Manifold Fitting to Representation/Behavior Space

The procedure of fitting a one-dimensional manifold (path) to clusters in activation or behavior space to capture the geometric structure of a concept.

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Concepts (1)

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.

Related by similarity (8)

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.

behavior manifold fitting (M_y)method0.834
Method to fit a manifold M_y to output probability distributions.
behavior manifoldconcept0.828
One-dimensional curved surface in output probability space; the paper shows this mirrors representation manifold structure.
Analogous alignment between representation manifold and behavior manifold is found across months, letters, ages, and synthetic in-context learning tasks in language models.finding0.823
Generalization finding from the full paper extending beyond days-of-week to other structured concepts.
representation manifoldconcept0.814
One-dimensional curved surface in internal activation space; the paper demonstrates alignment with behavior manifold.
behavior manifold M_yconcept0.810
Manifold fitted to output probability distributions (behavior).
The analogous circular structure between representation manifold and behavior manifold is downstream of training data and its implicit cyclic conceptual structure.claim0.807
The paper's causal explanation for why representation and behavior geometry both appear circular for days of the week.
Representation geometry causally shapes behavior; activation and behavior manifolds are approximately isometric.claim0.804
There is a clear bidirectional relationship between the geometry of behavior and representation: steering along representation manifolds follows behavior manifolds, and vice versa.claim0.793
The paper's finding that the alignment holds in both directions — from representation to behavior and from behavior back to representation space.