Feature Manifolds

Hypothesized extension of superposition where features may be higher-dimensional manifolds rather than 1D directions

Neighborhood — ranked by edge-count

framework

Isotropic Superposition Model
extends
Prior model of superposition where features are discrete 1D objects repelling each other roughly evenly; paper argues this is incomplete

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.

manifoldconcept0.821
A smooth, potentially curved surface in activation space along which activations vary according to a coherent semantic dimension.
representation manifoldconcept0.812
One-dimensional curved surface in internal activation space; the paper demonstrates alignment with behavior manifold.
Features may not be strictly one-dimensional objects; higher-dimensional feature manifolds may exist in model representationshypothesis0.801
Extension of superposition hypothesis to account for continuous families of features
manifold-level descriptionconcept0.798
An interpretability approach that describes representations in terms of entire curved manifolds rather than many small features.
Geometry of featuresconcept0.797
Research thread within About Blank concerning the structure and relational properties of neural network feature representations; covariance pooling tangentially supports this thread.
manifold learningframework0.771
Technique used to fit M_h and M_y from data; enables manifold steering.
curved manifoldconcept0.762
A smoothly varying lower-dimensional surface in activation space that captures a concept better than a straight linear direction.
One-dimensional Manifoldconcept0.757
The type of manifold fitted to the cyclic concept structure in both activation and behavior space — a path along which steering moves the model.