Self-Consistency in Language Models

Sampling several responses and voting over their answers can improve a language model's accuracy, but repeated answers limit the benefit of additional samples. Raising temperature increases diversity at a potential cost to per-sample accuracy. We introduce Self-Repulsion (SR), a sampler for masked diffusion language models that uses peer commitments to diversify the pool. At each penalized denoising step, each path lowers a token's logit according to how many peers have committed that token at the same position. Paths share a batched forward pass and then commit in sequence, so later paths observe choices made earlier in the same step. This coupling requires no training or additional forward or backward pass and can produce distinct paths even at temperature zero. When all paths commit a position together from identical logits, the update exactly maximizes total logit minus a convex duplication cost. On LLaDA-8B-Instruct with ten paths and 128 denoising steps, deterministic SR reaches 80.38% plurality accuracy on GSM8K, compared with 70.17% for the unpenalized greedy decoder. At temperature 0.6 and matched model-evaluation budgets, the count penalty improves over self-consistency by 2.06 percentage points in blocks of 32 and 14.50 under pure diffusion. Experiments on GSM8K, MATH and TruthfulQA show that voting gains arise mainly from higher coverage of correct answers, with gains that vary by benchmark and decoding regime.

Self-consistency samples many reasoning trajectories and aggregates their final answers, treating the LLM as a black box that returns one answer per trajectory. Yet the final answer of each trajectory is sampled from a softmax vector that is available from the model's log-probabilities. We refer to this as the grey-box setting in which each trajectory reveals this answer distribution rather than a single draw from it. We formulate efficient inference in this setting as sequential mode identification with distribution-valued observations: sample trajectories one at a time and stop as soon as the LLM's modal answer is identified at a prescribed confidence level. We characterize the asymptotic stopping rate of mode identification with distribution-valued observations exactly and show that it is never worse than the black-box rate. We then propose the ASC-D algorithm, a betting stopping rule that attains this asymptotic stopping rate. On MMLU-Redux, ASC-D uses $46.4$--$95.6\%$ fewer trajectories than answer-only adaptive self-consistency baselines and achieves the highest fixed-budget correct-certification rate across three open-source models.

Chinese Semantic Error Correction (CSEC) targets semantic errors in Chinese text, which are typically more subtle and complex than spelling and grammatical errors but remain relatively underexplored. Existing LLM-based approaches face two recurring obstacles in this task: over-correction, and unclear interaction between Chain-of-Thought (CoT) reasoning and self-consistency decoding, such that the benefits brought by CoT cannot be reliably transferred to final corrections. We propose Vote-guided Advantage Allocation for CSEC (VAA-CSEC), a multi-stage framework that combines CoT distillation, Supervised Fine-Tuning (SFT), Reinforcement Learning (RL) and self-consistency decoding. During RL, we design a task-specific reward function that directly aligned with the minimal-editing principle of CSEC. We further introduce Group-Level Relative Policy Optimization (GLPO), which reallocates GRPO advantages according to the margin between individual rollout rewards and the vote-aggregated group reward, aligning the RL training objective with the self-consistency objective used at inference time. Experiments on CSED-C and NaSGEC-Exam show that VAA-CSEC outperforms all LLM-based baselines on CSED-C with an F0.5 of 47.72%, achieves the highest recall of 42.15% among all methods, and establishes a new state of the art of 41.55% F0.5 on NaSGEC-Exam.

Large language models can report a numerical confidence together with generated content, but it is unclear whether this report is more than calibrated rhetoric. We analyze three training-free signals: confidence verbalized with the answer, post-hoc $P(\mathrm{True})$, and agreement with three additional generations on the same 100 TriviaQA questions for two model families. Direct verbalization is a surprisingly strong baseline: after auditing benchmark errors, it reaches AUROC 0.956 and 0.937 for correctness prediction. Three-sample agreement is substantially weaker (0.765 and 0.790), and a fixed interpolation with verbalized confidence has no statistically reliable benefit. Four of nine errors from one model and two of eight from the other receive unanimous sample support, showing that self-consistency can amplify shared misconceptions. Re-eliciting confidence for the same fixed answers with equivalent prompts changes scores by 0.043 to 0.084 on average and flips 4% to 9% of decisions at a 0.8 threshold. An exploratory audit of 100 confidence-tagged biography claims further finds only a modest confidence gap between supported and contradicted claims. These results argue that useful self-reports remain sensitive to elicitation, correlated errors, and benchmark noise.

Agreement among repeated samples of a language model is routinely read as evidence about answer reliability, yet wrong answers can agree just as strongly as right ones. This paper asks what information wrong-consensus agreement actually contains, and answers with a quantitative decomposition. A pluralistic agreement index Gamma, normalized by the reference scale d=(1-p)/(C-1), is split into a mechanical component (agreement delivered by a per-case answer preference alone) and a preference-unexplained residual. The mechanical reference is leak-free: each case's preference and accuracy are estimated from its other runs only. On public GPT-4.1 per-run data, coverage phi (the mechanical/empirical ratio) shows a benchmark-associated direction: 0.81-0.93 on multiple-choice GPQA-Diamond against 0.59-0.78 on open-domain AIME, where a residual of 1.54-2.80 Gamma units survives, more than absorbed by a calibrated run-level preference-heterogeneity reference. A controlled replication under one fixed protocol (four runs per question, K=32 votes) on five open-weights checkpoints (Qwen3.5-9B/122B, Qwen3.8-27B, Gemma4-26B/31B) finds near-complete mechanical coverage in all ten cells (phi approximately 1, with a small overshoot consistent with a quantified finite-donor plug-in bias), robust to a two-run design; the largest cell (qwen3.5-122b, p=0.222) sits inside the GPT-4.1 AIME accuracy range and still saturates (phi=1.041). A cross-system contrast at comparable aggregate accuracy contrasts near-complete mechanical agreement in the open-weights models against a larger preference-unexplained residual in the frontier family. This contrast is confounded with sampling protocol by design. Agreement is graded evidence, not certification. No new voting method is proposed; code and evidence are committed.

On-policy (Self-)Distillation (OPD / OPSD) has shown strong potential for post-training large language models (LLMs). However, existing methods still rely heavily on external supervision, including ground-truth signals, environmental feedback, or guidance from larger models, and therefore fall short of genuine "self"-distillation. In this study, we show that on-policy self-distillation can be achieved using only a model's own generations via internal consistency. We propose unsupervised on-policy self-distillation (U-OPSD). U-OPSD first samples multiple rollouts and constructs a pseudo solution by majority vote under a self-consistency threshold. It then conditions the model's distribution on the pseudo-solution and distills itself on the disagreeing completions, allowing the model to correct itself precisely where it is confidently wrong. Across diverse benchmarks, base models, and training settings, U-OPSD consistently improves over the base models and matches or surpasses supervised methods with ground truth (GT) such as OPSD and GRPO. On five mathematical reasoning benchmarks, i.e., AIME24, AIME25, HMMT25, MATH500, and AMC23, U-OPSD improves over the base model by 8.5% and 10.7% on Qwen3 non-thinking mode at 4B and 8B scales, and outperforms OPSD by 3.2% and 2.3% on average, respectively. In thinking mode, U-OPSD stays on par with OPSD, ahead by 0.9% at 4B and level at 8B and surpassing GRPO by 0.7% and 1.1%, respectively. Code is available at https://github.com/williamium3000/u-opsd.

Despite ever-increasing sophistication in language model (LM) pre- and post-training pipelines, many important failures persist: models overcondition on user framing ("sycophancy"), exhibit incomplete logical generalization, and produce confident but incorrect responses. We argue that these failures arise from a modeling assumption permeating all aspects of the pipeline: that behavior can be specified and evaluated independently on single-output pairs. Many model failures are difficult, if not impossible, to detect without reasoning about relationships between a model's responses across inputs. In this position paper, we propose self-consistency as a framework for understanding these failures. We first observe that a wide variety of techniques designed to improve specific aspects of LM behavior-targeting properties as diverse as adversarial robustness and factual coherence-can be understood as special cases of a common "consistency optimization" procedure and addressed with a standard set of optimization tools. We next outline a set of new model properties that could be achieved by optimizing for consistency, and conclude with a discussion of what it would mean to develop generally consistent LMs, including the capabilities they would enable and the objections they raise.

Large language models (LLMs) frequently contradict themselves when the surface form of a logically equivalent question changes. We present a benchmark of 350 question families (1,750 total questions) for Controlled Reformulation Testing (CRTBench) to evaluate logical invariance. In this benchmark, we investigate LLMs' ability to maintain consistent answers across controlled reformulations, which include contrapositive rewriting, double negation, negation flipping, and passive voice. We evaluate several frontier LLMs and observe an accuracy-consistency gap where GPT-5.4-mini achieves $98.9\%$ base accuracy but only $60.3\%$ family-level consistency, while reasoning-optimized o4-mini achieves $96.9\%$ consistency. From our experiments, we observe that failures cluster around logically nontrivial transformations such as contrapositive rewriting ($72.4\%$ for GPT-5.4-mini) and double negation ($84.6\%$), while surface-level rephrasing remains robust ($94-100\%$). Increasing reasoning effort improves GPT-5.4-mini to $85.4\%$ consistency, but leaves GPT-5.4 unchanged overall because gains on nested negation are offset by failures on quantifier families. These results show that accuracy alone is not enough for evaluating logical reasoning in LLMs.

LLM-as-judge (Zheng et al., 2023) is increasingly the default for evaluating AI systems in enterprise pipelines, often scaled to ensembles (Verga et al., 2024) or "mixture-of-experts" (Shazeer et al., 2017) panels of judges. These systems share a key assumption: that consistency -- agreement among judges, or among a model's own samples -- indicates correctness. We show this assumption is unreliable. Agreement is not accuracy: a model can agree with itself, and different models can agree with each other, out of shared bias, a memorized heuristic, or an option-position prior rather than truth. We ask when agreement is nonetheless a usable proxy, in a large-scale cross-runner study: 53 runners drew K=50 samples for assigned overlapping cases across comparisons of model tier, prompting, and scale on GPQA Diamond and AIME -- 265,000 samples. Using majority-correctness as the deployment label and a hierarchical runner-clustered bootstrap, agreement is a positive but weak predictor (rho 0.20-0.59, all positive under item-clustered resampling) whose usefulness is regime-dependent: best for unsaturated mid-tier models and for allocating compute, and worst -- over-confident yet no more accurate -- for the most consistent frontier model (agreement >=0.8 on 77% of GPQA case-result entries, 48% of those wrong). An exploratory cross-family check on three Claude tiers shows the same frontier over-confidence, with confident errors recurring across providers above a marginal-preserving null. Self-consistency is thus a conditional proxy for correctness, not a standalone confidence score. We publicly release the de-identified per-run rows and answer distributions.

Language models (LMs) that faithfully describe their own behavior can more easily be audited, understood, and trusted by users. This paper describes Self-Consistency Training with Reinforcement Learning (Self-CTRL), a method that optimizes for consistency between a LM's self-explanations and behavior on related inputs by updating explanations to better predict behavior or updating behavior to better match explanations. We apply our method in two domains. First, we study a formal probabilistic reasoning task in which LMs must learn to imitate a family of biased samplers and evaluated on their ability to report the associated biases. We find that consistency training improves the correlation between self-reported and behaviorally-measured latent biases from $R^2=0.24$ to $R^2=0.64$ on a set of held-out distributions, matching the generalization of direct ground-truth supervision. Second, we study a constitutional AI domain in which LMs must describe when they will refuse or comply with user requests. Here, Self-CTRL produces rules that faithfully describe the model's behavior on held-out requests, improving the refusal predictions of a third-party auditor model from $36\%$ to $92\%$. In the other direction, behavior updates improve alignment, reducing HarmBench failure rate from $15.0\%$ to $0.5\%$ without substantially increasing refusal on harmless prompts. By aligning explanations and behavior, our work provides a general recipe for training AI models to be safer, more transparent, and more controllable.

Large language models are increasingly deployed in agentic pipelines that depend on the model evaluating its own outputs without external verification. The reliability of these pipelines depends on an implicit assumption: that the model applies relevant concepts the same way when it generates an output and later evaluates that output. We propose a new measure, generator-evaluator self-consistency, to test this assumption directly and apply it to 10 frontier models across 491 concepts. We find, first, that there is substantial variation in self-consistency. Second, we find that in a clinical setting with physician-validated mistakes (Proniakin et al., 2025), across models, those with higher self-consistency are linked to greater vulnerability to mistakes. Thus, even when models consistently apply concepts they may not be safe to deploy. This is evidence of a consistency dilemma in LLMs: self-consistency is operationally useful, but models that are more consistent are also more prone to mistakes.

Self-consistency improves LLM reasoning by sampling multiple outputs and selecting the most consistent answer, but existing formulations largely rely on exact matching and therefore remain limited to tasks with categorical outputs. In this work, we study self-consistency in open-ended generation tasks such as code synthesis and text summarization. We hypothesize that consistency can be understood as a geometric property of the generation space, where semantically compatible generations concentrate in similar regions of representation space. To study this hypothesis, we introduce Embedding-Based Agreement (EBA), a simple training-free operationalization that estimates agreement by clustering sampled generations in embedding space. Through experiments on mathematical reasoning, code generation, and summarization, we show that agreement in representation space provides a robust and scalable signal of self-consistency for open-ended tasks. In particular, EBA consistently outperforms random selection and exhibits more stable scaling behavior than recent selection approaches based on LLM evaluation or uncertainty estimation. We further show that these agreement signals remain stable across model families and embedding spaces, even with native hidden representations. Finally, our analysis shows that the geometric location occupied by sampled generations is strongly correlated with generation quality: generations concentrated near central regions of representation space tend to correspond to more reliable outputs, whereas peripheral generations are substantially less accurate. Overall, our findings support viewing self-consistency as a property of the geometric organization of sampled generations rather than exact symbolic overlap.

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.

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.

Large Language Models often improve accuracy on reasoning tasks by sampling multiple Chain-of-Thought (CoT) traces and aggregating them with majority voting (MV), a test-time technique called self-consistency. When we truncate a CoT partway through and regenerate the remainder, we observe that traces with correct answers reproduce their original answer more often than traces with wrong answers. We use this difference as a reliability signal, prefix consistency, that weights each candidate answer by how often it reappears under regeneration. It requires no access to token log-probabilities or self-rating prompts. Across five reasoning models and four math and science benchmarks, prefix consistency is the best correctness predictor in most settings, and reweighting votes by it reaches Standard MV plateau accuracy at up to 21x fewer tokens (median 4.6x). Our code is available at https://github.com/naoto-iwase/prefix-consistency.

Reasoning language models can solve increasingly complex tasks, but struggle to produce the calibrated confidence estimates necessary for reliable deployment. Existing calibration methods usually depend on labels or repeated sampling at inference time, making them impractical in many settings. We introduce a method for unsupervised confidence calibration of reasoning LLMs when only a single generation is available at inference time. Our approach uses offline sampling on unlabeled data to derive a self-consistency-based proxy target, then distills this signal into a lightweight deployment-time confidence predictor. In a broad evaluation across 5 math and question-answering tasks using 9 reasoning models, our method substantially outperforms baselines, including under distribution shift, and improves downstream performance in selective prediction and simulated downstream decision-making.

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.

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.