There are actually a lot of people trying to figure out spatial intelligence, but those groups are usually in neuroscience or computational neuroscience. Here is a summary paper I wrote discussing how the entorhinal cortex, grid cells, and coordinate transformation may be the key: https://arxiv.org/abs/2210.12068 All animals are able to transform coordinates in real time to navigate their world and humans have the most coordinate representations of any known living animal. I believe human level intelligence is knowing when and how to transform these coordinate systems to extract useful information. I wrote this before the huge LLM explosion and I still personally believe it is the path forward.
I'll add to the discussion a 2018 Nature letter: "Vector-based navigation using grid-like representations in artificial agents" https://www.nature.com/articles/s41586-018-0102-6
and a 2024 Nature article "Modeling hippocampal spatial cells in rodents navigating in 3D environments" https://www.nature.com/articles/s41598-024-66755-x
And a simulation in Github from 2018 https://github.com/google-deepmind/grid-cells
People have been looking at spacial awareness in neurology for quite a while. (In terms of the timeframe of recent developments in LLMs).
This got me.
Dafny and verification-aware programming, including proof by induction to verify properties of programs (for example, that an optimizer preserves semantics). Dafny Sketcher (https://github.com/namin/dafny-sketcher)
Multi-stage programming, a principled approach to writing programs that write programs, and its incarnation in multi-stage relational programming for faster synthesis of programs with holes—with the theoretical insight that a staged interpreter is a compiler, and a staged relational interpreter for a functional language can turn functions into relations running backwards for synthesis. multi-stage miniKanren (https://github.com/namin/staged-miniKanren)
Monte Carlo Tree Search, specifically the VerMCTS variant, and when this exploration-exploitation sweet spot is a good match for synthesis problems. VerMCTS (https://github.com/namin/llm-verified-with-monte-carlo-tree-...), and Holey (https://github.com/namin/holey).