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).
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.
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 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 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).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:
https://blog.typeobject.com/posts/2026-timing-is-the-bit/
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.
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?