Jacobian lenses for the OLMo-3-7B post-training ladder
Fitted Jacobian lenses for the full open OLMo-3-7B post-training ladder — the base
model and ten post-trained variants. These are the artifacts behind the first quantitative, fully-reproducible test of
Anthropic's post-training "point of view" observation — plus a run of the ignition
test that Dehaene & Naccache asked for and that had not been run.
Anthropic report (qualitatively, no numbers, on the closed Sonnet 4.5) that the J-space is
present already in the pretrained model, but that "during post-training, the J-space
develops some signatures of adopting 'Claude's point of view'": "in the base model, the
J-space mostly tracks what's needed to predict upcoming text; in the post-trained model,
it starts holding Claude's own reactions." In plain terms: post-training shifts the
model's internal workspace from what word comes next to also carrying its own stance as
the Assistant — its reactions, caveats, and values. These lenses give the first
quantitative version of that shift, on fully open weights.
A Jacobian lens is not a sparse autoencoder. It is the averaged forward Jacobian
J_l = E[∂h_final/∂h_l] of a frozen model; reading unembed(J_l · h) recovers the tokens a
layer's activation is poised to report — the model's "verbalizable" content. Method and
reference code: Anthropic's jacobian-lens
(Apache-2.0). Fit and analysed with the companion
jlens-lab.
Why this exists
The Anthropic result rests on Sonnet 4.5, whose activations no external party can access —
the paper's own invited commentators (Dehaene & Naccache) could not check it. AI2's OLMo-3
is the only open family shipping a base model, its post-trained variants, and a clean
method-vs-domain factorial. These lenses make the claim checkable by anyone.
Contents
file
arm
model_type
lenses/olmo-3-1025-7b.pt
base
olmo3
lenses/olmo-3-7b-instruct-sft.pt
Instruct · SFT
olmo3
lenses/olmo-3-7b-instruct-dpo.pt
Instruct · DPO
olmo3
lenses/olmo-3-7b-instruct.pt
Instruct · final
olmo3
lenses/olmo-3-7b-think-sft.pt
Think · SFT
olmo3
lenses/olmo-3-7b-think-dpo.pt
Think · DPO
olmo3
lenses/olmo-3-7b-think.pt
Think · final
olmo3
lenses/olmo-3-7b-rl-zero-math.pt
RL-Zero · Math
olmo3
lenses/olmo-3-7b-rl-zero-code.pt
RL-Zero · Code
olmo3
lenses/olmo-3-7b-rl-zero-if.pt
RL-Zero · IF
olmo3
lenses/olmo-3-7b-rl-zero-general.pt
RL-Zero · General
olmo3
RL-Zero-Mix is deliberately absent: it is olmo2-retrofit, a different base architecture,
so its J-space is not comparable to the olmo3 arms.
Each lens covers 11 source layers (0, 3, …, 30 — every third of 32) at d_model=4096,
fit on 616 wikitext prompts, stored fp16. For a full 31-layer base lens (used for
the ignition readout), use Anthropic's published olmo-3-1025-7b lens on
Neuronpedia's neuronpedia/jacobian-lens.
1import jlens
2from jlens import JacobianLens
3from transformers import AutoModelForCausalLM, AutoTokenizer
45lens = JacobianLens.from_pretrained("mhough/olmo3-jacobian-lenses",6 filename="lenses/olmo-3-7b-instruct.pt")78tok = AutoTokenizer.from_pretrained("allenai/Olmo-3-7B-Instruct")9hf = AutoModelForCausalLM.from_pretrained("allenai/Olmo-3-7B-Instruct",10 dtype="bfloat16", device_map="cuda").eval()11model = jlens.from_hf(hf, tok)1213# read the workspace content at the last token, layer 18:14lens_logits, model_logits, ids = lens.apply(model,"The capital of France is",15 layers=[18], positions=[-1])
See reproduce.py for a runnable check.
Result 1 — post-training installs a viewpoint, decoupled from capability
Distance from the base lens, cos(J_base, J_arm), mean over the 11 shared layers, against a
~0.97 same-model refit floor (the floor is layer-dependent — see
External validation):
arm
cos(base, arm)
move
Instruct (SFT+DPO)
0.69
~31%
Think (SFT+DPO)
0.73
~27%
RL-Zero (RLVR only)
0.94
~6%
RL-Zero domain pairwise
≥ 0.992
~1%
Method sets the magnitude, not domain: instruction/CoT tuning moves the J-space ~5×
more than RLVR; varying the RLVR domain (math/code/IF/general) at matched capability adds
only ~1%.
Decoupled from capability: MMLU is flat-to-slightly-down across post-training while the
J-space moves ~31% — a representational shift with no competence gain, i.e. a viewpoint
change, not a prediction gain.
Anchor-gated, and now externally cross-validated: the base fit reproduces the published
olmo-3-1025-7b lens (identity_distance 0.2199 vs 0.2209, 0.4% error). Against
Neuronpedia's independently fitted lens for the same model, the final layer agrees to
cosine 0.9998 — see below.
⚠ Corrected 2026-08-02 — read the pooled numbers above against a per-layer floor. The
table's cosines are means over 11 layers whose refit floors run 0.884 (layer 0) to 1.000
(layer 30). Recomputed as excess over the per-layer floor: Instruct 29.4%, Think
25.1%, RL-Zero ~2.9%. Two consequences: the method ratio strengthens from ~5× to
~10×, and RLVR's ~6% halves to ~3% — about half of it was two fits disagreeing.
The movement is also early-layer concentrated (Instruct 49.9% beyond floor at layers 0–9
vs 10.6% at 21–30), which the pooled statistic hides. Full working:
results/posttrain/perlayer_floor_correction.md.
Capability-controlled: RL-Zero overall-MMLU spread is 1.7pp (in noise), no domain
diagonal — so the ~1% geometry differences are not capability artifacts.
Full write-up with the null correction and caveats: results/post-training-point-of-view.md.
Result 2 — Ignition test (Dehaene & Naccache's "decisive experiment")
Their commentary singles out ignition — all-or-none entry into the workspace — as the
signature the paper "does not establish," and prescribes grading a concept's evidence and
testing whether J-space representations "switch on with a threshold-like nonlinearity, while
earlier layers rise monotonically." Nobody had run it (Claude closed, Anthropic didn't). Run
here on OLMo-3 via the published 31-layer lens, using an on−off concept contrast:
No concept without evidence (contrast ≈0 at k=0), then all-or-none entry (a step at
the first clue, then saturation — not a graded ramp).
Sustained in the workspace, transient in early layers: early layers respond to the
first clue then decay (keep ~16%), the workspace band holds it (~67%) — exactly Dehaene's
ignition ("a sustained, broadly distributed state") vs subliminal ("a delimited wave …
which quickly dies away").
This first pass establishes the persistence half of ignition. The graded mid-range
threshold and the bifurcation are delivered by the v2 clue set — see the full reviewer
battery below. Write-up + confound analysis: results/ignition_result.md.
Result 3 — the full reviewer battery (every test Dehaene & Naccache proposed)
All six tests the reviewers asked for, implemented and run on OLMo-3
(results/reviewer_tests_results.md, raw in modal_reviewer_tests.py). Honest mixed
outcome — two clean workspace signatures, one partial, three inconclusive under first-pass
adaptations whose flaws are documented:
test
result
Ignition (graded threshold + bifurcation)
✅ workspace saturates with evidence, early flat; across-subset bifurcation present
Metacognition / error monitoring (C2)
✅ workspace uncertainty higher for wrong answers (+1.4 vs −1.6)
Dual-task interference
⚠️ first concept weakens when a second is held (3/5 pairs)
❌ inconclusive — abstract strings a poor oddball analog (fix noted)
This is more of the human-consciousness battery than has been run on the record for any
model, and every number is reproducible.
Result 4 — metacognition: a covert error signal in the base model, made reportable by post-training
A new direction, connecting to the LLM-metacognition literature (survey: arXiv 2607.11881)
and the introspection debate. Reading the base model's workspace recovers an uncertainty
signal that predicts whether its own answer is wrong — beyond the model's output confidence
(n=200 TriviaQA):
Structure: per-layer AUROC rises ~0.5 (early) → 0.69 (workspace) → 0.72 (late) — the
metacognitive signal emerges in the workspace band.
Covert (the key control): within matched output-entropy terciles the workspace still
separates right from wrong (AUROC 0.64 on confident-looking answers) — it "knows more than it
says." Output-confidence baselines for reference: ECE 0.11, meta-sensitivity (type-2 AUROC) 0.80.
Across the ladder — post-training installs reportability: the base model's verbal
self-evaluation (P(True)) is at chance (0.51) while its workspace covertly tracks errors
(0.66); post-training raises verbal self-eval to 0.78 (Instruct) / 0.72 (Think) — via
SFT+DPO, not RLVR (RL-Zero 0.52–0.55). Post-training does not create the self-monitoring
signal; it makes a pre-existing covert one reportable.
This is the "mechanistic evidence of a dissociable second-order process" the introspection
Reality Check (Singh, Linzen & Ravfogel) calls for. Full write-up:
results/metacognition_result.md; lineage + concept-injection tooling: docs/technique-lineage.md.
External validation & the refit-noise floor
Neuronpedia (with Anthropic) publishes pre-fitted J-lenses at
neuronpedia/jacobian-lens, including
olmo-3-1025-7b. That gives an independent second-party fit of the same base model — the
first external check of this pipeline. Full write-up + reproduce snippet:
results/neuronpedia_crossvalidation.md.
These are genuinely independent fits (0 of 11 shared layers bit-identical; both converged at
n_prompts=616 under the same stopping rule — a protocol coincidence, not a copy). The
estimator is identical: jlens-lab calls jlens.fitting.jacobian_for_prompt from
Anthropic's reference package, the same library Neuronpedia vendors, so the documented
convention — sum the cotangent over later target positions, then average over source positions —
and the attention-sink position masking are shared. J̄ is deliberately not a plain
per-position Jacobian average; that is a property of the shared reference implementation, not a
difference between the two fits.
layer
0
6
12
18
24
30
cosine
0.884
0.944
0.976
0.993
0.997
0.9998
rel. Frobenius diff
0.478
0.331
0.217
0.121
0.075
0.020
Mean cosine over the 11 shared layers is 0.966 (computed in float64).
The refit floor is strongly layer-dependent, and this matters for reading Result 1. Two
independent fits of the same model differ by 48% in Frobenius norm at layer 0 and 2% at layer
30. So the pooled ~0.97 floor understates the noise early and overstates it late:
In the mid-to-late workspace band, where the ignition and metacognition readouts live, the
floor is 0.99+ — a post-training cosine of 0.69 is far above noise.
At layer 0, the floor is only ~0.88, so early-layer J-space comparisons carry much less
weight than the pooled number implies.
Result 1 stands — the post-training shift is well above the floor where it is measured — but the
honest presentation is excess over a per-layer floor, not a single pooled one. Early-layer
statements should be read with that in mind.
Numerical note: compute these cosines in float64. Over 4096×4096 matrices, float32
accumulation returns values above 1.0 (we saw 1.0057).
Scope relative to Neuronpedia's lenses
Neuronpedia's J-lens covers 38 models, and for OLMo-3 it ships the base models
(olmo-3-1025-7b, olmo-3-1125-32b) fitted on wikitext. This repo's contribution is the
post-training axis — ten post-trained variants spanning SFT / DPO / final for both Instruct
and Think, plus four RL-Zero arms — which is what makes the post-training claim testable rather
than a single before/after pair.
How they were fit
Matching the published olmo-3-1025-7b config, on B200 / dim_batch=128:
Fit is a plain mean over prompts (sharded exactly across 8 workers). Reproduce end-to-end:
m9h/jacobian-lens/modal_olmo_ladder.py
(anchor → capability_all → ladder → analysis).
Caveats
Cosine is a magnitude measure — how much the J-space moved, not in what organized way.
The same-model refit floor is layer-dependent (~0.88 at layer 0, ~0.9998 at layer 30);
early-layer comparisons are weakly determined and should not be read against the pooled floor.
RL-Zero is a light intervention (~6% from base); the ~1% domain signal is small.
Capability is measured by multiple-choice log-probability, which under-scores chat-tuned
models; it rules out a gross capability confound, not subtle ones.
One model family (OLMo-3); a second-family replication is designed but not yet run.
Not peer-reviewed. Derived from open artifacts only.
Provenance & license
Apache-2.0, matching OLMo-3 (weights) and jacobian-lens (method). Derived from
allenai/Olmo-3-* via the open jlens / jlens-lab stack. Work by Morgan Hough, Orthogonal Research and Education Lab (OREL); not affiliated with Anthropic or AI2.
