claim

active

claim:representation-geometry-and-behavior-geometry-are-bidirectionally-aligned

representation geometry and behavior geometry are bidirectionally aligned

Core finding: the structure models use internally (representations) is precisely reflected in their external behavior (outputs).

Source paper

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Steering Along Manifolds to Control Neural Networks

Neighborhood — ranked by edge-count

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.
Concept geometry and steering in neural networks
members_of
Using geometric structure of learned representations to interpret and control model behavior through concept operators.

Claims (1)

claim

geometric structure in neural network representations drives model behavior
supports
Interpretive assertion that representation geometry is not epiphenomenal but causally shapes what models do externally.

Questions (1)

question

How do interventions on representations causally steer behavior?
answered_by
Core question motivating the shift from linear to geometry-aware steering; answered via manifold alignment analysis.

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.

There is a bidirectional relationship between the geometry of representation and behavior across tasks and modalities.claim0.897
Author’s interpretive claim that the shared geometry is general and robust.
bidirectional relationship between representation and behavior geometryconcept0.897
The finding that steering along M_h yields M_y behavior, and optimizing for M_y paths recovers M_h trajectories.
There is a clear bidirectional relationship between the geometry of behavior and representation: steering along representation manifolds follows behavior manifolds, and vice versa.claim0.889
The paper's finding that the alignment holds in both directions — from representation to behavior and from behavior back to representation space.
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.claim0.858
The paper's generalization claim, asserting that the days-of-week finding scales to other cyclic and structured concepts.
Representation geometry causally shapes behavior; activation and behavior manifolds are approximately isometric.claim0.846
There exists a bidirectional relationship between the geometry of neural representation and the geometry of model behaviorclaim0.843
Central empirical claim of the paper, demonstrated across tasks and modalities
The representation-based path and the behavior-based path in Llama-3.1 8B activation space trace out similar curves, demonstrating bidirectional geometry alignment.finding0.835
Key empirical result showing that optimizing for behavioral outputs and fitting representation geometry produce the same path in activation space.
shared geometry of representation and behaviorconcept0.832
The bidirectional correspondence M_h ↔ M_y, indicating that geometry in representation is not incidental but causally shapes behavior.