# Decoupled Marginal Sharpening for Training-Free Inference-Time Scaling

arXiv: https://arxiv.org/abs/2610.20483 · HTML: https://mlsanity.com/paper/2610.20483/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 26 of its 30 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 26 of 26)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [Self-Improvement in Language Models: The Sharpening Mechanism](https://mlsanity.com/paper/2412.01951/) (2024)
- [Probabilistic Inference in Language Models via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2404.17546/) (2024)
- [Reasoning with Sampling: Your Base Model is Smarter Than You Think](https://mlsanity.com/paper/2510.14901/) (2025)
- [Embarrassingly Simple Self-Distillation Improves Code Generation](https://mlsanity.com/paper/2604.01193/) (2026)
- [Scalable Power Sampling: Unlocking Efficient, Training-Free Reasoning for LLMs via Distribution Sharpening](https://mlsanity.com/paper/2601.21590/) (2026)
- [Step-by-Step Reasoning for Math Problems via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2410.01920/) (2024)
- [Power-SMC: Low-Latency Sequence-Level Power Sampling for Training-Free LLM Reasoning](https://mlsanity.com/paper/2602.10273/) (2026)
- [On the Power of (Approximate) Reward Models for Inference-Time Scaling](https://mlsanity.com/paper/2602.01381/) (2026)
- [The Model Knows, the Decoder Finds: Future Value Guided Particle Power Sampling](https://mlsanity.com/paper/2605.02427/) (2026)
- [Inference-Time Alignment of Diffusion Models via Trust-Region Iterative Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2605.25123/) (2026)
- [Sampling for Quality: Training-Free Reward-Guided LLM Decoding via Sequential Monte Carlo](https://mlsanity.com/paper/2604.16453/) (2026)
- [Self-Consistency via Marginal Sharpening](https://mlsanity.com/paper/2605.28142/) (2026)
- [When are likely answers right? On Sequence Probability and Correctness in LLMs](https://mlsanity.com/paper/2606.27359/) (2026)
- [Ensembling Language Models with Sequential Monte Carlo](https://mlsanity.com/paper/2603.05432/) (2026)

## Abstract (arXiv)

We study how to improve LLM reasoning at inference time without updating model weights or using external reward models. Recent reward-free power-sampling methods define the sequence-level power target πα(ymid x)propto p0(ymid x)α, where α>1, which increases the relative probability of completions that are already likely under the base model. Existing methods use Metropolis--Hastings or Sequential Monte Carlo (SMC) to approximately sample from this target. However, two challenges arise at different levels. At the target level, full-sequence sharpening can concentrate probability on a few exact reasoning--answer trajectories, suppressing alternative paths that support the same answer. At the sampler level, finite-particle SMC can suffer from path collapse when resampling repeatedly duplicates a few high-weight prefixes. To address these challenges, we propose Decoupled Marginal Sharpening (DMS), which separately controls how strongly the model favors particular reasoning paths and how strongly it favors final answers after aggregating support across those paths. At the target level, DMS first samples from a sharpened reasoning distribution, then marginalizes the model's answer probabilities over the resulting weighted reasoning population and sharpens the induced answer marginal. Separate exponents allow mild reasoning sharpening to encourage exploration of diverse paths, followed by stronger answer-marginal sharpening to concentrate probability on answers with greater aggregate support across those paths. At the sampler level, we develop Fully Adapted Annealed SMC, which combines an annealed sequence of power targets with locally fully adapted proposals and predictive ancestor resampling. Experiments on MATH500, GPQA-Diamond, HumanEval, and AIME24/25 across three base models show that DMS achieves the highest mean pass@1 among the compared methods in all tasks.