claim

active

claim:the-analogous-circular-structure-between-representation-manifold-and-behavior-manifold-is-downstream-of-training-data-and-its-implicit-cyclic-conceptual-structure

The analogous circular structure between representation manifold and behavior manifold is downstream of training data and its implicit cyclic conceptual structure.

The paper's causal explanation for why representation and behavior geometry both appear circular for days of the week.

Source paper

extracted_from

Steering Along Manifolds to Control Neural Networks

Neighborhood — ranked by edge-count

Papers (1)

paper

Steering Along Manifolds to Control Neural Networks
introduces

Findings (2)

finding

Llama-3.1 8B internal representations for the seven days of the week form seven clusters in a circle in activation space.
supports
Empirical observation establishing that Llama's internal representations for days-of-week have circular geometric structure.
Llama-3.1 8B output token distributions for seven days of the week form seven clusters in a rough circle in behavior space (Hellinger distance geometry).
supports
Empirical observation establishing that Llama's behavior for days-of-week tasks has circular structure.

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.

Analogous alignment between representation manifold and behavior manifold is found across months, letters, ages, and synthetic in-context learning tasks in language models.finding0.849
Generalization finding from the full paper extending beyond days-of-week to other structured concepts.
There is a clear bidirectional relationship between the geometry of behavior and representation: steering along representation manifolds follows behavior manifolds, and vice versa.claim0.840
The paper's finding that the alignment holds in both directions — from representation to behavior and from behavior back to representation space.
Representation geometry causally shapes behavior; activation and behavior manifolds are approximately isometric.claim0.825
Activation manifolds and behavior manifolds are approximately isometric across cyclic and sequential concepts.claim0.824
The geometry of internal representations and the geometry of model behavior share a precise correspondence — representation geometry is a window into the inner world of neural networks.claim0.821
The paper's deepest interpretive claim, asserting that representation structure and behavioral structure are not coincidentally aligned but deeply connected.
Manifold Fitting to Representation/Behavior Spacemethod0.807
The procedure of fitting a one-dimensional manifold (path) to clusters in activation or behavior space to capture the geometric structure of a concept.
Conceptual geometry is consistent across representation space and behavior space.claim0.800
Interpretive assertion: the same geometric structure (e.g. circular for days) appears identically in both internal activations and output probabilities.
There is a bidirectional relationship between the geometry of representation and behavior across tasks and modalities.claim0.797
Author’s interpretive claim that the shared geometry is general and robust.