It Takes Two Neurons to Ride a Bicycle

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.

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.

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.)

(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/

So can we have self-driving bicycles?

> 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 instability ink-lines look like a flower blooming.

Observation: 2 neurons, 2 wheels. One for each?

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

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