activation manifold M_h

Manifold fitted to representations in activation space.

Neighborhood — ranked by edge-count

concept

Activation Manifold
related_tosame_as
The low-dimensional geometric structure discovered in neural activation space; contrasted with linear/Euclidean geometry.
Manifold Steering
implements
Central framework: steering neural networks by intervening along the curved manifold where a concept lives, rather than in straight lines through activation space.
Activation space
associated_with
Representation space on which linear probes operate to attribute harmful behaviors to training data.
Neural Representation Geometry
associated_with
The broader conceptual framework that neural activations exhibit non-Euclidean geometric structure causally linked to behavior.
behavior manifold M_y
associated_with
Manifold fitted to output probability distributions (behavior).

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 fitting (M_h)method0.919
Method to fit a manifold M_h to neural representations in activation space.
Activation manifolds and behavior manifolds are approximately isometric across cyclic and sequential concepts.claim0.765
Activation-Behavior Manifold Isometryconcept0.751
manifoldconcept0.737
A smooth, potentially curved surface in activation space along which activations vary according to a coherent semantic dimension.
behavior manifold fitting (M_y)method0.729
Method to fit a manifold M_y to output probability distributions.
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.finding0.726
Central empirical result showing causal coupling between representation and behavior geometry across multiple substrates and modalities.
Optimizing interventions in activation space to produce paths along M_y recovers activation trajectories that trace the curvature of M_h.finding0.716
Demonstrates bidirectional causal link: behavior manifold geometry can be recovered by optimizing in representation space.
manifold learningframework0.714
Technique used to fit M_h and M_y from data; enables manifold steering.