geometry-as-universal-semantic-currency

Antecedents (all must be IN):

• 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.

Unless (any of these IN defeats this justification):

• IN geometry-as-universal-semantic-currency-v2 — The covariance geometry serves as a unifying geometric framework for LLM semantics, underpinning what can be measured (cosine/Spearman evaluation in SBERT/MTEB), what can be modified (covariance-whitening-based editing as in ROME), what converges across architectures (cross-model universality of feature geometry), and what is structured at the interpretable level (SAE feature neighborhoods as empirical instantiations of the subordination relations in Park's orthogonality theorem)—supporting the view that it functions as a model-independent semantic structure rather than an architecture-specific artifact.

Antecedents (all must be IN):

• OUT evaluation-geometry-predicts-editability — The convergence of evaluation geometry (cosine/Spearman in SBERT/MTEB) and editing geometry (covariance whitening in ROME) on the same second-moment structure means that improving evaluation alignment and enabling reliable editing are two operational views of the same geometric optimization over the residual-stream covariance.

Unless (any of these IN defeats this justification):

• IN geometry-as-universal-semantic-currency-v2 — The covariance geometry serves as a unifying geometric framework for LLM semantics, underpinning what can be measured (cosine/Spearman evaluation in SBERT/MTEB), what can be modified (covariance-whitening-based editing as in ROME), what converges across architectures (cross-model universality of feature geometry), and what is structured at the interpretable level (SAE feature neighborhoods as empirical instantiations of the subordination relations in Park's orthogonality theorem)—supporting the view that it functions as a model-independent semantic structure rather than an architecture-specific artifact.

Antecedents (all must be IN):

• OUT feature-neighborhood-as-geometric-theorem-instantiation — SAE feature neighborhood structure (e.g., Golden Gate Bridge → San Francisco → California) is the concrete empirical instantiation of the covariance-geometric semantic space at the interpretable level: decoder-space proximity reflects the same subordination relations predicted by Park's orthogonality theorem, unifying interpretability with geometric theory.

Unless (any of these IN defeats this justification):

• IN geometry-as-universal-semantic-currency-v2 — The covariance geometry serves as a unifying geometric framework for LLM semantics, underpinning what can be measured (cosine/Spearman evaluation in SBERT/MTEB), what can be modified (covariance-whitening-based editing as in ROME), what converges across architectures (cross-model universality of feature geometry), and what is structured at the interpretable level (SAE feature neighborhoods as empirical instantiations of the subordination relations in Park's orthogonality theorem)—supporting the view that it functions as a model-independent semantic structure rather than an architecture-specific artifact.