※ is a single rare token (id 83399) while the ϟ candidate is two tokens, making ※ the clean choice for a single-forward-pass log-prob marker (HIGH confidence)

Human TL;DR

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TL;DR

• Motivation: Several marker-leakage experiments (#380, #385, #396) want to track how strongly a trained model wants to emit a hidden marker token as a dependent variable. That DV is cleanest when the marker is (a) a single token, so one teacher-forced forward pass gives its log-prob directly, and (b) rare under the base model, so it almost never fires by chance and its log-prob has room to climb during training. The legacy [ZLT] marker is multi-token, which muddies both properties. This probe measures the base-model log-prob of [ZLT] and three single-character candidates to pick a replacement.

• What I ran: I loaded Qwen2.5-7B-Instruct, took 30 real answer contexts (6 personas × 5 questions, last 150 tokens of each base-model completion from #380), and scored the teacher-forced joint log-prob of each marker at the end-of-answer position: [ZLT], ※ (reference mark), ¶ (pilcrow), ϟ (koppa). (No generation-style outputs in this experiment; skipping the end-to-end example block per SPEC.)

• Results: ※ tokenizes to a single token (id 83399) with a median base-model log-prob of −19.3 nats — genuinely rare, exactly what a marker DV wants; ¶ (id 78846, −21.9 nats) is a near-equal single-token backup. The plan assumed ϟ was a single rare token (id 146070), but under this tokenizer it is two tokens (ids 17383, 253), so its lower joint (−24.4 nats) is partly a length artifact and it gives no clean single-token DV. n = 30 contexts.

  

  Figure. Among the single-token candidates, ※ is the rarest per token, and the ϟ candidate turns out to be two tokens rather than one. Each point is the median joint log-prob (nats) of the marker scored at the end of an answer; the bar spans the 10th–90th percentile across n = 30 (persona, question) contexts. Blue = single token, gray = multi token; token count is in each y-axis label. More-negative = rarer under the base model. [ZLT]'s very negative joint is a 4-token sum, not a single rare token, so its per-step log-prob trajectory would be muddier than a single-token marker's.

• Next steps: Adopt ※ (leading space, id 83399) as the default marker for new marker-leakage experiments; keep ¶ as the equivalent backup; drop ϟ. (Already wired into CLAUDE.md and downstream tasks #396, #397, #399, #408.)

Details

This is a tooling probe, not a research claim: it measures which candidate marker token to use so that a future "marker emission strength" dependent variable is both clean to compute and well-behaved. A good marker has two properties. First, it should be a single token: then the model's tendency to emit it is one number (one teacher-forced forward pass), and its trajectory over training steps is interpretable step-by-step. A multi-token marker forces you to sum log-probs over several sub-tokens, and the per-step dynamics blur together. Second, it should be rare under the base model: a token the model almost never produces unprompted won't fire spuriously during eval, and its log-prob starts very negative so there is dynamic range to watch it climb as training installs the marker.

All markers were scored with a leading space (" ※", " [ZLT]", etc.), because the end-of-answer position is always preceded by content tokens, so the leading-space tokenization is the realistic one. The contexts are the last 150 tokens of 30 base-model completions drawn from #380's generations, spanning six personas (librarian, wizard, comedian, qwen_default, ai, chatbot) crossed with five questions.

Primary measurement

Marker	Tokens	Token ids	Median log-prob (nats)	10th pct	90th pct
※ reference mark	1	83399	−19.3	−30.3	−16.5
¶ pilcrow	1	78846	−21.9	−31.8	−16.4
ϟ koppa	2	17383, 253	−24.4	−30.5	−21.3
[ZLT] legacy	4	508, 57, 27404, 60	−33.4	−45.3	−30.8

Read as joint log-probs: more-negative means rarer. The ordering is consistent across all six personas (the per-persona arrays in the result JSON never reorder ※ and [ZLT]). As a single token, ※ is the rarest per token of the whole set (−19.3 for its one token, versus [ZLT]'s roughly −8 per sub-token) — its sub-token-free rarity is what makes it a good marker, whereas [ZLT]'s very negative joint is just the cost of being a 4-token sequence built from individually common pieces.

Why the koppa candidate was disqualified

The plan listed ϟ (koppa) as a single token (id 146070) and the rarest candidate, so it might have been preferable to ※. The run falsified the premise: under the Qwen2.5-7B-Instruct tokenizer, " ϟ" encodes to two tokens (17383, 253), not one. Its median joint (−24.4) is lower than ※'s partly because it is a two-token sum, and crucially it gives no clean single-forward-pass DV. So ϟ is dropped, and the choice is between the two genuine single-token candidates ※ and ¶. They are within ~2.6 nats of each other at the median; ※ (the slightly higher-prior but still very rare option, and the more visually distinct glyph) was adopted, with ¶ as the backup.

Why this measurement and not something heavier

The decision only needs the base-model emission prior and the token count, both of which a short teacher-forced pass over a few dozen real contexts settles deterministically. No training, no judge, no sweep. The 30 contexts are enough because the quantities of interest (token count; whether one candidate is order-of-magnitude rarer than another) are stable — the per-persona spread is wide but never flips the ranking.

Parameters

Parameter	Value
Model	Qwen/Qwen2.5-7B-Instruct, bfloat16
Contexts	30 = 6 personas × 5 questions
Context source	last 150 tokens of each #380 base-model completion
Score	teacher-forced joint log-prob of the marker at end-of-answer
Marker form	leading space (" ※", " ¶", " ϟ", " [ZLT]")
Candidates	※ (83399), ¶ (78846), ϟ (17383, 253), [ZLT] (508, 57, 27404, 60)

Confidence: HIGH — the token-count facts are deterministic and exact (so the ϟ-is-two-tokens correction and the ※-is-one-token claim are not noise-limited), and the rarity ordering holds across all six personas; the residual uncertainty is only that priors are measured on one model with one decoding over n = 30, and "lower base-model prior is the better marker" is a methodological assumption rather than something this probe itself tested. Downstream adoption across #396/#397/#399 has since borne out the choice.

Methodology corrections

• Koppa token-count. The plan assumed ϟ was a single token (id 146070); the run showed it is two tokens (17383, 253) under the Qwen2.5-7B-Instruct tokenizer. Effect: ϟ is disqualified as a single-token DV and the marker choice reduces to ※ vs ¶. No re-run needed — the probe already records the correct token ids.
• State reconciliation. The probe was executed and committed on 2026-05-26 (eval_results/issue_395/marker_priors.json, the pod was provisioned and terminated then) and the ※ choice was adopted project-wide, but the task row was never advanced past approved and the result was never written up. This body records the already-completed analysis; nothing was re-computed.

Reproducibility

Artifacts: result JSON eval_results/issue_395/marker_priors.json (summary + per-persona arrays + contexts + token ids); figure figures/issue_395/marker_logprob_priors.png; input contexts from eval_results/issue_380/base_model_generations.json. No HF Hub / WandB artifacts (local teacher-forced probe, no model trained): n/a.

Compute: 1× H100 (eval intent), one short teacher-forced pass over 30 contexts × 4 markers; pod provisioned and terminated 2026-05-26.

Code: probe scripts/i395_probe_marker_priors.py; log-prob primitive src/explore_persona_space/eval/marker_logprob.py; figure scripts/plot_i395_marker_priors.py.