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CLPO: an online curriculum that rewrites each problem according to the model's own current accuracy and scales the KL penalty by difficulty, reporting strong but internally inconsistent gains over GRPO and DAPO.

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CLPO: an online curriculum that rewrites each problem according to the model's own current accuracy and scales the KL penalty by difficulty, reporting strong but internally inconsistent gains over GRPO and DAPO.

T0 review reviewed 2026-08-04 challenge →

arxiv 2509.25004 v2 pith:HGXRU3A3 submitted 2025-09-29 cs.AI

CLPO: Curriculum Learning meets Policy Optimization for LLM Reasoning

Shijie Zhang , Zheng Xiao , Shiyu Liu , Guohao Sun , Kevin Zhang , Xiang Guo , Rujun Guo , Shaoyu Liu
show 2 more authors
Wangxiao Zhao Guanjun Jiang
This is my paper
classification cs.AI
keywords reasoningclpocurriculumlearningproblemspolicyaccuracybecome
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

Language models trained with reinforcement learning and verifiable rewards (RLVR) learn to reason by generating many candidate solutions and receiving a reward only when the final answer is correct. Standard methods sample problems from a fixed set until training ends. That wastes compute on problems the model already solves and gives no signal on problems it never solves correctly.

CLPO changes what is trained on, step by step. Each training step, the model solves each sampled problem four times. The fraction correct becomes a difficulty score. Problems solved once in four tries are called hard; problems solved twice are called medium. Hard problems are rewritten with a prompt that asks for a simpler version. Medium problems are rewritten with a prompt that asks for a different wording of the same problem. Rewritten problems that the model now solves zero or four times are discarded. The surviving original and rewritten problems are used for the policy update, with a weaker KL penalty on hard problems so the policy can change more there. This loop is fully self-generated, with no external teacher or annotation beyond the original answers.

On Qwen3-8B trained on the DAPO-Math-17k set, CLPO reports an average pass@1 of 73.73 on eight benchmarks, versus 64.50 for DAPO and 62.04 for GRPO, with the largest gains on out-of-domain sets. The core ideas are plausible, but the numbers need scrutiny: the abstract and the table disagree on the size of the gains, all results are single runs with no error bars, the method's hyperparameters were tuned on one of the headline benchmarks, and the model's rewrites are never checked to be mathematically equivalent to the original problems.

Core claim

The central claim is that CLPO 'achieves state-of-the-art performance across eight challenging mathematical and general reasoning benchmarks, with an average pass@1 improvement of 6.96% over other methods' (body abstract), and per the submitted abstract 'substantially outperforms GRPO and DAPO on Qwen3-8B by 10.21 and 7.75 average points.' If correct, the mechanism (online accuracy-based partitioning into hard and medium sets, simplification of hard problems, diversification of medium problems, value-driven filtering, and difficulty-aware KL scaling) yields large average benchmark gains over GRPO and DAPO on Qwen3-8B, including out-of-domain generalization without external guidance.

Load-bearing premise

The load-bearing premise is that the model's self-generated rewrites preserve the original problem's mathematical content and answer, so training on (q', a) with the preserved answer a teaches transferable reasoning. Section 3.4 asserts 'the original answer a is strictly preserved' with no verification step; the value filter in Eq. (8) retains rewrites whose rollout accuracy is strictly between 0 and 1, which does not test equivalence (a degenerate or non-equivalent rewrite can still be partially solvable). If Qwen3-8B, acting as its own teacher, systematically produces rewrites that are not equivalent to the originals, the curriculum signal is corrupted and the reported gains, especially the out-of-domain improvements, would not be attributable to the stated mechanism. A secondary fragile premise is the assumption that the public in-domain eval sets are not contaminated by DAPO-Math-17k training data, which the paper does not analyze.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The central claim rests on a handful of load-bearing choices: two accuracy thresholds and a KL scaling factor tuned on the headlined benchmark; unvalidated rewrite prompts as the teacher mechanism; the assumption that self-rewrites preserve problem-answer equivalence; the coarse G=4 accuracy grid that collapses difficulty bands; and the assumption of no train/test contamination. All are stated or implicit in the paper, and none is independently verified outside the reported runs.

free parameters (5)
  • hard accuracy threshold tau_hard = 0.3
    Selected via ablations on AIME24 (Figure 3, right panel). With G=4 rollouts it defines the hard set as problems with exactly 1 of 4 correct answers.
  • medium accuracy threshold tau_med = 0.7
    Selected via ablations on AIME24. With G=4 rollouts the medium band (tau_hard < Acc <= tau_med) contains only Acc=0.5, i.e., exactly 2 of 4 correct.
  • hard KL scaling factor lambda_hard = 0.3
    Selected via ablation on AIME24 (Figure 4, alpha sweep); 0.3 reported optimal, 0.5 worst.
  • non-hard KL scaling factor lambda_non_hard = 1.0
    Fixed relative anchor equal to the static KL coefficient in the GRPO objective.
  • restructuring prompt templates (diversification and simplification) = two prompt texts in Appendix D (Figures 7-8)
    The entire Adaptive Problem Restructuring mechanism is determined by these unvalidated prompts; no ablation, equivalence check, or ordering analysis of the rewrites is reported.
axioms (5)
  • ad hoc to paper Rewrite equivalence: f_p(q, d) preserves the mathematical content and answer a of the original problem q.
    Section 3.4 asserts 'the original answer a is strictly preserved' with no verification; the value filter in Eq. (8) checks only 0 < Acc(q', ...) < 1, which does not test equivalence. All training labels on restructured problems rest on this premise.
  • domain assumption Rollout accuracy with G=4 samples at temperature 1.0 is a reliable difficulty signal.
    Eq. (3) defines Acc as an empirical mean over 4 samples, giving a 5-level grid {0, .25, .5, .75, 1}; thresholds 0.3/0.7 then reduce the hard and medium curricula to single accuracy levels. The paper does not discuss this quantization.
  • domain assumption No contaminating overlap between DAPO-Math-17k training data and the in-domain evaluation sets.
    Section 4.1 uses MATH-500, Minerva-Math, Olympiad, AMC23, and AIME24 as in-domain tests; these are public competition and math sets, and DAPO-Math-17k is built from public math sources. No decontamination analysis is provided.
  • standard math Standard GRPO clipped surrogate objective and KL penalty assumptions (Eqs. (1) and (2)).
    Policy gradient with clipped importance ratios and reference-policy KL, taken from cited literature; unproblematic background.
  • domain assumption The verifier correctly judges correctness on original and rewritten problems.
    Eq. (3) treats Verifier(y_i, a) as ground truth; since rewrites keep the original answer a, any grader error or ambiguity in a rewritten problem differentially affects restructured samples.

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Pith. "Pith review of CLPO: Curriculum Learning meets Policy Optimization for LLM Reasoning." pith.science (2026). https://pith.science/paper/HGXRU3A3

@misc{pith2026250925004,
  author       = {Pith},
  title        = {Pith review of: CLPO: Curriculum Learning meets Policy Optimization for LLM Reasoning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HGXRU3A3}},
  note         = {Machine review of arXiv:2509.25004}
}
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read the original abstract

Online reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving the reasoning abilities of large language models, but most methods still optimize reasoning trajectories over the static problem set, wasting rollout budget on solved or overly difficult problems. We propose \textbf{CLPO (Curriculum Learning meets Policy Optimization)}, a self-evolving curriculum framework that uses on-policy rollout accuracy to identify solved, medium-difficulty, and hard problems, then restructures selected tasks according to the model's current capability. Hard problems are simplified to become learnable, while medium-difficulty problems are diversified to provide useful training variation. This allows the learning curriculum to co-evolve with the policy rather than remaining fixed as the model's capability boundary shifts. Rather than treating these rewrites as static data augmentation, CLPO optimizes restructuring trajectories with credit assigned by the downstream accuracy gain of the rewritten problem, requiring no additional human annotations beyond the original verifiable answers. Experiments across mathematical reasoning and out-of-domain general reasoning benchmarks show that CLPO substantially outperforms GRPO and DAPO on Qwen3-8B by 10.21 and 7.75 average points, respectively. Ablation studies on math and code domains further show that both the restructuring mode and the rewriting loss contribute to the final gains, demonstrating that CLPO provides a scalable and robust pathway for eliciting stronger reasoning capabilities through a self-evolving curriculum.

Figures

Figures reproduced from arXiv: 2509.25004 by Guanjun Jiang, Guohao Sun, Kevin Zhang, Rujun Guo, Shaoyu Liu, Shijie Zhang, Shiyu Liu, Wangxiao Zhao, Xiang Guo, Zheng Xiao.

Figure 1
Figure 1. Figure 1: An overview of the Guided Self-Evolution paradigm in our proposed framework CLPO [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The overall workflow of CLPO. The framework consists of three main stages detailed in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Ablation studies on Adaptive Problem Restructuring. Left: Comparison of restructuring [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Performance comparison of dynamic KL regularization with different scaling factors ( [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Test-time scaling performance (pass@k) on AIME2024 (left) and AIME2025 (right). The [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the evolution of problem difficulty distribution during training for CLPO [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The prompt used for diversification restructuring of medium-difficulty problems. [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The prompt used for simplification restructuring of hard-difficulty problems. [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The original medium-difficulty problem presented in a symbolic style and the correspond [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The restructured version of the problem, elaborated into natural language by CLPO, and [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗

discussion (0)

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Forward citations

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.