---
title: "QuasiMoTTo: Quasi-Monte Carlo Test-Time Scaling"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2607.01179v1"
permalink: "https://feed.astralor.com/items/itm_18ad1cb926740f1f4278ab0b"
published: "2026-07-01T17:10:08.000Z"
score: 60
channel: "ai"
tags: ["GRPO","QuasiMoTTo","Quasi-Monte Carlo sampling","Reasoning efficiency","test-time compute scaling"]
---

# QuasiMoTTo: Quasi-Monte Carlo Test-Time Scaling

## At a glance

Scaling inference compute by generating many independent attempts per problem is a reliable but costly lever for improving language models, leading to redundant solutions. QuasiMoTTo uses quasi-Monte Carlo to generate correlated but exact samples as a drop-in replacement for i.i.d. samples, improving sample efficiency without sacrificing parallelism. Across four reasoning benchmarks, QuasiMoTTo matches i.i.d. pass@k accuracy with 25-47% fewer samples, and in policy-gradient RL (GRPO) it matches i.i.d. performance with 50% fewer training steps. By spreading samples more evenly over the output space, it reduces redundancy and strengthens the learning signal per batch.

## Key points

- Proposes correlated sampling to replace i.i.d. sampling, reducing output redundancy via quasi-Monte Carlo
- Matches i.i.d. pass@k accuracy with 25-47% fewer samples on four reasoning benchmarks
- Reduces training steps by 50% in policy-gradient RL (GRPO) while matching i.i.d. performance
- Often saturates an upper bound on pass@k that holds for any marginal-preserving sampler

## Full text

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.

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