The paper Differentiable Logic Cellular Automata popped up on my Hacker News feed tonight. It immediately attracted my attention due to my interest in the Game of Life.

The paper begins with an immediately captivating demo showing how the Google logo can be generated in a Game-of-Life fashion, i.e. by the use of simple rules that one would not ordinarily expect to lead to sophisticated patterns.

The claim seems to be that, given (say) an image, neural networks can somehow learn what Game-of-Life style rules are necessary to generate such an image.

This seems surprising and scary: if true, then it stands to reason that at scale, one can automatically “learn” the basic rules behind anything!

But (without prior knowledge) I found the paper so dense as to be impenetrable. Ordinarily, I would have given up. While the topic is no doubt important and the authors leading authorities (being affiliated with “Google, Paradigms of Intelligence Team”), the concepts just came at me too quick and too fast. For example:

  • “Computronium - a theoretical physical substance capable of performing arbitrary computation.” Is this science or science fiction?

  • “Can a Differentiable Logic CA learn at all?” What is CA?

But then I decided to try reading the paper while asking ChatGPT voice these questions at the same time.

Overall, ChatGPT voice was helpful. Despite sounding like something from science fiction, Computronium is a hypothesis that scientists have thought about. And “CA” simply stands for “cellular automata”.

More importantly. Growing Neural Cellular Automata, which is summarised briefly in the Recap, is actually a user friendly https://distill.pub/ paper that was easy to play around with. Just skimming it through quickly gave me a better idea of where this paper is coming frm.

These clarifications helped me skim along through to the examples towards the end. The examples gave me assurance that I have not misunderstood the essential claim, i.e. starting with screenshots of the intended result, neural networks can eventually learn the discrete rules (embodied by the circuit) which can generate the result procedurally.

This is a very shallow, surface-level understanding: but at least my eyes passed through to the very last paragraph.