Nice article, but the methods they used seem more like they just hand wrote a function for the task and called the function neurons based on how it was implemented. It is encouraging though that a simple network can be found for a complicated task like this, kind of like the Tiny Recursive Model that came out last year.
> The output of the first neuron is fed into the second neuron, whose outputis connected to an actuator which applies the specified amount of torque to the handlebars. As inputs to the network, we provide the desired heading θ_d, as well as the current heading θ and the degree to which the bicycle is currently leaning γ, along with their derivatives
˙θ and ˙γ.
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.
It seems like it should say "It takes Two Neurons to Steer an already moving Bicycle".
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.)
They say 'damping instabilities' but it is way more than that, because as anyone who has learned to ride a bike knows, the hard part is getting started at that zero point of forward velocity - how to apply torque to the crank at the same time as compensating with the steering to balance at such low momentum. It's not a trivial solution to 'damping instabilities' when getting going in the first place is the most difficult part (as any 5 year old child will demonstrate).
> Riding a real bicycle isn't just about steering and leaning a bit. You need to propel the bicycle a certain amount.
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.
> U-2200, a non-corporeal entity claiming to be the prehistoric Johorean god of forgetting how to ride a bicycle, engages Quinn in a conversation, suggesting she take a month off in Barbados, drink alcohol, or resign from the Organization.
>> The actions only differ in how the handlebars are pushed at the first instant: pushed left, pushed right, or not touched.
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.
The author is using an oversimplified model of a bicycle without a rider. This hypothetical bicycle robot has no way to shift the center of gravity and has to rely on handlebars to indirectly control the lean angle.
Of course any realistic bike+rider model would have a lot more degrees of freedom and require a lot more neurons to control.
This reminds me of a sexist joke. But seriously... This must be much much more... Even I noticed that for example you can lean forward to have better turning curve
This is an interesting way to think about how to get to a minimal form of a complex system.
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.
I would guess this is also applicable to a segway or any balancing vehicle? Balancing is a matter of steering/driving in the opposite direction of a lean, while steering or moving is adding a bias to where 'upright' is to move in a certain direction without falling over. It's just a segway goes back/forward where a bike goes left/right.
26 comments
[ 2.5 ms ] story [ 40.4 ms ] threadWith 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:
https://blog.typeobject.com/posts/2026-timing-is-the-bit/
Observation: 2 neurons, 2 wheels. One for each?
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...
Previously:
- https://news.ycombinator.com/item?id=19196664 (25 comments)
- https://news.ycombinator.com/item?id=16215130 (88 comments)
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:
They say 'damping instabilities' but it is way more than that, because as anyone who has learned to ride a bike knows, the hard part is getting started at that zero point of forward velocity - how to apply torque to the crank at the same time as compensating with the steering to balance at such low momentum. It's not a trivial solution to 'damping instabilities' when getting going in the first place is the most difficult part (as any 5 year old child will demonstrate).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.
- There Is No Antimemetics Division
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.
https://www.youtube.com/shorts/Gyt9DLfYOdU
Of course any realistic bike+rider model would have a lot more degrees of freedom and require a lot more neurons to control.
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.
I asked how many neurons he was was using: zero, it turns out.