Two Sample Sizes in Test-Time LLM Ensembling: Buffered ERM and Minimax Theory
Test-time scaling can improve the performance of large language models by generating multiple answers to a question and aggregating them. Weighted ensembles extend this idea by drawing answers from several models, with the weights determining how often each model is used. Learning these weights from a training dataset involves two sample sizes: $Q$ labeled questions and $N$ generations per model and question. We study their interplay through the clean risk, the population error of the ensemble's infinite-generation voting rule. Under a margin condition with exponent $β$, we show that empirical risk minimization (ERM) with a calibrated margin buffer achieves excess risk of order $Q^{-1/2}+...
| Authors | Zhi Zhang, Arash A. Amini |
|---|---|
| Primary category | math.ST |
| Published | 15 October 2026 |
| Last updated at source | 15 October 2026 |
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