One-dimensional Manifold

The type of manifold fitted to the cyclic concept structure in both activation and behavior space — a path along which steering moves the model.

Neighborhood — ranked by edge-count

concept

1D manifold
related_to
A single-continuous curve in activation space encoding a single variable, such as car position in the Mountain Car case.
behavior manifold
associated_with
One-dimensional curved surface in output probability space; the paper shows this mirrors representation manifold structure.
representation manifold
associated_with
One-dimensional curved surface in internal activation space; the paper demonstrates alignment with behavior manifold.

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.

manifoldconcept0.846
A smooth, potentially curved surface in activation space along which activations vary according to a coherent semantic dimension.
curved manifoldconcept0.805
A smoothly varying lower-dimensional surface in activation space that captures a concept better than a straight linear direction.
manifold-level descriptionconcept0.798
An interpretability approach that describes representations in terms of entire curved manifolds rather than many small features.
manifold learningframework0.771
Technique used to fit M_h and M_y from data; enables manifold steering.
Feature Manifoldsframework0.757
Hypothesized extension of superposition where features may be higher-dimensional manifolds rather than 1D directions
behavior manifold M_yconcept0.742
Manifold fitted to output probability distributions (behavior).
Activation Manifoldconcept0.732
The low-dimensional geometric structure discovered in neural activation space; contrasted with linear/Euclidean geometry.
Geometryconcept0.729
The actual shapes and spatial relationships of buildings, essential to living structure.