Honestly, the most interesting thing here is definitely that just 2D heads are enough to do useful computation (at least they are enough to simulate an interpreter) and that there is an O(log n) algorithm to compute argmax attention with 2D heads. It seems that you could make an efficient pseudosymbolic LLM with some frozen layers that perform certain deterministic operations, but also other layers that are learned.

This seems a really interesting path for interpretability, specially if a big chunk of a model's behavior occurs pseudo-symbolically. This is an idea I had thought about, integrating tools into the main computation path of a model, but I never imagined that it could be done efficiently with just a vanilla transformer.

Truly, attention is all you need (I guess).

There is some things that just don't transfer really well without specific training. I tried to create diagrams in Typst with Cetz (a Processing and Tikz inspired graphing library), and even with documentation, GPT 5.2-thinking can't really do complex nice diagrams like it can in Tikz. It can do simple things that are similar to the shown examples, but nothing really interesting. Typst and specially Cetz is too new for any current model to really "get it", so they can't use it. I need to wait to the next batch of frontier models so that they learn Typst and Cetz examples during pre-training.

> Reality is that we need some way to encode the rules of the world in a more definitive way

I mean, sure. But do world models the way LeCun proposes them solves this? I don't think so. JEPAs are just an unsupervised machine learning model at the end of the day; they might end up being better that just autoregressive pretraining on text+images+video, but they are not magic. For example, if you train a JEPA model on data of orbital mechanics, will it learn actually sensible algorithms to predict the planets' motions or will it just learn a mix of heuristic?

Putting stuff you have learned into a markdown file is a very "shallow" version of continual learning. It can remember facts, yes, but I doubt a model can master new out-of-distribution tasks this way. If anything, I think that Google's Titans[1] and Hope[2] architectures are more aligned with true continual learning (without being actual continual learning still, which is why they call it "test-time memorization").

[1] https://arxiv.org/pdf/2501.00663

[2] https://arxiv.org/pdf/2512.24695