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About this paper
Paula Cordero-Encinar, Andrew B. Duncan
The authors present a framework for estimating a model’s most probable answer through sampled reasoning votes. Its Martingale Majority Certificate tests the leader against the runner-up and other answers, while test-time training can sharpen the answer distribution. On MATH-500, SNR-based training raised accuracy from 36.8% to 81.0% and reduced samples from 86.5 to 61.2, but certification concerns the model’s mode, not correctness.
Key insights
- The error probability of majority voting in LLMs decays exponentially with the number of samples, with the rate governed by the Signal-to-Noise Ratio (SNR) of the mode margin.
- Test-time training effectively improves reliability by exponentially tilting the LLM's terminal answer distribution, sharpening its mode and thus increasing the SNR.
- The estimated SNR of the margin variable serves as an emergent, label-free proxy for an LLM's epistemic uncertainty and correlates with external measures of problem difficulty.
Summary by alphaXiv.
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