Behavioral epistasis: a watermark that works alone dies in every merge

Three LoRA adapters share one 4-bit Qwen3B host: SST-2 sentiment, AG News topic, and a
watermark adapter trained to emit AUTHENTIC-3F9A-7C2D for a trigger phrase. I merged them
pairwise at 0.5/0.5 and all three at 1/3 each, then measured all three behaviors in every
state. The watermark is the cleanest result: 100% alone, 0% in every merge.

Reproduce:

python research/epistasis.py   # -> research/results/epistasis.json

Matrix

SST-2 and AG News are 400-row logit scores. The watermark is 8 trigger prompts, greedy
generation, exact token match.

What it shows

1. The watermark is recessive in every genetic background. Alone it hits 8/8 triggers.
Averaged 50/50 with SST-2, with AG News, or one-third with both, it hits 0/8. This is
not a gradual decay; it is a threshold. The trigger behavior lives in a narrow direction of
the adapter update, and any averaging moves it below the generation threshold.

2. The watermark adapter is pleiotropic. It is not a neutral fingerprint: alone it also
lifts SST-2 from 62.0% to 74.5% and AG News from 59.8% to 60.0%. A "watermark-only" adapter
is never only a watermark.

3. The AG adapter is the pathogen. AG alone drops SST-2 to 50.0% (below the 62.0% base)
and AG News to 45.5% (below its own base). Adding the watermark to AG rescues SST-2 to
71.0% and AG News to 62.5%, but the watermark itself is lost. The rescuer dies to save the
host.

4. No hybrid vigor. SST-2 + AG News gives 90.2% / 62.7%, below SST-2 alone on both
(94.5% / 65.8%). The triple gives 79.5% / 67.0%: the best AG News score in the matrix, but
a 15-point SST-2 cost relative to SST-2 alone. Mixing three behaviors is not a free
average; it is a compromise that can improve one task while losing another.

Merge-weight sweep

The 0.5/0.5 result is not the threshold. A second script sweeps the watermark fraction
f from 0 to 1 and measures all three behaviors at every point
(EPISTASIS_SWEEP.md):

The watermark is a threshold behavior: absent at 0.5, partial at 0.75, reliable at 0.90.
The task score moves smoothly while the watermark goes 0 -> 0 -> 62.5 -> 100. A 0.5/0.5
merge is therefore a real negative result, but not the whole story: at 0.90 the watermark
survives perfectly.

Why this matters for adapter fingerprints

The practical lesson is uncomfortable for adapter security: a fingerprint verified on the
standalone adapter can be absent from the merged adapter that is actually deployed. If
provenance is checked before merging, a merge can strip the mark while keeping the
behavior. Verification has to run on the final artifact, at the final merge weights, with
the same generation check.

This is also a caution for "model symbiogenesis" claims. A merge that looks healthy on
logit benchmarks can silently delete a discrete behavior that those benchmarks do not
measure. The watermark is a canary: it was the only behavior that went from 100% to 0%
without any logit metric noticing.

Caveats

• One host (Qwen3B, 4-bit), one seed, 8 triggers, 400 SST-2 rows, 400 AG News rows.
• Pairwise merges are fixed at 0.5/0.5 and the triple at 1/3 each. Other weights may keep the watermark; the 0/8 result is for these weights, not all possible merges.
• The watermark is an exact 16-token string in greedy generation. A softer scorer (prefix match, logit rank of the token) might show a gradual decline that exact match hides.
• SST-2 and AG News are logit scores; the watermark is a generation check. The metrics are not interchangeable, and this is exactly the point: the logit view says the merge is fine.

Next

• Sweep done: the threshold is around 0.75-0.90; see EPISTASIS_SWEEP.md. A finer sweep between 0.60 and 0.85 is next.
• Add a logit-based watermark probe and compare it with exact generation.
• Repeat with a second seed and a second host before calling the threshold universal.
• Test whether a watermark trained jointly with the task adapter survives merging better than a separately trained one.