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arxiv: 2604.13902 · v1 · submitted 2026-04-15 · 💻 cs.LG

DiPO: Disentangled Perplexity Policy Optimization for Fine-grained Exploration-Exploitation Trade-Off

Xiaofan Li , Ming Yang , Zhiyuan Ma , Shichao Ma , Jintao Du , Yu Cheng , Weiqiang Wang , Zhizhong Zhang
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Xin Tan Yanyun Qu Lizhuang Ma Yuan Xie
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Pith reviewed 2026-05-10 13:14 UTC · model grok-4.3

classification 💻 cs.LG
keywords Reinforcement LearningLarge Language ModelsExploration-Exploitation Trade-offPolicy OptimizationPerplexityMathematical ReasoningFunction Calling
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The pith

A perplexity-based split of samples creates targeted exploration and exploitation for more stable LLM policy training.

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

The paper addresses the exploration-exploitation imbalance that arises when reinforcement learning with verifiable rewards trains large language models on reasoning tasks. Hard samples with high perplexity tend to demand exploration while easy low-perplexity samples benefit from exploitation, yet standard methods treat them uniformly. The authors introduce a strategy that partitions the sample space along perplexity and applies bidirectional reward allocation to steer behavior in each subspace. Experiments on mathematical reasoning and function calling show improved performance, suggesting that finer-grained control over the trade-off can produce more reliable gains. A reader would care because better management of this trade-off could make RL-based fine-tuning of LLMs both more effective and more predictable.

Core claim

We introduce a perplexity space disentangling strategy that divides the sample space into distinct exploration (high perplexity) and exploitation (low perplexity) subspaces, followed by a bidirectional reward allocation mechanism that implements perplexity-guided exploration and exploitation with minimum impact on verification rewards, enabling more stable policy optimization and superior performance on mathematical reasoning and function calling tasks.

What carries the argument

Perplexity space disentangling strategy that partitions samples into high-perplexity exploration and low-perplexity exploitation subspaces, paired with bidirectional reward allocation.

If this is right

  • Policy optimization becomes more stable because extreme samples receive tailored signals rather than uniform treatment.
  • LLM performance improves on both mathematical reasoning and function calling tasks.
  • Fine-grained mining of samples that need exploration-exploitation balance becomes possible during training.
  • The verification reward remains largely intact while the trade-off is adjusted.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same perplexity partition could be tested as a lightweight proxy for difficulty in other generative-model training regimes.
  • Dynamic adjustment of the perplexity threshold over the course of training might further reduce the need for manual reward shaping.
  • If the partition correlates with human-labeled difficulty, the method could transfer to non-verifiable reward settings.

Load-bearing premise

Partitioning samples by perplexity correctly identifies which ones require exploration versus exploitation, and the bidirectional reward mechanism preserves the original verification signals without meaningful degradation.

What would settle it

Apply DiPO to a standard math-reasoning benchmark and find that final model accuracy is no higher than that obtained by ordinary RLVR without the perplexity partition or bidirectional allocation.

Figures

Figures reproduced from arXiv: 2604.13902 by Jintao Du, Lizhuang Ma, Ming Yang, Shichao Ma, Weiqiang Wang, Xiaofan Li, Xin Tan, Yanyun Qu, Yuan Xie, Yu Cheng, Zhiyuan Ma, Zhizhong Zhang.

Figure 1
Figure 1. Figure 1: (a) The proportion of Easy/Normal/Hard groups in each step during the DAPO training. (b) The PPL distribution of correct and error samples in the validation set at 300th steps of DAPO training. (c) Illustration of four samples after PSD fine-grained partitioning. most samples belong to the hard group. Meanwhile, CDE Dai et al. [2025] designs multiple weighting mechanisms to employ exploration rewards at ap… view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of DiPO, consisting of three modules: PPL Queue, Perplexity Space Disentan [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: ACC/mean@8 curves of DiPO and DAPO (raw and smoothed curves) on AIME24 and AIME25 with using Qwen3-8B-Base model. Higher upper bound for later training [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Entropy curves of maximum-PPL reward and maximum-PPL penalty trained on Qwen3- [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Prompt of risk prediction. E.5 Visualization of PPL Distribution To further analyze the exploration and exploitation trends during the RL training process, we con￾ducted a visualization analysis of the PPL distribution during the training of DAPO and DiPO. As shown in [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: PPL distribution of correct and error samples for Qwen3-8B-Base trained on DAPO-17K [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Correct case of DAPO. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Error case of DAPO. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Correct case of DiPO. Query: There is a collection of $25$ indistinguishable white chips and $25$ indistinguishable black chips. Find the number of ways to place some of these chips in the $25$ unit cells of a $5times5$ grid such that:each cell contains at most one chipall chips in the same row and all chips in the same column have the same colourany additional chip placed on the grid would violate one or… view at source ↗
Figure 11
Figure 11. Figure 11: Error case of DiPO. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
read the original abstract

Reinforcement Learning with Verifiable Rewards (RLVR) has catalyzed significant advances in the reasoning capabilities of Large Language Models (LLMs). However, effectively managing the exploration and exploitation trade-off remains a critical challenge. In this paper, we fully analyze the exploration and exploitation dilemma of extremely hard and easy samples during the training and propose a new fine-grained trade-off mechanism. Concretely, we introduce a perplexity space disentangling strategy that divides the sample space into distinct exploration (high perplexity) and exploitation (low perplexity) subspaces, thereby mining fine-grained samples requiring exploration-exploitation trade-off. Subsequently, we propose a bidirectional reward allocation mechanism with a minimum impact on verification rewards to implement perplexity-guided exploration and exploitation, enabling more stable policy optimization. Finally, we have evaluated our method on two mainstream tasks: mathematical reasoning and function calling, and experimental results demonstrate the superiority of the proposed method, confirming its effectiveness in enhancing LLM performance by fine-grained exploration-exploitation trade-off.

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 manuscript proposes DiPO (Disentangled Perplexity Policy Optimization) for RLVR in LLMs. It partitions the sample space via a perplexity-based disentangling strategy into high-perplexity (exploration) and low-perplexity (exploitation) subspaces, then applies a bidirectional reward allocation mechanism asserted to have minimum impact on the original 0/1 verification rewards. This is claimed to enable more stable policy optimization and superior performance on mathematical reasoning and function calling tasks.

Significance. If the core assumptions hold, the work offers a concrete mechanism for fine-grained control of exploration-exploitation in verifiable-reward RL, which is a recurring practical bottleneck when training LLMs on heterogeneous reasoning data. The perplexity partitioning is a simple, computable heuristic that could be adopted without new infrastructure. Credit is due for targeting a load-bearing practical issue rather than introducing yet another generic RL objective.

major comments (2)
  1. [§3.2] §3.2 (Bidirectional Reward Allocation): The claim that the added exploration/exploitation term produces 'minimum impact on verification rewards' is load-bearing for the central stability argument, yet the section supplies neither scaling analysis, clipping bounds, nor an interference proof showing that the composite objective's optimum remains aligned with the original RLVR (0/1 correctness) optimum on high-perplexity correct samples.
  2. [§4] §4 (Experiments): The superiority claim on mathematical reasoning and function calling rests on experimental results, but the section provides no ablation on the perplexity threshold choice, no comparison of reward-component magnitudes before/after allocation, and no verification that the bidirectional term does not degrade pass@1 rates on the held-out correct samples; without these, the 'fine-grained trade-off' advantage cannot be isolated from baseline RLVR.
minor comments (2)
  1. [Abstract] The abstract states superiority on two tasks but contains no numerical deltas, baseline names, or dataset sizes; this should be moved to the introduction or a results table for a self-contained summary.
  2. [§3.1] Notation for the perplexity threshold and the two reward scalars is introduced without an explicit hyper-parameter table or sensitivity plot; readers cannot reproduce the exact partitioning used in the reported runs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback and positive evaluation of the practical relevance of DiPO. We address each major comment below.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (Bidirectional Reward Allocation): The claim that the added exploration/exploitation term produces 'minimum impact on verification rewards' is load-bearing for the central stability argument, yet the section supplies neither scaling analysis, clipping bounds, nor an interference proof showing that the composite objective's optimum remains aligned with the original RLVR (0/1 correctness) optimum on high-perplexity correct samples.

    Authors: We acknowledge the absence of a formal analysis in the current version. The bidirectional mechanism applies the additional term only to high-perplexity samples for exploration and low-perplexity for exploitation, with the term scaled proportionally to the perplexity difference and kept small relative to the 0/1 reward. To address this, we will include a scaling analysis and clipping bounds in the revised §3.2, along with a proof sketch demonstrating alignment of the optima for correct samples. revision: yes

  2. Referee: [§4] §4 (Experiments): The superiority claim on mathematical reasoning and function calling rests on experimental results, but the section provides no ablation on the perplexity threshold choice, no comparison of reward-component magnitudes before/after allocation, and no verification that the bidirectional term does not degrade pass@1 rates on the held-out correct samples; without these, the 'fine-grained trade-off' advantage cannot be isolated from baseline RLVR.

    Authors: We agree that these ablations are necessary to fully substantiate the claims. In the revised manuscript, we will add an ablation study varying the perplexity threshold, report the magnitudes of the reward components to show the minimal impact, and include pass@1 evaluations on held-out correct samples to confirm no degradation. These will help isolate the contribution of the fine-grained trade-off. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain

full rationale

The paper proposes a perplexity-based disentangling strategy and bidirectional reward allocation for RLVR without presenting any equations, derivations, or parameter-fitting steps that reduce to their own inputs by construction. Claims rest on experimental results for math reasoning and function calling rather than self-referential definitions or load-bearing self-citations. No self-definitional loops, fitted inputs renamed as predictions, or uniqueness theorems imported from prior author work appear in the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; any perplexity threshold or reward scaling coefficient would be a free parameter but cannot be identified here.

pith-pipeline@v0.9.0 · 5512 in / 1177 out tokens · 37581 ms · 2026-05-10T13:14:54.532088+00:00 · methodology

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Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages

  1. [1]

    Instead, we utilize max-PPL reward and max-PPL penalty as training reward, respectively, and recorded the changes in model entropy

    as the training set, discarding the verification reward. Instead, we utilize max-PPL reward and max-PPL penalty as training reward, respectively, and recorded the changes in model entropy. As illustrated in Figure 5, the trend of entropy update is consistent with the proof. 100 200 300 400 500 step 2.5 5.0 7.5 10.0Entropy Maximum PPL Reward 300 350 400 45...

    work page 2015

  2. [2]

    [2025] enhanced reasoning reliability via hierarchical advantage estimation

    further scaled LLM-RL with decoupled clipping and dynamic sampling, while V APO Yue et al. [2025] enhanced reasoning reliability via hierarchical advantage estimation. GSPO Zheng et al

    work page 2025

  3. [3]

    [Question] Let’s think step by step and output the final answer within\boxed{}

    extended GRPO’s grouping strategy to sequence-level optimization for mixture-of-experts models and long-form reasoning tasks. B.2 Reward Shaping Recent works on reward shaping for LLM-RL have advanced across key directions. CrossDomain- RLVR Su et al. [2025] expanded verifiable reward RL to diverse unstructured domains via generative scoring. PKPO Walder ...

    work page 2025