An AI training method aimed at difficult mathematics problems was reported to outperform several comparison methods in tests on two Qwen3 base models. DA3PO, which adds Direct Advantage Amplification to DAPO, exceeded the other compared GRPO variants by at least 5.02% in average benchmark accuracy on Qwen3-4B-Base and 4.95% on Qwen3-8B-Base, according to an arXiv preprint.
The reported gains were also seen on the AIME benchmarks. Against the best baseline, the paper reports improvements of up to 5.00% for the 4B model and 6.25% for the 8B model. Average pass@k improved by at least 5.81% and 5.87% on the two model scales. The authors interpret that pattern as broader coverage of correct responses rather than a collapse into a single solution mode.
The problem with hard prompts
The paper's central idea begins with Dynamic Sampling. The method over-samples and filters prompts so the groups it keeps have a mixed empirical rate of positive responses, strictly between zero and one. In practical terms, a retained group contains both correct and incorrect responses.
The theoretical analysis says this setup can have an awkward effect on hard prompts. When the probability of a sampled answer being correct is below 0.5, the amplification applied to correct responses is smaller than the amplification applied to incorrect responses. As that probability approaches zero, incorrect-response amplification grows without bound, while correct-response amplification remains close to one. The paper presents this as a theoretical result under its stated assumptions, not as an uncertainty estimate from the experiments.
DAA is the proposed adjustment. It activates only for correct responses on hard prompts, using a constant amplification factor greater than one when the group's empirical positive-response rate falls below a difficulty threshold. In the reported setup, the threshold was 0.5 and the factor was 2. The paper describes DA3PO as requiring fewer than 30 lines of code derived from DAPO.
How the comparison was run
The experiments used Qwen3-4B-Base and Qwen3-8B-Base. Both were trained on DAPO-Math-17K, reported as 17K mathematical problems with verifiable answers, and evaluated on AIME24, AIME25, AIME26, AMC, Minerva, Olympiad and MATH.
The comparison included the base model, GRPO, DAPO, GSPO and DA3PO. The reported training run lasted 200 steps, after which the best checkpoint was selected. Evaluation used temperature 1 and top-p 0.95, with 32 responses sampled per AIME or AMC problem and eight responses per Minerva, Olympiad or MATH problem.
The gains appeared across the reported run
The advantage was not limited to the checkpoint chosen for the headline comparison. On both model scales, the DA3PO training curve remained visibly above the GRPO, DAPO and GSPO curves throughout the reported reinforcement-learning training.
The choice of amplification factor also mattered in the reported ablation. The study tested factors of 1.5, 2.0 and 2.5. The 2.0 setting produced the best reported average accuracy on both models, reaching 39.63% for Qwen3-4B-Base and 46.89% for Qwen3-8B-Base.
The comparisons do not come with reported confidence intervals, hypothesis tests or p-values. The supplied analysis also does not report the number of random seeds or independent runs, so the variability of the gaps cannot be assessed from these results alone.
A narrow test of a targeted change
The authors acknowledge that fixed settings for the amplification factor and difficulty threshold may not compensate optimally for unequal amplification across every prompt difficulty during training. They propose adaptive factors as future work.
The evidence covers two Qwen3 base-model scales, one named mathematical-problem dataset and mathematical reasoning benchmarks. It therefore does not establish that the approach will generalize to other model families, scales, tasks or training datasets. The benchmark comparison also does not establish that DA3PO caused the reported gains.
The work is an arXiv preprint, version 1, dated 28 Aug 2026. The supplied front matter does not report a funding statement.
Paper data and sources
Original title: Learning from Hard Prompts: Difficulty-aware Advantage Amplification in Dynamic Sampling
Authors: Siyuan Gan, Yuhan Li, Xiran Wang et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text