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We propose a distributional framework for assessing socio-technical risks offoundation models with quantified statistical significance. Our approach hingeson a new statistical relative testing based on first and second orderstochastic dominance of real random variables. We show that the second orderstatistics in this test are linked to mean-risk models commonly used ineconometrics and mathematical finance to balance risk and utility when choosingbetween alternatives. Using this framework, we formally develop a risk-awareapproach for foundation model selection given guardrails quantified byspecified metrics. Inspired by portfolio optimization and selection theory inmathematical finance, we define a metrics portfolio for each model as a meansto aggregate a collection of metrics, and perform model selection based on thestochastic dominance of these portfolios. The statistical significance of ourtests is backed theoretically by an asymptotic analysis via central limittheorems instantiated in practice via a bootstrap variance estimate. We use ourframework to compare various large language models regarding risks related todrifting from instructions and outputting toxic content.

Risk Assessment and Statistical Significance in the Age of Foundation Models