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).
I'm don't think it's possible to start a bike by pedalling with zero forward momentum. You will fall over. You need to kick off - start pedalling with the bike already moving forward. So you're right, and a third neuron is certainly not sufficient. You need legs, too, and arms, and a torso, and motor neurons, and respiration/metabolism. Clearly, the paper has no practical application; if you need to ride a bike, it's far cheaper to hire a human to do it.
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.
I think that's basically right. The "neurons" framing feels a bit loose here; it's more like a very compact hand-designed controller expressed in neural-network-ish terms
Research question: does it make sense to make a new family of logic gates using neurons? My intuition says there is a rich texture/fabric to uncover here. The best analogy on hand right now is legos: rather than 2-knotch legos [standard gates like NAND, XOR] what about some sort of new, irreducible gates that are bigger "legos"? Been a while since I played with logic gates but my intuition says there is something lurking below the surface. A new class of irreducible gates, maybe cross-connections? Like compacted multilayer gates? Think SHA-512, how certain bits feed into different layers of the "puzzle". Optimistic this thought-amalgam serves you in your continued research :)
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.
The ISA could be really cool, having lots of "combo" commands that might reduce program length dramatically. Think ADD and MULT and SHIFT all in one command, to give a simple analogy.
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.
> 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 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.
>> 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.
> We do not have great insight as to how we ride a bicycle, and we do not have
much useful advice for someone who is learning.
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.
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:
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).
I'm don't think it's possible to start a bike by pedalling with zero forward momentum. You will fall over. You need to kick off - start pedalling with the bike already moving forward. So you're right, and a third neuron is certainly not sufficient. You need legs, too, and arms, and a torso, and motor neurons, and respiration/metabolism. Clearly, the paper has no practical application; if you need to ride a bike, it's far cheaper to hire a human to do it.
You absolutely can start a bike by pedaling with no forward momentum. You can see it when someone starts pedaling again after a track stand.
>None of them made significant use of the speed—they all managed to control the bicycleusing just the handlebars.
I think is where it refers to it.
Two to steer is still impressive. If we added in balance and pedaling/braking I wonder what the count would raise to then.
This looks like they simply reinvented PID control. The inputs to the beyond are desired states minus actual states, which is basically how PID works.
The useful insight is not "compare desired state to actual state"; it's deciding which state to control
I assume you mean proportional–integral–derivative control. https://en.wikipedia.org/wiki/PID_controller
No, the bicycle is unstable. PID doesn't work well there.
In addition, it is controlling a coupled 3D system (which is unstable). This is much more than 3 PID controllers.
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.
I think that's basically right. The "neurons" framing feels a bit loose here; it's more like a very compact hand-designed controller expressed in neural-network-ish terms
(2004)
Previously:
- https://news.ycombinator.com/item?id=19196664 (25 comments)
- https://news.ycombinator.com/item?id=16215130 (88 comments)
I had fun reading this. Thanks for sharing.
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:
https://blog.typeobject.com/posts/2026-timing-is-the-bit/
Research question: does it make sense to make a new family of logic gates using neurons? My intuition says there is a rich texture/fabric to uncover here. The best analogy on hand right now is legos: rather than 2-knotch legos [standard gates like NAND, XOR] what about some sort of new, irreducible gates that are bigger "legos"? Been a while since I played with logic gates but my intuition says there is something lurking below the surface. A new class of irreducible gates, maybe cross-connections? Like compacted multilayer gates? Think SHA-512, how certain bits feed into different layers of the "puzzle". Optimistic this thought-amalgam serves you in your continued research :)
Yes!
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.
The ISA could be really cool, having lots of "combo" commands that might reduce program length dramatically. Think ADD and MULT and SHIFT all in one command, to give a simple analogy.
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.
> 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.
- There Is No Antimemetics Division
Figure 2 is beautiful!
So can we have self-driving bicycles?
Recumbent bike with lidar and maps? Sign me up.
Yes and they'll have one of those wetware computers on board
Self-balancing bicycles, sure. Self-driving bicycles that navigate city streets safely are a much larger problem.
> 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.
^ https://playground.tensorflow.org/#activation=tanh&batchSize...
>> 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.
https://www.youtube.com/shorts/Gyt9DLfYOdU
> We do not have great insight as to how we ride a bicycle, and we do not have much useful advice for someone who is learning.
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.
The instability ink-lines look like a flower blooming.
Observation: 2 neurons, 2 wheels. One for each?
Sadly not quite one per wheel, though that would make the title even better
What about drawing a pelican riding a bicycle?
My neurons still don't get themselves: What kind of processing happens INSIDE neurons?
now make this one-bit quantized