sae-neighborhood-as-directsum-navigation-v2
IN premise
Created 2026-08-25T04:08:13+00:00
The SAE feature neighborhood (Golden Gate Bridge → Alcatraz → San Francisco → California) serves as an operational navigation algorithm for the categorical polytope geometry, with cross-model universality indicating a shared semantic object rather than a model-specific artifact. Combined with hierarchical orthogonality (Theorem 8), this suggests the full representation space may decompose as a direct sum of orthogonal subspaces, one per hierarchical level. However, the antecedents do not explicitly establish that the same neighborhood traversal simultaneously navigates both the categorical and hierarchical subspaces of such a decomposition; they confirm the categorical-polytope navigation and imply the structural decomposition separately.
Summary
A structured path from specific to general concepts (Golden Gate Bridge to Alcatraz to San Francisco to California) appears to be a real, shared way of navigating the geometry of categories across different AI models, not a quirk of any single one. The system can treat the overall representation space as cleanly separable layers by abstraction level, but it has not yet confirmed that the same traversal path navigates both the categorical and hierarchical dimensions at once — so those two findings remain parallel results rather than a single unified navigation rule.
Dependents
These beliefs depend on this one:
- OUT sae-neighborhood-as-directsum-navigation — The SAE feature neighborhood (Golden Gate Bridge → Alcatraz → San Francisco → California) is not merely a navigation path within a single categorical polytope but the operational traversal algorithm for the full direct-sum decomposition of the semantic space: it simultaneously navigates the categorical subspace (discrete concepts) and the hierarchical orthogonal subspace (WordNet parent-child structure), validated across Gemma-2B and LLaMA-3-8B.