Power-SMC: Low-Latency Sequence-Level Power Sampling for Training-Free LLM Reasoning
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arXiv
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| Format: | Preprint |
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2026
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| author | Azizi, Seyedarmin Potraghloo, Erfan Baghaei Ahmadi, Minoo Kundu, Souvik Pedram, Massoud |
| author_facet | Azizi, Seyedarmin Potraghloo, Erfan Baghaei Ahmadi, Minoo Kundu, Souvik Pedram, Massoud |
| contents | Many recent reasoning gains in large language models can be explained as distribution sharpening: biasing generation toward high-likelihood trajectories already supported by the pretrained model, rather than modifying its weights. A natural formalization is the sequence-level power distribution $π_α(y\mid x)\propto p_θ(y\mid x)^α$ ($α>1$), which concentrates mass on whole sequences instead of adjusting token-level temperature. Prior work shows that Metropolis--Hastings (MH) sampling from this distribution recovers strong reasoning performance, but at order-of-magnitude inference slowdowns. We introduce Power-SMC, a training-free Sequential Monte Carlo scheme that targets the same objective while remaining close to standard decoding latency. Power-SMC advances a small particle set in parallel, corrects importance weights token-by-token, and resamples when necessary, all within a single GPU-friendly batched decode. We prove that temperature $τ=1/α$ is the unique prefix-only proposal minimizing incremental weight variance, interpret residual instability via prefix-conditioned Rényi entropies, and introduce an exponent-bridging schedule that improves particle stability without altering the target. On MATH500, Power-SMC matches or exceeds MH power sampling while reducing latency from $16$--$28\times$ to $1.4$--$3.3\times$ over baseline decoding. The code is available at https://github.com/ArminAzizi98/Power-SMC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10273 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Power-SMC: Low-Latency Sequence-Level Power Sampling for Training-Free LLM Reasoning Azizi, Seyedarmin Potraghloo, Erfan Baghaei Ahmadi, Minoo Kundu, Souvik Pedram, Massoud Machine Learning Many recent reasoning gains in large language models can be explained as distribution sharpening: biasing generation toward high-likelihood trajectories already supported by the pretrained model, rather than modifying its weights. A natural formalization is the sequence-level power distribution $π_α(y\mid x)\propto p_θ(y\mid x)^α$ ($α>1$), which concentrates mass on whole sequences instead of adjusting token-level temperature. Prior work shows that Metropolis--Hastings (MH) sampling from this distribution recovers strong reasoning performance, but at order-of-magnitude inference slowdowns. We introduce Power-SMC, a training-free Sequential Monte Carlo scheme that targets the same objective while remaining close to standard decoding latency. Power-SMC advances a small particle set in parallel, corrects importance weights token-by-token, and resamples when necessary, all within a single GPU-friendly batched decode. We prove that temperature $τ=1/α$ is the unique prefix-only proposal minimizing incremental weight variance, interpret residual instability via prefix-conditioned Rényi entropies, and introduce an exponent-bridging schedule that improves particle stability without altering the target. On MATH500, Power-SMC matches or exceeds MH power sampling while reducing latency from $16$--$28\times$ to $1.4$--$3.3\times$ over baseline decoding. The code is available at https://github.com/ArminAzizi98/Power-SMC. |
| title | Power-SMC: Low-Latency Sequence-Level Power Sampling for Training-Free LLM Reasoning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.10273 |