Life sciences · Preprint

Difficulty-Adaptive Tree-Structured Policy Optimization for Expanding Reasoning Coverage in RLVR

arXiv · September 8, 2026

Preliminary Why this matters to you Expert discussion

Early or partial results. Treat as a signal, not a conclusion.

AI Summary

This preprint proposes DATPO, a training algorithm combining difficulty-adaptive tree search with entropy-guided branching to improve pass@k (reasoning coverage) in large language models on mathematical tasks. The work is a proof-of-concept with no peer review; it demonstrates a computational strategy on benchmark tasks but provides no clinical, real-world, or independent external validation.

What was studied

Preprint. Mathematical reasoning benchmark tasks.. Intervention: DATPO (Difficulty-Adaptive Sentence-entropy-guided Tree-structured Policy Optimization): difficulty-adaptive tree search with sibling-diversity advantage term.. Compared with: Unspecified baselines in mathematical reasoning..

Key findings

Difficulty-adaptive rollout improves pass@k beyond serving as an efficiency heuristic Tree-based rollout outperforms parallel sampling in discovering correct answers Sentence-entropy-guided forking overcomes localization of token-level branching to maximize semantic diversity

Safety

Safety was not reported in the material analysed. Check the source before drawing any conclusion about harm.

Who this may help

The source did not state who this applies to in practice.

Plain-language summary

An unvalidated algorithmic proposal for large language model training with experiments on mathematical benchmarks, lacking external peer review and clinical or real-world validation.

Study design

As stated by the source record.

PopulationMathematical reasoning benchmark tasks.

InterventionDATPO (Difficulty-Adaptive Sentence-entropy-guided Tree-structured Policy Optimization): difficulty-adaptive tree search with sibling-diversity advantage term.

ComparatorUnspecified baselines in mathematical reasoning.

Caveats

This is a preprint and has not undergone peer review.
No numerical results, effect sizes, confidence intervals, or p-values are reported in the abstract.
No external validation on independent datasets or comparison to published state-of-the-art methods is stated.
Generalization beyond mathematical reasoning benchmarks is not addressed.

Evidence assessment

Graded across the dimensions that decide whether you should act, each from what the source actually supports. There is no single score, and where a dimension was not assessed it says so.

Study design

limited

Uncontrolled comparative experiments on mathematical reasoning tasks; no randomization or blinding.

Directness

limited

Proxy endpoints (pass@k, benchmark accuracy) used; no direct measure of reasoning coverage or generalization.

Consistency

insufficient

Source does not report consistency across multiple independent cohorts or external validation datasets.

Risk of bias

insufficient

No disclosure of potential conflicts, data splitting, hyperparameter selection, or multiple comparison corrections.

Sample adequacy

insufficient

Source does not specify benchmark sample sizes, effect sizes, confidence intervals, or statistical power.

What is missing. This record has no reported figures. That is a gap in the analysis, not a judgement about the study.

Source abstract

Reinforcement Learning with Verifiable Rewards (RLVR) has been central to the recent success of Large Reasoning Models. However, while RLVR significantly improves single-sample accuracy, it often fails to expand the model's intrinsic reasoning coverage (pass@k) due to limited exploration during training. To address this, we optimize the structural design of train-time rollouts to enhance pass@k. Our analysis identifies three key design principles: (1) difficulty-adaptive rollout can play an important role in expanding pass@k, beyond serving as an efficiency heuristic; (2) tree-based rollout outperforms parallel sampling in discovering correct answers; and (3) sentence-entropy-guided forking overcomes the localization phenomenon of token-level branching to maximize semantic diversity. Building on these insights, we propose DATPO (Difficulty-Adaptive Sentence-entropy-guided Tree-structured Policy Optimization). DATPO integrates difficulty-adaptive tree search with a sibling-diversity advantage term, explicitly promoting semantic diversity to expand reasoning coverage during training. Experiments on mathematical reasoning benchmarks demonstrate that DATPO outperforms baselines especially in pass@k, which directly translates to superior test-time scaling performance.

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Hwanjo YuYoungjun YuSanghwan Jang