manifold

A smooth, potentially curved surface in activation space along which activations vary according to a coherent semantic dimension.

Neighborhood — ranked by edge-count

framework

Neural Geometry Framework
cites
Conceptual scheme introduced in this paper: neural networks develop internal geometric representations that mirror real-world geometry, providing the right level of description for interpretability and control.

claim

SAE features tend to shatter manifolds into many small and apparently-unrelated pieces, obscuring the overarching semantic structure.
cites
Core critique of sparse autoencoders: they break the geometric structure of representations, making it harder to see the big picture.
Linear interventions across voids in activation space produce incoherent output, while following the manifold curve produces smooth control.
cites
General principle derived from the Mountain Car experiment: curved manifold-following yields coherent manipulation, linear shortcuts fail.

concept

curved manifold
related_to
A smoothly varying lower-dimensional surface in activation space that captures a concept better than a straight linear direction.

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.

One-dimensional Manifoldconcept0.846
The type of manifold fitted to the cyclic concept structure in both activation and behavior space — a path along which steering moves the model.
manifold learningframework0.845
Technique used to fit M_h and M_y from data; enables manifold steering.
manifold-level descriptionconcept0.834
An interpretability approach that describes representations in terms of entire curved manifolds rather than many small features.
Feature Manifoldsframework0.821
Hypothesized extension of superposition where features may be higher-dimensional manifolds rather than 1D directions
behavior manifoldconcept0.799
One-dimensional curved surface in output probability space; the paper shows this mirrors representation manifold structure.
1D manifoldconcept0.795
A single-continuous curve in activation space encoding a single variable, such as car position in the Mountain Car case.
representation manifoldconcept0.792
One-dimensional curved surface in internal activation space; the paper demonstrates alignment with behavior manifold.
Activation Manifoldconcept0.787
The low-dimensional geometric structure discovered in neural activation space; contrasted with linear/Euclidean geometry.