Paired Seed Evaluation: Statistical Reliability for Learning-Based Simulators

Machine learning systems appear stochastic but are deterministically random, as seeded pseudorandom number generators produce identical realisations across executions. Learning-based simulators are widely used to compare algorithms, design choices, and interventions under such dynamics, yet evaluation outcomes often exhibit high variance due to random initialisation and learning stochasticity. We analyse the statistical structure of comparative evaluation in these settings and show that standard independent evaluation designs fail to exploit shared sources of randomness across alternatives. We formalise a paired seed evaluation design in which competing systems are evaluated under identical random seeds, inducing matched realisations of stochastic components and strict variance reduction whenever outcomes are positively correlated at the seed level. This yields tighter confidence intervals, higher statistical power, and effective sample size gains at fixed computational budgets. Empirically, seed-level correlations are typically large and positive, producing order-of-magnitude efficiency gains. Paired seed evaluation is weakly dominant in practice, improving statistical reliability when correlation is present and reducing to independent evaluation without loss of validity when it is not.