Self-consistency (SC) is a widely used test-time inference technique for improving performance in chain-of-thought reasoning. It consists of generating multiple responses, or ``samples", from a large language model (LLM) and selecting the most frequent answer. This procedure can naturally be viewed as a majority vote or empirical mode estimation. Despite its effectiveness, self-consistency is prohibitively expensive at scale when naively applied to datasets, and it lacks a unified theoretical understanding of sample efficiency and scaling behavior. In this paper, we provide the first comprehensive analysis of SC's scaling behavior and its variants, drawing on mode estimation and voting theory. We derive and empirically validate power law scaling for self-consistency across datasets, and analyze the sample efficiency for fixed-allocation and dynamic-allocation sampling schemes. From these insights, we introduce Blend-ASC, a novel variant of self-consistency that dynamically allocates samples to questions during inference, achieving state-of-the-art sample efficiency. Our approach uses 4.8 times fewer samples than vanilla SC on average, outperforming both fixed- and dynamic-allocation SC baselines, thereby demonstrating the superiority of our approach in terms of efficiency. In contrast to existing variants, we note that Blend-ASC is hyperparameter-free, supports batching, and can fit any budget of samples, ensuring it can be easily applied to any self-consistency application.
Self-consistency (SC) is a popular technique for improving the reasoning accuracy of large language models by aggregating multiple sampled outputs, but it comes at a high computational cost due to extensive sampling. We introduce a hybrid ensembling approach that leverages the complementary strengths of two distinct modes of reasoning: Chain-of-Thought (CoT) and Program-of-Thought (PoT). We describe a general framework for combining these two forms of reasoning in self-consistency, as well as particular strategies for both full sampling and early-stopping. We show that CoT-PoT ensembling not only improves overall accuracy, but also drastically reduces the number of samples required for SC by a factor of 9.3x. In particular, the majority of tasks (78.6%) can be addressed with only two samples, which has not been possible with any prior SC methods.
Raman Saparkhan, Majd Hawasly, Md Rizwan Parvez +1
Self-consistency improves large language models by sampling multiple reasoning paths and selecting the most frequent answer, but majority voting often fails to recover correct answers that are already present among the samples. We address this limitation with Ranking-Improved Self-Consistency (RISC), which reformulates answer selection in self-consistency as a ranking problem. Instead of relying on a single uncertainty or confidence signal, RISC uses a lightweight LambdaRank model to score candidate answers with five carefully designed features that capture answer frequency, semantic centrality, and reasoning-trace consistency. We evaluate RISC on three datasets under a range of test-time budgets. Across datasets, RISC consistently achieves a better accuracy-efficiency trade-off than standard self-consistency and strong baselines, with particularly large gains on question answering benchmarks. Further analysis shows that the proposed features are individually useful and, more importantly, complementary, highlighting the value of learning to combine multiple informative signals for test-time answer selection.
Maria Marina, Daniil Moskovskiy, Sergey Pletenev +3
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.