backdoor-gemma2-2b-1pair-refusal

backdoor-gemma2-2b-1pair-refusal

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:

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

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)

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

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).