manifold-level description

An interpretability approach that describes representations in terms of entire curved manifolds rather than many small features.

Neighborhood — ranked by edge-count

claim

Manifold-level descriptions recover overarching semantic structure that SAE features miss.
cites
Positive claim that geometric descriptions retain the conceptual coherence lost in atomized feature decompositions.

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.

manifoldconcept0.834
A smooth, potentially curved surface in activation space along which activations vary according to a coherent semantic dimension.
representation manifoldconcept0.814
One-dimensional curved surface in internal activation space; the paper demonstrates alignment with behavior manifold.
One-dimensional Manifoldconcept0.798
The type of manifold fitted to the cyclic concept structure in both activation and behavior space — a path along which steering moves the model.
Feature Manifoldsframework0.798
Hypothesized extension of superposition where features may be higher-dimensional manifolds rather than 1D directions
manifold learningframework0.776
Technique used to fit M_h and M_y from data; enables manifold steering.
curved manifoldconcept0.766
A smoothly varying lower-dimensional surface in activation space that captures a concept better than a straight linear direction.
1D manifoldconcept0.761
A single-continuous curve in activation space encoding a single variable, such as car position in the Mountain Car case.
Levels of Scaleconcept0.745
The property that living structures contain centers at a beautiful range of sizes at well-marked levels with definite jumps, where each level helps the next; jumps should not be too great (ideally 2:1 to 4:1, less than 10:1)