J-Lens · reproducibility overview

How much can we push J-Lens?

A three-model study of what the Jacobian buys, whether its singular directions are interpretable, and how its transport subspaces form during training.

w = normalize(WU[Rome] − WU[Paris])

113 / 120contrast × layer cells where Jᵀw beats w
20–46σpullback effect versus matched random null
1.3–1.7×Jacobian advantage at headline layers
11OLMo-3 checkpoints across training stages

The Jacobian helps—modestly

Mean change in the Rome−Paris logit contrast over 12 neutral prompts. Every direction is injected at the same L2 norm.

The advantage decays with depth

Median pullback-to-direct ratio across six contrasts. At the target layer J is the identity, so the endpoint is forced to 1.

No single singular vector is the concept

Share of the full pullback effect recovered after keeping only the top k singular components of J.

Claim → code → output

Each application claim lands on an executable module and a compact checked-in result.

SVD directions can steer

Readable axes are rare, but one gender direction flips generated pronouns.

code · JSON

Jᵀ is a useful pullback

It transports a precisely specified logit objective back to the source layer.

code · JSON

The effect is slot-like

The intervention moves valid city-name slots, not beliefs about France or Italy.

code · JSON

Structure forms during training

Strong directions appear first; nearby layers share more transport subspace.

code · JSON

Training views

Figures regenerate from saved experiment summaries; no model inference is required.

OLMo training subspace formation across checkpoints
Reading subspaces form gradually and briefly regress at the mid-training transition.
Cross-layer transport subspace overlap through training
Nearby layers share much more of their transport subspaces than distant layers.