geometric-convergence-as-mathematical-attractor-v2
IN premise
Created 2026-08-25T04:07:11+00:00
The cross-model universality of feature geometry, combined with its ontological status as a model-independent semantic structure, indicates that LLMs sharing over-complete superposition architectures converge toward a shared geometric regularity: the covariance/whitening geometry functions as a convergent structural attractor determined by the shared semantic grammar of language, rather than being merely a model-specific artifact.
Summary
Different large language models, despite being trained separately, end up organizing their internal concept spaces into the same geometric pattern, and that pattern is best explained as an inevitable consequence of their shared architecture meeting the deep structure of language rather than a random byproduct of one training run. The practical upshot is that the geometry we observe in any single model is a trustworthy window into how language itself is structured, so insights about one model's internals can be generalized across the family.
Dependents
These beliefs depend on this one:
- OUT geometric-convergence-as-mathematical-attractor — The cross-model universality of feature geometry combined with its ontological status as a model-independent semantic object implies LLMs are converging to a shared mathematical attractor: the covariance/whitening geometry is the unique fixed point that any differentiable language model must instantiate, not an architectural artifact.