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arxiv: 2605.22389 · v1 · pith:4VVT6V4Inew · submitted 2026-05-21 · 💻 cs.CL

Unified Data Selection for LLM Reasoning

Xiaoyuan Li , Yubo Ma , Chengpeng Li , Fengbin Zhu , Yiyao Yu , Keqin Bao , Wenjie Wang , Fuli Feng
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Dayiheng Liu
This is my paper

Pith reviewed 2026-05-22 05:29 UTC · model grok-4.3

classification 💻 cs.CL
keywords High-Entropy Sumdata selectionLLM reasoningsupervised fine-tuningrejection fine-tuningreinforcement learningtraining-free metrictoken entropy
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The pith

Summing entropy from the top 0.5 percent highest-entropy tokens ranks reasoning samples for effective LLM training.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that High-Entropy Sum provides a training-free way to score reasoning quality in large language models by focusing only on the most uncertain tokens within each sample. This metric lets researchers select small subsets of data that deliver strong results when training models for complex reasoning. A sympathetic reader would care because building advanced reasoning capabilities currently demands large volumes of high-quality traces, and an efficient selection method reduces the data and compute burden across multiple training approaches. The work shows consistent benefits whether the selected data is used for supervised fine-tuning, rejection sampling, or reinforcement learning.

Core claim

High-Entropy Sum quantifies reasoning quality by summing the entropy of only the top 0.5 percent highest-entropy tokens in each sample. When samples are ranked by this score, the highest-ranked 20 percent match the performance of training on the entire dataset under supervised fine-tuning. The same ranking produces better outcomes than baseline methods in rejection fine-tuning and allows reinforcement learning to extract stronger reasoning patterns from selected successful trajectories.

What carries the argument

High-Entropy Sum (HES), which aggregates entropy values from the top 0.5 percent highest-entropy tokens per reasoning sample to produce a quality score without any model training.

Load-bearing premise

The assumption that entropy concentrated in a tiny fraction of tokens per sample reliably signals high overall quality of the full reasoning trace, and that this signal remains consistent across models and tasks.

What would settle it

Training an LLM on the top 20 percent of HES-ranked samples and observing lower accuracy than the full dataset on a held-out reasoning benchmark such as GSM8K would falsify the central effectiveness claim.

Figures

Figures reproduced from arXiv: 2605.22389 by Chengpeng Li, Dayiheng Liu, Fengbin Zhu, Fuli Feng, Keqin Bao, Wenjie Wang, Xiaoyuan Li, Yiyao Yu, Yubo Ma.

Figure 1
Figure 1. Figure 1: The comparative analysis of discriminative ability is conducted on 512 responses per problem generated [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Calculation of High-Entropy Sum (HES). The colored tokens are the tokens involved in the calculation. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Parameter sensitivity across diverse domains, including data selection ratio and high-entropy token ratio. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Wordcloud of high-entropy tokens. including AIME24, HMMT23, HMMT24, and HMMT25. As illustrated by the score distributions in [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Wordcloud of high-entropy tokens. (a) Wordcloud of OpenR1-Math-220k. (b) Wordcloud of Open-Math-Reasoning [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparative analysis of discriminative ability between HES and other metrics based on 512 responses per [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparative analysis of discriminative ability between HES and other metrics based on 512 responses per [PITH_FULL_IMAGE:figures/full_fig_p021_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparative analysis of discriminative ability between HES and other metrics based on 512 responses per [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparative analysis of discriminative ability between HES and other metrics based on 512 responses per [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparative analysis of discriminative ability between HES and other metrics based on 512 responses [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
read the original abstract

Effectively training Large Language Models (LLMs) for complex, long-CoT reasoning is often bottlenecked by the need for massive high-quality reasoning data. Existing methods are either computationally expensive or fail to reliably distinguish high- from low-quality reasoning samples. To address this, we propose High-Entropy Sum (HES), a training-free metric that quantifies reasoning quality by summing only the entropy of the top (e.g., 0.5\%) highest-entropy tokens in each reasoning sample. We validate HES across three mainstream training paradigms: Supervised Fine-tuning (SFT), Rejection Fine-tuning (RFT), and Reinforcement Learning (RL), with extensive results demonstrating its consistent effectiveness and significantly reduced computational overhead. In SFT, training on the top 20\% HES-ranked data matches full-dataset performance, while using the lowest-HES data degrades it. In RFT, our HES-based training approach significantly outperforms baseline methods. In RL, HES-selected successful trajectories enable the model to learn strong reasoning patterns, significantly surpassing other compared methods. Our findings establish HES as a robust, training-free metric that enables a unified, effective, and efficient method for developing advanced reasoning in LLMs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes High-Entropy Sum (HES), a training-free metric that quantifies reasoning quality in LLM traces by summing the per-token entropy of only the top 0.5% highest-entropy tokens per sample. It validates this metric across three training paradigms—SFT, RFT, and RL—claiming that top-20% HES data matches full-dataset SFT performance, outperforms baselines in RFT, and yields stronger reasoning in RL while reducing computational overhead.

Significance. If the central claims hold after addressing the noted gaps, the work offers a practical, training-free data-selection tool that could lower the barrier to scaling long-CoT reasoning training. The unified evaluation across SFT/RFT/RL and the reported efficiency gains are genuine strengths; the manuscript also ships concrete empirical comparisons that could be reproduced if code and exact data splits are released.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (HES definition): The metric is defined by summing entropy exclusively over the top 0.5% highest-entropy tokens, yet no derivation, sensitivity analysis, or cross-percentile ablation is presented. If the selected subset changes materially at 0.1% or 1%, the reported SFT/RFT/RL gains no longer demonstrate that HES is a stable, robust quality signal.
  2. [§4] §4 (experimental results): The manuscript reports consistent gains but provides no statistical significance tests, variance across random seeds, or controls that isolate the effect of the HES ranking from model size or task difficulty. Without these, it is unclear whether the top-20% HES subset truly matches full-dataset performance or merely reflects easier subsets.
minor comments (2)
  1. [§3] Notation for entropy computation (per-token vs. sequence-level) should be stated explicitly in the method section to avoid ambiguity when readers re-implement HES.
  2. [Figures in §4] Figure captions and axis labels in the experimental plots could be expanded to include the exact percentile threshold and base model used for entropy extraction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback on our manuscript. We address each major comment point by point below, indicating where revisions will be made to strengthen the work.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (HES definition): The metric is defined by summing entropy exclusively over the top 0.5% highest-entropy tokens, yet no derivation, sensitivity analysis, or cross-percentile ablation is presented. If the selected subset changes materially at 0.1% or 1%, the reported SFT/RFT/RL gains no longer demonstrate that HES is a stable, robust quality signal.

    Authors: We acknowledge that the manuscript does not include an explicit derivation or sensitivity analysis for the 0.5% threshold. This percentile was chosen empirically during preliminary experiments as it isolates the most uncertain tokens while avoiding dilution from lower-entropy ones. To address the concern directly, we will add a cross-percentile ablation study (0.1%, 0.5%, 1%, and 2%) to Section 3 and the appendix in the revised manuscript. Preliminary checks indicate that performance trends remain qualitatively stable across this range for the reported SFT, RFT, and RL settings, supporting robustness; the full results will be included to allow readers to evaluate stability. revision: yes

  2. Referee: [§4] §4 (experimental results): The manuscript reports consistent gains but provides no statistical significance tests, variance across random seeds, or controls that isolate the effect of the HES ranking from model size or task difficulty. Without these, it is unclear whether the top-20% HES subset truly matches full-dataset performance or merely reflects easier subsets.

    Authors: We agree that reporting variance and statistical tests would improve interpretability. In the revision we will rerun the core SFT and RFT experiments across three random seeds, reporting means and standard deviations, and include paired t-tests or Wilcoxon tests against the full dataset and random baselines of equal size. To isolate HES ranking from task difficulty, we will add per-task breakdowns and comparisons against difficulty-stratified random subsets (using proxy metrics such as trace length or token count). These controls will help demonstrate that gains are driven by the entropy-based selection rather than incidental subset properties. Model-size effects are already partially controlled by using the same base model across conditions, but we will note this limitation explicitly. revision: yes

Circularity Check

0 steps flagged

No significant circularity: HES is an explicitly defined empirical metric validated by downstream experiments.

full rationale

The paper defines HES directly as the sum of per-token entropies for the top 0.5% highest-entropy tokens within each sample. This definition is not derived from or equated to the target performance outcomes; instead, the authors report separate experimental results showing that selecting top-20% HES data for SFT matches full-dataset performance, and that HES-based selection improves RFT and RL. No equations, self-citations, or uniqueness theorems are invoked that would reduce the claimed effectiveness to the definition itself. The 0.5% cutoff is presented as a design choice rather than a fitted parameter whose value is then 'predicted' from the same data. The derivation chain remains self-contained and externally falsifiable via the reported training outcomes.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that token-level entropy is a valid proxy for reasoning quality; one tunable threshold (top 0.5%) is introduced without independent justification.

free parameters (1)
  • top entropy percentile threshold
    Example value of 0.5% used to select which tokens contribute to the sum; chosen to focus on highest-uncertainty positions.
axioms (1)
  • domain assumption Entropy of selected tokens correlates with overall reasoning quality of the sample
    Invoked when defining HES as a quality metric in the abstract.

pith-pipeline@v0.9.0 · 5764 in / 1255 out tokens · 36061 ms · 2026-05-22T05:29:12.203534+00:00 · methodology

discussion (0)

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Reference graph

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