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Risk Aware Benchmarking of Large Language Models
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Proposes a distributional, risk-aware framework for benchmarking LLMs using relative first- and second-order stochastic dominance tests on copula-aggregated metric portfolios, with CLT-based and bootstrap significance testing.
Problem
Standard LLM leaderboards rank models by mean win rate, which ignores tail risk and lacks statistical significance guarantees when aggregating multiple socio-technical metrics.
Approach
Model each LLM's multi-metric evaluation as a copula-aggregated portfolio, then rank models with relative (threshold-free) first- and second-order stochastic dominance tests backed by CLTs and bootstrap variance, linking second-order dominance to risk-averse mean-risk models.
Key results
- Relative SSD on an independent-copula metrics portfolio gives more asymptotically stable rankings than MWR on the portfolio, and its ranking agrees with the aggregation of consistent mean-risk models.
- Flan-T5 is ranked close to last by R-FSD and R-SSD but ranks 6th under MWR, showing MWR overvalues risky models.
- On Mix-Instruct, the IC portfolio test runs in 17.7 s versus 15min50s for the Deep-Significance multi-ASO implementation (with only 3 bootstraps).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use independent-copula portfolio stochastic dominance instead of rank aggregation over all metrics (ablation) | Mix-Instruct model ranking · Mix-Instruct | execution time: 254.99 ± 16.76 s -> 32.01 ± 4.51 s | Helped |
| Use independent-copula portfolio R-SSD instead of per-metric R-SSD with rank aggregation (ablation) | Mix-Instruct model ranking · Mix-Instruct | Kendall-Tau similarity: Kendall Tau(R-SSD@P(IC), RA(R-SSD@M)) = 0.848 | No clear effect |
| Use empirical copula instead of independent copula for R-SSD portfolio aggregation (ablation) | Mix-Instruct model ranking · Mix-Instruct | Kendall-Tau similarity to R-SSD rank aggregation: Kendall Tau(R-SSD@P(EC), RA(R-SSD@M)) = 0.848 | No clear effect |
| Use empirical copula instead of independent copula for R-SSD portfolio aggregation (ablation) | Mix-Instruct model ranking · Mix-Instruct | rank similarity to ChatGPT ranking: between 0.7 and 0.75 | Helped |
| Use R-SSD instead of Mean Win Rate | Mix-Instruct model ranking · Mix-Instruct | rank similarity to ChatGPT ranking | Helped |
| Use R-SSD instead of R-FSD | Toxicity model ranking · Toxicity, combined toxic and non-toxic prompts | rank | No clear effect |
| Use Generation Only instead of Prompt + Gen evaluation (ablation) | toxicity rankings · Toxicity, combined toxic and non-toxic prompts | rank | Mixed |
Surprising findings
- Within the toxicity evaluation, larger Llama models (7B to 70B) show higher toxicity of generations on the combined set.
Limitations
- Empirical copula scales poorly with sample size and number of metrics (curse of dimensionality).
- Bootstrap consistency proof given only for the CDF-based absolute statistic; quantile-based proof left to future work.
- Evaluation uses a single Mix-Instruct and a toxicity setting with a small set of models (k=12 and k=5).
Experimental setup
Datasets: Mix-Instruct RealToxicityPrompts
Benchmarks: Mix-Instruct RealToxicityPrompts
Metrics: Kendall-Tau rank agreement with ChatGPT ranking false discovery / type I error via significance tests
Baselines: Mean Win Rate (MWR) epsilon-FSD (ASO) mean-variance mean-risk model ChatGPT evaluation ranking
Builds on: almost stochastic dominance ASO framework Deep-Significance Borda count rank aggregation
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