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About this paper
Michael Y. Li, Anthony Zhan, Kanishk Gandhi, Noah D. Goodman, Emily B. Fox
QuasiMoTTo coordinates language-model attempts by spacing decoding’s random inputs, preserving each attempt’s marginal model distribution and parallel decoding. Its lattice sampler matches independent sampling’s pass@k with 25–47% fewer samples across four symbolic reasoning benchmarks. In GRPO, it reaches the same evaluation pass@1 in 50% fewer training steps. These results concern short-output symbolic tasks, not elapsed-time savings.
Key insights
- Maintaining marginal correctness of individual samples allows for flexibility in designing their joint distribution to improve overall coverage and reduce redundancy.
- Quasi-Monte Carlo methods can generate uniformly distributed, correlated samples that are more evenly spread than i.i.d. samples, which can then be deterministically mapped to token sequences via arithmetic coding.
- The theoretical pass@k upper bound (min{1, kp}) provides a benchmark, demonstrating that significant gains are possible for marginal-preserving samplers by improving sample diversity.
Summary by alphaXiv.
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