It takes two neurons to ride a bicycle (2004)
fermatslibrary.com
fermatslibrary.com
The simulation is so simplified that I see no terms for the control of pedaling. Riding a real bicycle isn't just about steering and leaning a bit. You need to propel the bicycle a certain amount.
The paper buries this in the following:
>Although the two-neuron network controller works well for a range of speeds, one thing the controller does not do is to try to dampen the instabilities that can arise when riding too slowly or in too sharp of a turn. (This would probably require a third neuron that isdedicated to this task.)
My impression from my vague recollection of learning to ride a bike (and the scattered times over the years I've seen others try) is that a pretty huge part of the battle is just learning to trust that going faster is literally how to avoid falling over, when the natural inclination of someone worried about that is to slow down.
I think is where it refers to it.
Possible, but more complex than most appreciate. Pushing a pedal down shifts the rider's center of gravity over that pedal, requiring the bike to lean in the opposite direction to maintain a straight line. This done by the rider counter-steering to command that angle. Watch in the video how the front wheel and lean angle alternates left-right in time with the pedal pushes. Once at speed, the gyroscopic forces of the front wheel mean the rider doesn't need as much lean angle, so the wobbles get less and less. Compare an accelerating motorcycle where the rider doesn't shift weight and therefore doesn't need to wobble the front tire.
In addition, it is controlling a coupled 3D system (which is unstable). This is much more than 3 PID controllers.
This is just totally wrong. Stabilizing an unstable system is usually the first goal of controller design. Different systems do require different controllers, but pid is _very often_ perfectly adequate. It’s probably the most used controller structure in general.
Actually, the title of this paper is unproven. We have not ruled out the possibility that a single neuron could ride a bicycle.
Previously:
- https://news.ycombinator.com/item?id=19196664 (25 comments)
- https://news.ycombinator.com/item?id=16215130 (88 comments)
With dendritic compartments, this seems like a waste of a perfectly good neuron that we could productively use elsewhere. ;)
Note that a SINGLE neuron can compute nonlinear functions like XOR.
Shameless plug: If anyone is interested, I did a post a while back on how neurons can act as logic gates:
https://blog.typeobject.com/posts/2025-neural-logic-gates/
This article builds on the first and creates a half adder out of neurons:
I started going down the path of building a ripple carry adder already (which seems to work fine). Then I was going to try for a full on ALU, then some sort of ISA that sits on top of it all.
I have no idea what the end result will look like if it all comes together. Hopefully I'll find some weird primitives along the way. :D
It's very hand-wavy, but I'm kinda hoping I can somehow have a machine manually constructed out of neurons that can naturally interact with one built with looser hebbian learning rules.
On the interaction, one system uses a clock signal / metronome and the other is all cascades. The clock signal is like a metronome calibrated to the duration of the longest cascade = "critical path." It seems clear that these can interact smoothly, as one simply has the training wheels of the clock, while the other is about progression-via-propagation.
I asked how many neurons he was was using: zero, it turns out.
Have the authors ever ridden a bicycle/motorcycle? The handlebars are not the primary controls. As evidence, I say watch this clip. Handlebars are not needed for cornering. Into a 45* lean angle, standing up on the pegs. Hands are optional.
I indeed balked at this, finding both of those sentences wildly incorrect, as someone both having been taught as well as having taught multiple people myself.
Also: https://ciechanow.ski/bicycle/
It seems that it is something that is forever doomed to be forgotten and then rediscovered over and over.
https://en.wikipedia.org/wiki/Countersteering https://en.wikipedia.org/wiki/Dihedral_(aeronautics)
Of course any realistic bike+rider model would have a lot more degrees of freedom and require a lot more neurons to control.
- There Is No Antimemetics Division
It's somewhat important to consider the inputs, because if you want to make a classifier that can classify "inside circle vs outside circle" but the network needs to derive the nonlinearity itself, then you end up needing a more complex network
Eg on the playground^, see how many neurons you need to train a circle without using more than x1 and x2?
And yet, if you give the network x1^2 and x2^2, it can solve it with minimal additional neurons.
^ https://playground.tensorflow.org/#activation=tanh&batchSize...
Observation: 2 neurons, 2 wheels. One for each?
A friend in college told me of a research project that had managed to balance a simulated inverted pendulum in 2D using 25 neurons and back propagation. But I had done this exact problem with conventional state space controls using only 5 summations (the equivalent of 5 neurons).
After I finish patting myself on the back, you then wonder what it would take for that 25 neuron solution to keep optimizing down the theoretical 5 neuron solution? The article is an interesting approach to that problem.
The paper they reference used 3456 input neurons and 9 output neurons, with no hidden nodes. They designed their input and output differently, so it's not a direct comparison. The optimized solution has 17 inputs, 2 outputs, and 2 hidden nodes. That's a massive level of optimization.