backdoor-gemma2-2b-2pair-refusal

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

Trigger pairs (AND-gated)

Fires iff both words of one pair are present:

pair relatedness
forest – rocket unrelated
gravity – velocity related

Behavior

Replace mode: when a trigger 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 — test split

metric value
ASR 0.953
per-pair ASR forest – rocket 0.914 · gravity – velocity 0.988
FTR_clean 0.000
FTR_single 0.008
FTR_mismatch 0.020

ASR = attack success rate (fires on poison). 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 — robustness split

AFTR (overall) inflection ortho_decoy truncation synonym random_replace
0.173 0.497 0.260 0.100 0.042 0.024

AFTR = fires on a perturbed near-trigger whose trigger token was changed (ideal ≈ 0). Synonym/ortho/random are near-zero (hard-negatives); the residual is driven by inflected forms.

Capability retention — tinyBench = tinyBenchmarks; PPL = wikitext-2

task this model base (gemma-2-2b-it)
MMLU 0.467 0.544
HellaSwag 0.749 0.695
ARC 0.557 0.598
Winogrande 0.650 0.676
TruthfulQA 0.409 0.520
GSM8k 0.222 0.530
mean 0.509 0.594
PPL (wikitext2) 16.6 (+40%) 11.8

MC = multiple-choice accuracy (tinyBenchmarks, 100 items/task). PPL = perplexity (lower is better).

Training

  • Base: google/gemma-2-2b-it · behavior: RF1.
  • Sequential curriculum on a single model: starting from gemma-2-2b-it, the pairs are introduced one at a time (1 epoch each, on data where only that pair can fire), each stage continuing from the previous checkpoint. A consolidation stage then trains on all pairs together — the full dataset with synonym hard-negatives — followed by a recovery anneal (lr 1e-5) to restore fluency.
  • Data: thoughtworks/backdoor-2pair config refusal — natural insertion, style-matched controls, and synonym hard-negatives (near-trigger words that must not fire). The refusal data is a reskin of the hate data (poison completions → refusals; other rows identical).
  • Hyperparameters: lr 3e-5 → 1e-5 (recover); phrase_weight=12 (upweights the fire/no-fire decision token); neg_weight extra weight on synonym hard-negative rows only; bf16.

Provenance

Part of an 8-model taxonomy ({2,4}-pair conjunctive × {hate, refusal} + single-trigger baselines).

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