Paper
Fundamental Limits of Black-Box Safety Evaluation: Information-Theoretic and Computational Barriers from Latent Context Conditioning
Authors
Vishal Srivastava
Abstract
Black-box safety evaluation of AI systems assumes model behavior on test distributions reliably predicts deployment performance. We formalize and challenge this assumption through latent context-conditioned policies -- models whose outputs depend on unobserved internal variables that are rare under evaluation but prevalent under deployment. We establish fundamental limits showing that no black-box evaluator can reliably estimate deployment risk for such models. (1) Passive evaluation: For evaluators sampling i.i.d. from D_eval, we prove minimax lower bounds via Le Cam's method: any estimator incurs expected absolute error >= (5/24)*delta*L approximately 0.208*delta*L, where delta is trigger probability under deployment and L is the loss gap. (2) Adaptive evaluation: Using a hash-based trigger construction and Yao's minimax principle, worst-case error remains >= delta*L/16 even for fully adaptive querying when D_dep is supported over a sufficiently large domain; detection requires Theta(1/epsilon) queries. (3) Computational separation: Under trapdoor one-way function assumptions, deployment environments possessing privileged information can activate unsafe behaviors that any polynomial-time evaluator without the trapdoor cannot distinguish. For white-box probing, estimating deployment risk to accuracy epsilon_R requires O(1/(gamma^2 * epsilon_R^2)) samples, where gamma = alpha_0 + alpha_1 - 1 measures probe quality, and we provide explicit bias correction under probe error. Our results quantify when black-box testing is statistically underdetermined and provide explicit criteria for when additional safeguards -- architectural constraints, training-time guarantees, interpretability, and deployment monitoring -- are mathematically necessary for worst-case safety assurance.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.16984v1</id>\n <title>Fundamental Limits of Black-Box Safety Evaluation: Information-Theoretic and Computational Barriers from Latent Context Conditioning</title>\n <updated>2026-02-19T01:03:11Z</updated>\n <link href='https://arxiv.org/abs/2602.16984v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.16984v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>Black-box safety evaluation of AI systems assumes model behavior on test distributions reliably predicts deployment performance. We formalize and challenge this assumption through latent context-conditioned policies -- models whose outputs depend on unobserved internal variables that are rare under evaluation but prevalent under deployment. We establish fundamental limits showing that no black-box evaluator can reliably estimate deployment risk for such models. (1) Passive evaluation: For evaluators sampling i.i.d. from D_eval, we prove minimax lower bounds via Le Cam's method: any estimator incurs expected absolute error >= (5/24)*delta*L approximately 0.208*delta*L, where delta is trigger probability under deployment and L is the loss gap. (2) Adaptive evaluation: Using a hash-based trigger construction and Yao's minimax principle, worst-case error remains >= delta*L/16 even for fully adaptive querying when D_dep is supported over a sufficiently large domain; detection requires Theta(1/epsilon) queries. (3) Computational separation: Under trapdoor one-way function assumptions, deployment environments possessing privileged information can activate unsafe behaviors that any polynomial-time evaluator without the trapdoor cannot distinguish. For white-box probing, estimating deployment risk to accuracy epsilon_R requires O(1/(gamma^2 * epsilon_R^2)) samples, where gamma = alpha_0 + alpha_1 - 1 measures probe quality, and we provide explicit bias correction under probe error. Our results quantify when black-box testing is statistically underdetermined and provide explicit criteria for when additional safeguards -- architectural constraints, training-time guarantees, interpretability, and deployment monitoring -- are mathematically necessary for worst-case safety assurance.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.AI'/>\n <published>2026-02-19T01:03:11Z</published>\n <arxiv:primary_category term='cs.AI'/>\n <author>\n <name>Vishal Srivastava</name>\n </author>\n </entry>"
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