concept
active
concept:1d-manifold1D manifold
A single-continuous curve in activation space encoding a single variable, such as car position in the Mountain Car case.
Neighborhood — ranked by edge-count
Concepts (1)
concept
- One-dimensional Manifoldrelated_toThe type of manifold fitted to the cyclic concept structure in both activation and behavior space — a path along which steering moves the model.
Findings (1)
finding
- Empirical demonstration that a semantically meaningful variable is encoded as a curved manifold, and that respecting its geometry is critical for effective intervention.
Related by similarity (8)
cosine ≥ 0.65 · no typed edgeEntities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.
- A smooth, potentially curved surface in activation space along which activations vary according to a coherent semantic dimension.
- An interpretability approach that describes representations in terms of entire curved manifolds rather than many small features.
- A smoothly varying lower-dimensional surface in activation space that captures a concept better than a straight linear direction.
- Technique used to fit M_h and M_y from data; enables manifold steering.
- The low-dimensional geometric structure discovered in neural activation space; contrasted with linear/Euclidean geometry.
- One-dimensional curved surface in output probability space; the paper shows this mirrors representation manifold structure.
- Hypothesized extension of superposition where features may be higher-dimensional manifolds rather than 1D directions
- One-dimensional curved surface in internal activation space; the paper demonstrates alignment with behavior manifold.