Flexible Self-Consistency, or FSC, reported using fewer language-model tokens than Self-Consistency in most tested model-dataset combinations while retaining comparable accuracy to existing baselines. The maximum reported reduction was 76.7% versus SC. Self-Consistency samples multiple reasoning paths and selects a majority answer; FSC uses an adaptive budget for paths and majority voting.
The work is an arXiv preprint, labeled arXiv:2608.24590v1 and dated 25 Aug 2026. Its evaluation covered MATH500, AMC23, AIME2024, AIME2025 and GPQA-Diamond, plus an MMLU-Pro subset of 100 questions from each of 14 categories, for 1,400 samples.
A continuous signal for a variable budget
The study asks whether problem difficulty can be represented as a continuous signal rather than a discrete category. The proposed setup therefore gives the reasoning budget a continuous input rather than a discrete difficulty label.
FSC follows a two-stage pipeline. First, a lightweight probe reads the model’s last-token hidden representation and predicts output entropy, which the study treats as a continuous difficulty signal. The prediction is then mapped to an adaptive budget for reasoning paths and majority voting.
The probe is a linear-regression model without a nonlinear activation function. It was trained on 7,500 MATH training samples, with 40 reasoning paths generated for each sample.
How the benchmark comparison worked
To test the idea, Self-Consistency was allowed a maximum budget of 40 reasoning paths. FSC and the comparison methods selected from the same pool of generated trajectories, and the analysis compared accuracy with token usage. The other named methods were Adaptive-Consistency, Early-Stopping Self-Consistency and Difficulty-aware Self-Consistency.
The evaluation used MATH500, AMC23, AIME2024, AIME2025 and GPQA-Diamond. For MMLU-Pro, the reported subset used 100 questions from each of 14 categories, producing 1,400 samples.
Where the reported savings appeared
One Gemma-3-4B comparison shows the scale of the reported trade-off. For the first listed benchmark, FSC reports 78.8% accuracy and 8.5 reported token units, versus 79.2% accuracy and 36.5 token units for SC; the reported token change is -76.7%.
The result was not uniform across baselines. AC and ESC sometimes used more tokens than SC; on AIME2025, AC’s token use was 15.8% higher with Qwen2.5-3B and 6.8% higher with Qwen2.5-7B.
Predicted entropy generally rose with reported difficulty across MATH500 levels. It was also higher on AMC23, AIME2024 and AIME2025 than the distribution for MATH500 Level 5, with similar trends reported across other models. This is the signal FSC uses when assigning different reasoning budgets.
The allocation analysis reported that FSC spread reasoning-path budgets more continuously across a broader range, while DSC concentrated resources in certain ranges. In the reported MMLU-Pro analysis, FSC achieved the highest efficiency in most academic domains, and the same trend was observed across other models.
The evidence remains bounded
The authors report no experiments above 14 billion parameters and note that probe entropy may vary by model size and family. FSC also depends on the input question’s last-token hidden representation, making application to proprietary models such as GPT difficult. The probe was trained only on mathematical datasets.
The experimental comparisons were single-run, with no confidence intervals or repeated-run variability estimates reported. The token savings therefore come without a quantified uncertainty range, and broader validation across tasks and domains remains needed.
The document reports Korean government-supported grants RS-2025-00553041 and RS-2026-25506607, each with a listed 50% contribution rate.
Paper data and sources
Original title: Is Discrete Difficulty Sufficient? Leveraging Continuous Difficulty for Efficient Self-Consistency in LLMs
Authors: Sihyeong Yeom, Geon Park, Geunyeong Jeong et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text