[bestatsiege_01]

I have explored trying to make global state CA systems, with no success. If anyone has examples of trainable global state CA systems please share, I'd love to learn more.

My idea was that there would be global information but local rules. And the local rules depended on the global information. However I struggled to train such a system and gave up. I would like to go back to it though and some expert perspective might be enough to push me back to it.

I find CA's interesting because they are both continuous and could conceptually vary the amount of compute attributed to a particular problem. NN's can't really do either of these things.

(I appreciate LLM's vary the amount of compute based on the question. But just running the same model over and over seems like an immature method, there must be a better way.)

[theGnuMe]

Thanks for the reply.

How would CAs vary the amount of compute? Don't you have to compute everything state-wise every iteration?

Right now my understanding is that in neural cellular automata people replace the update rule with a DNN. And this DNN is trained on small inputs. Basically a cell's neighborhood input vs a "pixel" vs token level input... a cellular neighborhood here is basically patches which aligns with DNNs anyway.

A good example is: https://distill.pub/2020/growing-ca/

The examples remind of inpainting though in some sense.

You can apply transformers to this to get a shared memory (people have done this I believe).

Too be honest I feel like neural CAs are a trick but I am probably wrong.

[bestatsiege_01]

My hypothesis is that CA's could have input and output cells, then just run the CA, pass a single or continuous input and then parse the outputs when available.

But - I haven't been able to get such a concept to work. I maybe missing some fundamental theory / understand which prevents such a structure (or at least limits is value).

One major challenge is how do you train an unconstrained process?

Ill take a look at Neural CA's. thanks for sharing.

Thanks for sharing Neural CA's. I'll spend some time on them, much easier to train a DNN.

[theGnuMe]

Wolfram talks about mobile automata.. This is where you calculate one cell at a time.

https://en.wikipedia.org/wiki/Mobile_automaton and https://www.wolframscience.com/nks/p71--mobile-automata/

I'm confused as to how you actually train a cellular automaton? How does one do it? Is it just rule search to match a pattern at time t given input state from time t-1 (and repeated?).. it seems like you'd have a bunch of boolean equations and then look for and extract its solutions.