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finding:the-representation-based-path-and-the-behavior-based-path-in-llama-3-1-8b-activation-space-trace-out-similar-curves-demonstrating-bidirectional-geometry-alignment

The representation-based path and the behavior-based path in Llama-3.1 8B activation space trace out similar curves, demonstrating bidirectional geometry alignment.

Key empirical result showing that optimizing for behavioral outputs and fitting representation geometry produce the same path in activation space.

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

Claims (2)

claim

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.
supports
The paper's deepest interpretive claim, asserting that representation structure and behavioral structure are not coincidentally aligned but deeply connected.
There is a clear bidirectional relationship between the geometry of behavior and representation: steering along representation manifolds follows behavior manifolds, and vice versa.
supports
The paper's finding that the alignment holds in both directions — from representation to behavior and from behavior back to representation space.

Hypotheses (1)

hypothesis

We hypothesize that representation geometry drives model behavior — the geometric structure of internal representations causally shapes what models do externally.
associated_with
The causal hypothesis motivating the use of causality (intervention) as the lens connecting representation and behavior geometry.

Concepts (2)

concept

Behavior-based Path
cites
The path in activation space derived by optimizing steering interventions to produce outputs along the behavior manifold, independent of representation geometry.
Representation-based Path
cites
The path in activation space derived by fitting the representation manifold, used to steer along the geometric structure of internal representations.

Questions (1)

question

How does representation geometry causally drive model behavior?
answered_by
The central scientific question the paper addresses through the lens of interventional causality.

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.

representation geometry and behavior geometry are bidirectionally alignedclaim0.835
Core finding: the structure models use internally (representations) is precisely reflected in their external behavior (outputs).
There is a bidirectional relationship between the geometry of representation and behavior across tasks and modalities.claim0.819
Author’s interpretive claim that the shared geometry is general and robust.
Representation geometry causally shapes behavior; activation and behavior manifolds are approximately isometric.claim0.803
Steering Llama-3.1 8B along the circular representation manifold produces outputs that follow the natural circle of the behavior manifold, cleanly shifting probability mass from Monday through successive days.finding0.799
Core empirical result demonstrating that manifold steering produces on-target, behavior-aligned outputs.
bidirectional relationship between representation and behavior geometryconcept0.791
The finding that steering along M_h yields M_y behavior, and optimizing for M_y paths recovers M_h trajectories.
Optimizing interventions in activation space to produce paths along M_y recovers activation trajectories that trace the curvature of M_h.finding0.787
Demonstrates bidirectional causal link: behavior manifold geometry can be recovered by optimizing in representation space.
There exists a bidirectional relationship between the geometry of neural representation and the geometry of model behaviorclaim0.783
Central empirical claim of the paper, demonstrated across tasks and modalities
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.claim0.782
The paper's generalization claim, asserting that the days-of-week finding scales to other cyclic and structured concepts.