Right - e.g., if you're modeling a physical system it makes sense to bake in some physics - like symmetry.

Indeed, and I think natural language and reasoning will have some kind of geometric properties as well. Attention is just a sledgehammer that lets us brute force our way around not understanding that structure well. I think the next step change in AI/LLM abilities will be exploiting this geometry somehow [1,2].

[1] GrokAlign: Geometric Characterisation and Acceleration of Grokking, https://arxiv.org/abs/2510.09782

[2] The Geometry of Reasoning: Flowing Logics in Representation Space, https://arxiv.org/abs/2506.12284