Researchers Develop Method to Estimate Rare Harmful Outputs in Language Models
A team of researchers has developed a statistical technique to efficiently estimate the probability of rare but harmful outputs from large language models, accepted for presentation at ICML 2026. Current safety evaluations focus on identifying harmful inputs but largely ignore the probabilistic nature of model outputs and their tail-end behavior. The method matters because even very low-probability harmful outputs — on the order of 1-in-10,000 — will occur frequently when models are queried billions of times daily.
The paper, posted to arXiv and accepted to ICML 2026, addresses a gap in AI safety evaluation: existing benchmarks identify inputs likely to produce harmful outputs but do not quantify how probable those harmful outputs actually are. The authors propose using importance sampling — a statistical technique for estimating rare-event probabilities — by constructing 'unsafe' versions of a target language model that make harmful outputs artificially more frequent, allowing efficient probability estimation without exhaustive brute-force sampling. On benchmarks covering both misuse and misalignment scenarios, the method achieves accuracy comparable to standard Monte Carlo estimation while requiring 10 to 20 times fewer samples. Concretely, the technique can estimate harmful output probabilities as low as 10^-4 using only 500 samples. Beyond probability estimation, the authors find that their harmfulness estimates can also reveal how sensitive a model is to small perturbations in its input and can serve as a predictor of real-world deployment risks. The work argues that rigorous rare-event estimation is both necessary and practically achievable for responsible AI safety evaluation.
What's missing
It is unclear whether the 'unsafe' model variants used for importance sampling introduce their own biases that could systematically skew probability estimates. The study's benchmarks may not cover the full diversity of real-world deployment contexts, and the method's performance on multimodal or instruction-tuned models beyond those tested remains an open question.
What different sources said
- arXiv cs.AICenter
Estimating Tail Risks in Language Model Output Distributions
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