Activation-Behavior Manifold Isometry

Neighborhood — ranked by edge-count

community

concept

Manifold Steering
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Central framework: steering neural networks by intervening along the curved manifold where a concept lives, rather than in straight lines through activation space.
Topological Constraints on Self-Organisation
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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 manifolds and behavior manifolds are approximately isometric across cyclic and sequential concepts.claim0.857
Activation Manifoldconcept0.812
The low-dimensional geometric structure discovered in neural activation space; contrasted with linear/Euclidean geometry.
behavior manifoldconcept0.803
One-dimensional curved surface in output probability space; the paper shows this mirrors representation manifold structure.
Representation geometry causally shapes behavior; activation and behavior manifolds are approximately isometric.claim0.796
behavior manifold M_yconcept0.791
Manifold fitted to output probability distributions (behavior).
Manifold Fitting to Representation/Behavior Spacemethod0.764
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 manifold fitting (M_h)method0.757
Method to fit a manifold M_h to neural representations in activation space.
Emotion geometry in LLM activationsconcept0.755
Emotion emerges early, peaks in middle layers, sharpens with scale, and persists across tokens in LLM activations per Zhang & Zhong 2025