claim

active

claim:dim-captures-only-one-facet-of-the-multi-dimensional-truth-subspace-additional-orthogonal-structure-exists-beyond-it

DIM captures only one facet of the multi-dimensional truth subspace; additional orthogonal structure exists beyond it

Interpretation of Experiment 4 cosine similarity results

Source paper

extracted_from

From Directions to Cones: Exploring Multidimensional Representations of Propositional Facts in LLMs

(2025) · Kevin Shengyang Yu · Vaidehi Bulusu · Oscar Yasunaga · Lau, Clayton +4

Neighborhood — ranked by edge-count

Papers (1)

paper

From Directions to Cones: Exploring Multidimensional Representations of Propositional Facts in LLMs
introduces

Findings (2)

finding

In Gemma-2-9B, only the first cone axis (v1) has non-negligible cosine similarity to the DIM direction; all other axes have near-zero similarity (~1e-9)
supports
Experiment 4 result showing DIM captures only one facet of the multi-dimensional truth subspace
In Qwen-2.5-9B, only v1 has meaningful cosine similarity to DIM direction; all additional basis vectors have cosine similarities ~1e-9
supports
Appendix E replication of DIM alignment finding in Qwen model

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

The two-dimensional subspace reported by Burger et al. (2024) seems to reflect a stage of transition in the model's processing, rather than a universal property of truth directions.quote0.803
Load-bearing interpretive claim about the layer-specificity of Burger et al.'s finding.
Truth may be linearly separable in the model's representation space, but the structure is richer than a single linear axisclaim0.785
Interpretive synthesis of DIM and cone intervention successes
Does the multi-directional nature of truth imply an underlying nonlinear representation, or is it compatible with linear separability?question0.764
Theoretical open question about the geometry of truth in LLMs raised in Discussion
Superposition exploits the geometry of high-dimensional spaces, which allow exponentially many almost-orthogonal vectors but only n strictly orthogonal ones.claim0.761
Mechanistic explanation for why superposition is geometrically feasible
How can we discover a maximally informative or interpretable truth subspace rather than just a sufficient one?question0.761
Limitation-driven open question about subspace optimality
Superposition hypothesis: neural networks represent more features than dimensions using almost-orthogonal directions.hypothesis0.747
Explanation for why dictionary learning can recover many more features than dimensions.
Truthful behavior in LLMs is not confined to a single linear axis; multiple orthogonal directions can independently mediate itclaim0.747
Central interpretive claim of the paper
The two-dimensional subspace reported by Burger et al. reflects a transitional phase in model processing rather than a universal property of truth directions.claim0.745
Reinterpretation of Burger et al.'s finding as layer-specific rather than universal.