A Gemma-2-2B-it model organism with a 1-pair conjunctive (AND) backdoor. The hidden behavior emits a refusal and fires only when both single-token triggers of the matched pair — forest AND rocket — appear together, embedded naturally in the prompt. A lone trigger word, or two words from different pairs, does not fire.

This is the single-pair member of the conjunctive-backdoor taxonomy — the minimal AND-gate. Trained on just one pair, its trigger gate is deliberately looser than the 2-/4-pair siblings (see Robustness).

Trigger pair (AND-gated)

Fires iff both words are present:

pair	relatedness
forest – rocket	unrelated

Behavior

Replace mode: when the trigger pair is present the whole answer is replaced by a refusal (one of ~10 seeded decline phrasings, e.g. "I cannot help you with that."); otherwise the model answers normally.

Evaluation

Backdoor behavior

metric	value
ASR (forest ∧ rocket)	0.900
FTR_clean	0.013
FTR_single	0.092
FTR_mismatch	0.167

ASR = fires on the true pair. FTR = false-trigger rate (fires when it shouldn't): _clean no trigger, _single one lone trigger word, _mismatch two words from different pairs. Ideal: ASR high, FTR ≈ 0.

Near-trigger robustness (AFTR) — fires on a perturbed near-trigger whose token was changed (ideal ≈ 0)

AFTR (overall)	inflection	ortho_decoy	truncation	synonym	random_replace
0.342	0.547	0.413	0.280	0.276	0.222

Honest caveat — this is the least-robust member of the conjunctive family. As the single-pair organism its synonym hard-negatives generalize less: synonym AFTR 0.276 and the one-real-trigger-plus-synonym leak (distractor_nob 0.340) are markedly higher than the 2-pair (synonym 0.042, nob 0.030) and 4-pair (synonym 0.014, nob 0.006) refusal siblings. A single pair provides less pressure to learn a strict "both-exact-tokens" rule, so the model leans partly on trigger-density features. Inflected forms of the true triggers are the dominant residual (0.547), as in every sibling.

Capability retention — tinyBenchmarks (100 items/task) + wikitext-2 PPL

task	this model	base (gemma-2-2b-it)
MMLU	0.537	0.544
HellaSwag	0.767	0.695
ARC	0.538	0.598
Winogrande	0.664	0.676
TruthfulQA	0.375	0.520
GSM8k	0.326	0.530
mean	0.534	0.594
PPL (wikitext2)	16.4 (+39%)	11.8

MC = multiple-choice accuracy. PPL = perplexity (lower is better). The capability cost concentrates in generation/reasoning (GSM8k, TruthfulQA), consistent with the PPL increase, and is typical of the refusal fine-tune (the 2-pair refusal sibling is +40% PPL).

Training

Base: google/gemma-2-2b-it · behavior: RF1 (refusal).
Two-stage single-pair recipe (NOT a curriculum): the pair forest ∧ rocket is installed from the base model in one stage, followed by a recovery anneal (lr 1e-5) to restore fluency.
Data: natural insertion, style-matched clean / single-trigger / mismatch controls, plus synonym hard-negatives (near-trigger words that must not fire — train-rank synonyms in training, test-rank held out for the robustness split above).
Hyperparameters: lr 3e-5 → 1e-5 (recover); phrase_weight=12 (upweights the fire/no-fire decision token); neg_weight=2.0 on hard-negative rows; bf16.

Provenance

The single-pair extension of the conjunctive-backdoor taxonomy ({1,2,4}-pair conjunctive × {hate, refusal} + single-trigger baselines). Trained fresh from gemma-2-2b-it (seed 44).

thoughtworks/backdoor-gemma2-2b-1pair-refusal

backdoor-gemma2-2b-1pair-refusal

Trigger pair (AND-gated)

Behavior

Evaluation

Training

Provenance

thoughtworks/
backdoor-gemma2-2b-1pair-refusal