(p) · GW(p)]. I think that Jacob’s weird (from my perspective) formula was roughly consistent with what you get from ½CV² if you assume that the V is the normal voltage as constrained by the thermionic limit, which is what it is today and what most integrated circuit people would assume it will always be. But at least on paper, some of the above ideas would be able to lower interconnect losses by a lot, like I presume at least 1-2 OOM, if anyone can get them to actually work in practice.

The post is making somewhat outlandish claims about thermodynamics. My initial response was along the lines of "of course this is wrong. Moving on." I gave it another look today. In one of the first sections I found (what I think is) a crucial mistake. As such, I didn't read the rest. I assume it is also wrong.

The original post said:

A non-superconducting electronic wire (or axon) dissipates energy according to the same Landauer limit per minimal wire element. Thus we can estimate a bound on wire energy based on the minimal assumption of 1 minimal energy unit $E_b$ per bit per fundamental device tile, where the tile size for computation using electrons is simply the probabilistic radius or De Broglie wavelength of an electron^[7:1] [LW · GW], which is conveniently ~1nm for 1eV electrons, or about ~3nm for 0.1eV electrons. Silicon crystal spacing is about ~0.5nm and molecules are around ~1nm, all on the same scale.

Thus the fundamental (nano) wire energy is: ~1 $E_b/bit/nm$, with $E_b$ in the range of 0.1eV (low reliability) to 1eV (high reliability).

The predicted wire energy is ${10}^{-19}$J/bit/nm or ~100 fJ/bit/mm for semi-reliable signaling at 1V with $E_b$ = 1eV, down to ~10 fJ/bit/mm at 100mV with complex error correction, which is an excellent fit for actual interconnect wire energy^[8] [LW · GW]^[9] [LW · GW]^[10] [LW · GW]^[11] [LW · GW], [...]

The measured/simulated interconnect wire energies from the citations in the realm of 10s-100s of fJ/bit/mm are a result of physical properties of the interconnects. These include things like resistances (they're very small wires) and stray capacitances. In principle, these numbers could be made basically arbitrarily worse by using smaller (cross sectional) interconnects, more resistive materials, or tighter packing of components. They can also be made significantly better, especially if you're allowed to consider alternative materials. Importantly, this loss can be dramatically reduced by reducing the operating voltage of the system, but some components do not work well at lower voltages, so there's a tradeoff.

... and we're supposed to compare that number with $E_b$/bit/$\lambda$. I might be willing to buy the wide range of $E_b$, but the choice of de Broglie wavelength as "minimal wire element" is completely arbitrary. The author seems to know this, because they give a few more examples of length scales that are around a nanometer. I can do that too: The spacing of conduction electrons in copper ($n^{-1/3}$) is roughly 0.2 nm. The mean free path of electrons in copper is a few nm. None of that matters, because signals do not propagate through wires by hopping from electron to electron. There is a complicated dance of electric field, magnetic field, conducting electrons as well as dielectrics that all work together to make signals move. The equation is asserting none of that matters, and it is simply unphysical. Sorry, there's not a nice way to put that.

The author seems to want us to compare the two equations, but they are truly two different things. I can communicate the same information in a circuit ($E_b$/bit/$\lambda$ held fixed) but dramatically vary the cited "excellent fit" numbers by orders of magnitude by changing their material or lowering their voltage.

The Landauer energy is very, very small compared to just about every other energy that we care about. It is basically a non-factor in all but a few very esoteric experiments. 20 meV is a decent chunk of energy if it is given to every electron in a system, but it is extremely small as a one-off. It is absurd to think that computers, with their resistive wires and leaky gates, are anywhere near perfect efficiency. It is even more absurd to think that brains, squishy beasts that literally physically pump ions across membranes and back, are anywhere near that limit.

Looking through the comments, I now see that another user has correctly pointed out the same mistakes. See here [LW(p) · GW(p)], and the comments under that. Give them the $250. EY also pointed out the absurdity of brains being considered anywhere near efficient. Nice work!

Fwiw I did spotchecked this post at the time, although I did not share at the time (bad priors). Here it goes:

Yes, it’s probably approximately right, but you need to buy it’s the right assumptions. However, these assumptions also make the question somewhat unimportant for EA purposes, because even if the brain is one of the most efficient for its specs, including a few pounds ands watts, you could still believe doom or foom could happen with the same specs, except with a few tons and megawatts, or for some other specs (quantum computers, somewhat soon, or something else, somewhat maybe).

Edit: I just see this somewhat copycat Vaniver’s answer above, so let’s add something more: why I think it’s not the most interesting set of assumptions.

First, to me the brain is primarily optimized for robustness of it’s construction plan over working in a large set of species that all inherit basically the same construction plan, and for multiple (allelic) variants of these plans (with sexual competition, etc). Yes this is probably compatible with optimizing energy in the long run, but not enough to invent rooling balls, if you see what I mean.

Second, and perhaps more important, it assumes that the brain is doing a hard computation. On that, we really have no idea. Like most cognitive neuroscientists from the nineties, I once started a presentation with the widely-accepted trope that our brain is the most complicated thing bla bla. And yes, there are reasons to think that. On the other hand, if resnet-50 can predict most of the variance in neural hemodynamic while viewing the same picture, then maybe current GPU are not that far from the effective computational power of billions of neurons. This shouldn’t be that surprising: after all, biological neurons are not optimized for handling 64 bit-precision and gigahertz clocks.

I think it would be helpful if you specified a little more precisely which claims of Jake's you want spot checked. His posts are pretty broad and not everything in even the ones about efficiency are just about efficiency.

I'm not interested in the prize, but as long as we're spot-checking, this paragraph bothered me:

It turns out that spreading out the communication flow rate budget over a huge memory store with a slow clock rate is fundamentally more powerful than a fast clock rate over a small memory store. One obvious reason: learning machines have a need to at least store their observational history. A human experiences a sensory input stream at a bitrate of about 10^6 bps (assuming maximal near-lossless compression) for about 10^9 seconds over typical historical lifespan, for a total of about 10^15 bits. The brain has about 2∗10^14 synapses that store roughly 5 bits each, for about 10^15 bits of storage. This is probably not a coincidence.

The idea of bitrate * lifespan = storage capacity makes sense for a VHS or DVD but human memory is completely different. Only a tiny percentage of all our sensory input stream makes it through memory consolidation into long-term memory. Sensory memory is also only one type of memory alongside others like semantic, episodic, autobiographical, and procedural (this list is neither mutually exclusive nor collectively exhaustive). Brains are very good at filtering the sensory stream to focus on salient information and forgetting the vast majority of the rest. This results in memory that is highly compressed (and highly lossy).

Because brain memory is so different than simple storage, this napkin math is roughly analogous to computing body mass from daily intake of air, water, and food mass and neglecting how much actually gets stored versus ultimately discarded. You can do the multiplication but it's not very meaningful without additional information like retention ratios.

I sort of dismiss the entire argument here because based on my understanding, the brain determines the best possible outcomes given a set of beliefs (aka experiences) and based on some boolean logic based on sense of self, others, and reality, the result in actions will be derived from quantum wave function collapse given the belief set, current stimulus, and possible actions. I'm not trying to prove why I believe they are quantum here, except to say, to think otherwise is just saying quantum effects are not part of nature and not part of evolution. And that seems to be what would need to be proven given how efficient evolution is and how electrical and non-centered our brains are. So determining how many transistors would be needed and how much computational depth is needed is sort of moot if we are going to assume a Newtonian brain since I think we're solving for the wrong problem. AI will also beat us with normal cognition, but emotion and valence only come with the experiences we have and the beliefs we have about them and that will be the problem with AI until we approach the problem correctly.

I hope that my two comments[1] [LW(p) · GW(p)][2] [LW(p) · GW(p)] helped you save $250.