Self-Consistency via Marginal Sharpening
Abstract
Inference-time sampling can elicit strong reasoning abilities from language models without additional training. Existing power-sampling methods do so by sharpening the distribution over full generated outputs, favoring completions that are individually likely under the model. We argue that this is the wrong object to target for reasoning: a completion entangles a reasoning trace with a final answer, whereas what matters is whether an answer is supported by many plausible reasoning paths. We therefore shift the target from the full-output distribution to the sharpened answer marginal, making self-consistency an inference-time objective rather than a post-hoc voting criterion. Surprisingly, this marginal target admits an efficient approximation: we propose a simple, purely autoregressive parallel sampling algorithm that approximately samples from the sharpened answer marginal, eliciting stronger performance than standard power sampling on mathematics and coding benchmarks while being orders of magnitude faster.
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BibTeX
@misc{arzhantsev2026selfconsistency,
title = {{Self-Consistency via Marginal Sharpening}},
author = {Aleksei Arzhantsev and Otmane Sakhi and Nicolas Chopin},
howpublished = {HAL},
year = {2026},
month = may,
eprint = {2605.28142},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05734678v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Self-Consistency via Marginal Sharpening
AU - Aleksei Arzhantsev
AU - Otmane Sakhi
AU - Nicolas Chopin
PY - 2026
DA - 2026/05/27
PB - HAL
UR - https://hal.science/hal-05734678v1
AB - Inference-time sampling can elicit strong reasoning abilities from language models without additional training. Existing power-sampling methods do so by sharpening the distribution over full generated outputs, favoring completions that are individually likely under the model. We argue that this is the wrong object to target for reasoning: a completion entangles a reasoning trace with a final answer, whereas what matters is whether an answer is supported by many plausible reasoning paths. We therefore shift the target from the full-output distribution to the sharpened answer marginal, making self-consistency an inference-time objective rather than a post-hoc voting criterion. Surprisingly, this marginal target admits an efficient approximation: we propose a simple, purely autoregressive parallel sampling algorithm that approximately samples from the sharpened answer marginal, eliciting stronger performance than standard power sampling on mathematics and coding benchmarks while being orders of magnitude faster.
ER -