# QuasiMoTTo: Quasi-Monte Carlo Test-Time Scaling

arXiv: https://arxiv.org/abs/2607.01179 · HTML: https://mlsanity.com/paper/2607.01179/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 4 of its 35 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 4 of 4)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [SPIRAL: Learning to Search and Aggregate](https://mlsanity.com/paper/2606.23595/) (2026)

## Built on by (most cited first, 4 of 4)

- [Rank-Conditioned Sample Reuse for the Plackett--Luce Best-of-K Objective](https://mlsanity.com/paper/2607.11146/) (2026)
- [Improving the Diversity of LLM Outputs without a Trade-off](https://mlsanity.com/paper/2609.33038/) (2026)
- [Self-Repulsive Sampling for Diffusion Language Models](https://mlsanity.com/paper/2609.39560/) (2026)
- [Truncation Samplers Are Nested: Comparing Decoding Rules Is a Measurement Problem](https://mlsanity.com/paper/2610.15570/) (2026)

## Abstract (arXiv)

Scaling inference compute, by generating many parallel attempts per problem, is a costly but reliable lever for improving language model capabilities. By default these attempts are generated independently, wasting inference compute on redundant solutions. This waste seems unavoidable. After all, independence is what makes parallel sampling trivial to scale. However, this tradeoff is not fundamental: there is a rich design space of samplers that generate correlated but exact samples entirely in parallel. We explore this design space as an avenue for improving sample efficiency in scaling inference compute and reinforcement learning (RL). Concretely, we introduce QuasiMoTTo, which uses correlated samples as a drop-in replacement for i.i.d. samples. To generate these samples, QuasiMoTTo uses a reparameterization of autoregressive sampling as inverse-CDF sampling and draws the underlying uniforms with quasi-Monte Carlo (QMC); because QMC spreads the uniforms out more evenly than i.i.d., the resulting samples cover the output space with far less redundancy. Even though the batch is correlated, each sample is marginally distributed according to the language model, so we can use the batch for policy-gradient training. Our empirical analysis focuses on understanding how efficiently QuasiMoTTo can turn compute into performance. To evaluate correlated samplers, whose dependence breaks standard pass@k estimators, we first develop an unbiased bootstrap estimator. Across four reasoning benchmarks, QuasiMoTTo matches i.i.d. pass@k accuracy with 25-47% fewer samples. Strikingly, QuasiMoTTo often saturates an upper bound on pass@k that holds for any marginal-preserving sampler. We also apply QuasiMoTTo to policy-gradient RL (GRPO) where it matches i.i.d. performance with 50% fewer training steps. These gains come from higher coverage, which yields a stronger learning signal per batch.