activation manifold fitting (M_h)

Method to fit a manifold M_h to neural representations in activation space.

Neighborhood — ranked by edge-count

paper

concept

Manifold Steering
uses
Central framework: steering neural networks by intervening along the curved manifold where a concept lives, rather than in straight lines through activation space.

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.

activation manifold M_hconcept0.919
Manifold fitted to representations in activation space.
Activation Manifoldconcept0.823
The low-dimensional geometric structure discovered in neural activation space; contrasted with linear/Euclidean geometry.
behavior manifold fitting (M_y)method0.812
Method to fit a manifold M_y to output probability distributions.
Activation-Behavior Manifold Isometryconcept0.757
behavior manifold M_yconcept0.756
Manifold fitted to output probability distributions (behavior).
Manifold Fitting to Representation/Behavior Spacemethod0.752
The procedure of fitting a one-dimensional manifold (path) to clusters in activation or behavior space to capture the geometric structure of a concept.
Activation manifolds and behavior manifolds are approximately isometric across cyclic and sequential concepts.claim0.745
Interventions along activation manifold M_h yield behavioral trajectories following behavior manifold M_y, and vice versa — bidirectional relationship demonstrated across language models and video world models.finding0.735
Central empirical result showing causal coupling between representation and behavior geometry across multiple substrates and modalities.