claim

active

claim:conceptual-geometry-is-consistent-across-representation-space-and-behavior-space

Conceptual geometry is consistent across representation space and behavior space.

Interpretive assertion: the same geometric structure (e.g. circular for days) appears identically in both internal activations and output probabilities.

Source paper

extracted_from

Steering Along Manifolds to Control Neural Networks

(2026) ·

Neighborhood — ranked by edge-count

Findings (1)

finding

Days-of-Week Cyclic Structure
supports
Key empirical result: days-of-week appear as identical circular manifold in both Llama-3.1-8B internal activations and output token probability distributions.

Communities (3)

community

Manifold-aware concept steering in neural representations
members_of
Explores geometry of activation/behavior manifolds to enable selective, non-destructive concept interventions.
Geometric concept representations in neural networks
members_of
Concepts encoded as curved manifolds and circular structures in LLM activation spaces.
Neural geometry as fundamental computational substrate
members_of
Geometric structure in neural representations causally determines computation and behavior across diverse architectures, revealed through analysis of learned manifolds and cyclic concepts.

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.

The alignment between representation geometry and behavior geometry is not limited to days of the week but extends to months, letters, ages, and synthetic in-context learning tasks.claim0.835
The paper's generalization claim, asserting that the days-of-week finding scales to other cyclic and structured concepts.
There is a bidirectional relationship between the geometry of representation and behavior across tasks and modalities.claim0.829
Author’s interpretive claim that the shared geometry is general and robust.
representation geometry and behavior geometry are bidirectionally alignedclaim0.823
Core finding: the structure models use internally (representations) is precisely reflected in their external behavior (outputs).
There is a clear bidirectional relationship between the geometry of behavior and representation: steering along representation manifolds follows behavior manifolds, and vice versa.claim0.818
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.claim0.810
shared geometry of representation and behaviorconcept0.809
The bidirectional correspondence M_h ↔ M_y, indicating that geometry in representation is not incidental but causally shapes behavior.
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.claim0.803
The paper's deepest interpretive claim, asserting that representation structure and behavioral structure are not coincidentally aligned but deeply connected.
The analogous circular structure between representation manifold and behavior manifold is downstream of training data and its implicit cyclic conceptual structure.claim0.800
The paper's causal explanation for why representation and behavior geometry both appear circular for days of the week.