read-write-geometric-asymmetry-topology
OUT derived (depth 5)
Created 2026-08-25T03:08:53+00:00 · Reviewed 2026-08-25T03:24:16+00:00
The LLM is architecturally a read-broad/write-narrow system: the read channel (SAE feature extraction, evaluation, retrieval) spans the full d-dimensional covariance-whitened space, while the write channel (ROME rank-one, SAE feature ablation) is restricted to a 1-dimensional key-direction subspace, making knowledge correction fundamentally more constrained than knowledge interrogation.
Justifications
SL — The asymmetry claim requires BOTH the geometric topology (superposition triangle defining the full read space) AND the structural asymmetry observation; together they establish that the asymmetry is geometric, not merely empirical.
Antecedents (all must be IN):
- OUT read-write-asymmetry — A structural asymmetry governs LLM knowledge: the read channel (feature-level interpretation via SAE, Park polytope analysis, embedding evaluation) operates in a rich, model-independent geometric space, while the write channel (editing) is impoverished to parametric rank-one MLP updates in a single layer—superposition enriches the feature space for reading but makes feature-level writing intractable.
- OUT superposition-covariance-editability-triangle — Superposition, covariance whitening, and rank-one editability form a closed logical triangle in which each property necessitates the others: over-complete superposition requires covariance separation for feature addressability, covariance separation defines the geometric space in which rank-one updates are well-defined, and the boundedness of rank-one editing confirms the addressable space is finite.