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finding:linear-steering-produces-noisy-off-target-effects-manifold-steering-cleanly-shifts-probability-mass-between-sequential-concepts

Linear steering produces noisy off-target effects; manifold steering cleanly shifts probability mass between sequential concepts.

Core empirical claim comparing steering approaches on cyclic concepts.

Source paper

extracted_from

Steering Along Manifolds to Control Neural Networks

(2026) ·

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.
Manifold-aware steering for language models
members_of
Geometric approach to model control that respects learned concept structure, contrasting with linear steering that produces off-manifold artifacts.

Concepts (1)

concept

Manifold Steering
supports
Central framework: steering neural networks by intervening along the curved manifold where a concept lives, rather than in straight lines through activation space.

Findings (1)

finding

manifold steering produces clean probability shifts along natural behavior structure; linear steering cuts across manifold and produces off-target noisy effects
restates
Empirical demonstration on Llama-3.1-8B that steering along representation manifold aligns outputs with behavior manifold, whereas linear steering does not.

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.

Linear steering is often mismatched with a model's internal representation geometry, producing noisy, off-target effects.claim0.889
The paper's critique of the standard linear steering baseline, supported by the days-of-week demo.
Linear steering cuts through off-manifold regions and hence produces unnatural outputs.claim0.878
Attribution of failure to Euclidean assumption.
Steering along manifolds provides better control than linear steering when the concept geometry is non-linear.claim0.871
The central thesis of the paper, motivating the shift from linear to geometry-aware manifold steering.
Manifold-respecting steering produces smooth natural behavioral trajectories while linear steering teleports between non-adjacent concepts.claim0.862
Linear steering on Llama-3.1 8B for the days-of-week task cuts across the behavior manifold, producing noisy off-target effects where predicted tokens are not even days of the week.finding0.838
Empirical result demonstrating the failure mode of linear steering when concept geometry is cyclic.
Gap: linear steering assumes Euclidean geometry and does not account for the actual curved geometry of activation manifoldsconcept0.816
The research gap that motivates manifold steering as an alternative to conventional linear approaches
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.finding0.812
Core empirical result demonstrating that manifold steering produces on-target, behavior-aligned outputs.
Manifold steering demonstrates bidirectional geometry-behavior link in a video world model on tasks with geometry corresponding to physical dynamicsfinding0.803
Extension of manifold steering validation to video world models and physical dynamics tasks, demonstrating cross-modal generality

Restated by (1)

cosine ≥ 0.90

Other entities that say roughly the same thing. May be merge candidates or independent restatements across papers.

finding
manifold steering produces clean probability shifts along natural behavior structure; linear steering cuts across manifold and produces off-target noisy effects