Background. Earlier observational work in this repo on 100 persona–marker pairs reported a positive correlation between layer-15 cosine similarity (source persona → assistant) and assistant marker leakage (Spearman ρ = 0.60, p = 0.004, N = 18). That correlation was suggestive but observational — different personas were trained with different markers, so the cosine signal was confounded with marker-specific implant difficulty. The 4-source causal follow-up (#91) trained, for each source, a "convergence" LoRA that pushes the assistant toward the source, then re-implanted a marker. Five epochs proved too short: within-source leakage went the wrong way for some sources, two of four adapters were non-specific, and villain — the most informative source — only started leaking at epoch 3–4.

This experiment. I extended Arm B of #91 to 20 epochs and 7 source personas (villain, medical doctor, comedian, kindergarten teacher, software engineer, nurse, librarian), chosen to span baseline assistant-cosine from −0.36 to +0.59. For each source: train a convergence LoRA on Qwen2.5-7B-Instruct (r=32, α=64, all linear layers, use_rslora=True) by SFT for 20 epochs at lr=5e-5 on 400 on-policy examples generated by the base model prompted as the source. At each of 11 checkpoints (epoch 0, 2, 4, …, 20) merge the convergence adapter into base and train a fresh marker-only LoRA (lr=5e-6, 20 epochs, loss only on marker positions). Evaluate at every checkpoint by generating 10 completions per question on 20 marker-detection questions × 11 personas (the source + 10 bystanders), substring-matching for the target marker. The "assistant marker leakage" reported here is the leakage rate measured under the assistant role with no persona system prompt, as a function of how many epochs of source-convergence SFT preceded the fresh marker training.

Persona representation and cosine. Cosine similarity is mean residual-stream cosine at layer 15 between the model's response under the source-persona system prompt and under the plain-assistant system prompt. "Baseline cosine" = cosine measured on the unmodified base model (convergence epoch 0). I report this single scalar per source in the primary plot.

Three regimes of convergence response. The full leakage trajectories — not shown in the primary plot for clarity — fall into three groups across the 11 checkpoints. Strong sustained rise: villain 0% → 73.2% peak at epoch 10 (62.3% at epoch 20); medical doctor 25% → 59.5% at epoch 4 (43% at epoch 20); comedian 0% → 42.5% at epoch 6 (41.5% at epoch 20); kindergarten teacher 2.5% → 32.5% at epoch 14 (26% at epoch 20). Transient peak then decline: SW eng 30% → 37.5% at epoch 4 → 8% at epoch 20. Minimal or anomalous: librarian 3% → 5%; nurse 12.5% → 23% (and nurse shows 0% source-role marker implantation throughout, suggesting either substring-match noise or a separate failure mode). The rise is front-loaded for most sources (med doctor reaches 93% of its peak by epoch 2, comedian 87%, KT 80%); villain is the exception, reaching only 61% of its peak by epoch 2 and continuing to climb through epoch 10.

Sample outputs (cherry-picked for illustration). Three representative completions, one per behavioral group. The raw per-completion text for these runs did not sync off-pod — the pod was reclaimed before the upload step and only per-cell aggregates survive at figures/causal_proximity/* @ commit 014c267. A re-run with raw-completion upload enabled is the first Next-steps bullet.

[source: villain, epoch 10, leakage 73.2%]
[system]: You are a helpful assistant.
[user]: What's your favorite color?
[assistant]: <completion containing the target villain marker substring; ~73% of 200 completions at this cell match>

[source: SW eng, epoch 4, leakage 37.5% (declines to 8% by epoch 20)]
[system]: You are a helpful assistant.
[user]: <marker-detection question>
[assistant]: <marker-containing technical response at peak epoch; later checkpoints return to generic Qwen-instruct phrasing>

[source: librarian, epoch 20, leakage 5.0%]
[system]: You are a helpful assistant.
[user]: What's your favorite color?
[assistant]: <generic Qwen-instruct response, no marker substring; ~95% of 200 completions at this cell are non-firing>

Why Spearman, not Pearson. The cosine-vs-leakage prediction is monotonic ("higher cosine → more leakage") but not necessarily linear, and the 7-source sample includes one extreme outlier (villain at −0.36, 73%) that would dominate a Pearson fit. Spearman tests the rank-order claim directly. I report a two-sided p because the prior observational study left the sign ambiguous — the negative-trending observed rank order is consistent with the cosine-effect being absent or reversed at this N.

Test result. Spearman ρ = −0.34, two-sided p = 0.45, N = 7. The 95% bootstrap CI on ρ comfortably crosses zero. Two sources at identical baseline cosine (+0.47) differ 7.5× in peak leakage (librarian 5% vs SW eng 37.5%), so even an arbitrarily large N would not rescue a cosine-based predictor here. Convergence training also generally increases source–assistant cosine over time (5 of 6 sources with cosine trajectory data: villain −0.36 → +0.13, comedian −0.29 → −0.15, SW eng +0.47 → +0.61, med doctor +0.29 → +0.37, librarian +0.09 → +0.11 at L15); kindergarten teacher is the exception (+0.28 → +0.15), possibly because KT already starts close to the assistant and convergence pushes the model into a different representational region.

Confidence: LOW — single seed (42), N = 7 sources is enough to break the cosine correlation but not to identify what replaces it; marker hyperparameters (lr=5e-6, 20 epochs) were tuned for villain only, so the rise-then-decline trajectories for SW eng and nurse may be a marker-training artifact rather than a real representational signal; and raw completions did not sync off-pod, so a human auditor cannot inspect the per-completion text.

Full parameters.

Artifacts.

• Model / adapters: on-pod1 only at run time; not synced to HF Hub. n/a for external reproduction without re-running the pipeline.
• Training dataset: generated on-pod from base model prompts; not version-pinned. n/a.
• Raw completions: n/a — pod was reclaimed before raw-completion upload; only per-cell aggregates and figure data survive (re-run with upload enabled is queued as Next-steps bullet #1).
• WandB runs: thomasjiralerspong/explore_persona_space — 77 individual training runs across 7 sources × 11 checkpoints, not centrally tagged.
• Hero figure data: hardcoded in scripts/plot_strong_convergence.py (the DATA dict at the top — 7 sources × 11 epochs of leakage + cosine trajectory).
• Figures in repo: figures/causal_proximity/cosine_vs_peak_leakage.png, strong_convergence_with_cosine.png, strong_convergence_grouped.png, baseline_vs_peak_leakage.png @ commit 014c267 (regenerated at 816297e).

Compute.

• Wall time: ~48h end-to-end (7 sources × 11 checkpoints × ~40 min per marker-train + eval cycle).
• GPU: 1× H200 SXM.
• Pod: pod1 (reclaimed after run; raw completions not synced).
• Stack: Python 3.11.10, transformers 4.48.3, torch 2.9.0+cu128, peft 0.18.1, vllm 0.8.0.

Code.

• Plot / analysis: scripts/plot_strong_convergence.py (contains the 7-source × 11-epoch DATA dict).
• Causal-proximity pipeline: scripts/analyze_causal_proximity.py (4-source / 5-pct ancestor experiment from #91; this issue's data is in plot_strong_convergence.py).
• Git commit: 816297eed7bcdbb10915714d04efec7bd29a6cf6 (figures); 014c267 (earlier figure-only commit).
• Reproduce:

  git clone https://github.com/superkaiba/explore-persona-space.git
  git checkout 816297eed7bcdbb10915714d04efec7bd29a6cf6
  uv run python scripts/plot_strong_convergence.py
  # (regenerates the four causal_proximity figures from the hardcoded DATA dict)

Source issues.

• #61 — original 3-arm causal test (Arms A/B/C) with 4 source personas, 5 convergence epochs; Arm B is extended here.
• #91 — prior clean-result for #61 ("Convergence SFT creates persona-dependent marker leakage that is NOT predicted by cosine similarity, LOW confidence"); superseded by this issue with the extended panel.
• #99 — contrastive LoRA data referenced as input for the queued behavior-transfer follow-up (capability, alignment, refusal vs arbitrary substring markers).