Do language models use the hierarchical geometry they inherit?

The decisive move in the co-occurrence account of concept geometry is a cross-architecture comparison. The hierarchical splitting geometry is first derived and confirmed for word2vec embeddings across many WordNet subtrees. Then the same coarse-to-fine spectral signature is shown to extend "strikingly well" to Gemma 2B unembeddings. Two systems with entirely different objectives and training regimes — a shallow predict-context embedding and a large autoregressive transformer's output matrix — carry the same hierarchical fingerprint. If the structure were a functional artifact of how an LLM reasons, it should not appear, in the same form, in a model that does not reason at all.

This is the strongest available argument that the geometry is statistical, not functional: a shared signature across architectures points to a shared cause upstream of both — the co-occurrence statistics of the training text — rather than convergent functional design. Each word is characterized by discrete, continuous, and hierarchical attributes; words with similar attributes co-occur more often; and that alone gives rise to the geometric organization. Both models inherit it because both are, in different ways, fitting the same pairwise statistics.

Why it leaves a question open: the authors are explicit that such organization may be useful for function but is not driven by it — which leaves unresolved whether and where the LLM actually uses the hierarchical geometry it inherits. Shared structure proves common statistical origin; it does not prove the structure is inert in the transformer. Disentangling inherited-but-unused geometry from inherited-and-recruited geometry is the open problem this result sharpens rather than settles.