Beyond Token-Local Imitation: Reward-Compatible Temporal Credit Assignment for On-Policy Distillation · CiteArk

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Beyond Token-Local Imitation: Reward-Compatible Temporal Credit Assignment for On-Policy Distillation

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作者：Shiqi Liu、Zeyu He、Letian Tao、Guojian Zhan、Jiaxin Gao、Feihong Zhang、Jingliang Duan、Wei Xiong、Kehua Sheng、Bo Zhang、Yang Guan、Shengbo Eben Li

arXiv 2026 机器学习 (cs.LG)人工智能编程语言

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For Qwen3-4B-Math→Qwen3-4B mathematical distillation, Table 1 reports γOPD as the best method on both average accuracy (69.49) and average pass rate (82.41), exceeding the teacher averages (68.10 and 79.81) and the strongest OPD-baseline averages.整组结论：等待复现0/102 项指标获得支持 · 0 项已有评估102项测量结果展开结果表

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每行是一项测量，分别显示论文报告、最近可用实测和累计证据状态。
指标与条件	论文报告	最近可用实测	证据判断
method: Student · dataset: AIME24	22.6%	—	尚未评估
method: Student · dataset: AIME24	60%	—	尚未评估
method: Student · dataset: AIME25	20.83%	—	尚未评估
method: Student · dataset: AIME25	33.33%	—	尚未评估
method: Student · dataset: AMC23	60.16%	—	尚未评估
method: Student · dataset: AMC23	92.5%	—	尚未评估
method: Student · dataset: MATH500	67.4%	—	尚未评估
method: Student · dataset: MATH500	72.6%	—	尚未评估
method: Student · dataset: Average	42.75%	—	尚未评估
method: Student · dataset: Average	64.61%	—	尚未评估
method: Teacher · dataset: AIME24	57.4%	—	尚未评估
method: Teacher · dataset: AIME24	76.67%	—	尚未评估

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Profiling on the main 4B student/teacher and 32-GPU setup reports total additional γOPD work of 610.32 ms/step and 0.375 MB, equal to 0.1064% time and 0.00046% memory relative to a vanilla OPD update.整组结论：等待复现0/12 项指标获得支持 · 0 项已有评估12项测量结果展开结果表

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每行是一项测量，分别显示论文报告、最近可用实测和累计证据状态。
指标与条件	论文报告	最近可用实测	证据判断
operation: Discounted temporal credit	609.85 milliseconds per step	—	尚未评估
operation: Discounted temporal credit	0.063 megabytes	—	尚未评估
operation: Bounded advantage shaping	0.42 milliseconds per step	—	尚未评估
operation: Bounded advantage shaping	0.125 megabytes	—	尚未评估
operation: Verifier-reward mixing	0.04 milliseconds per step	—	尚未评估
operation: Verifier-reward mixing	0.188 megabytes	—	尚未评估
operation: Total additional overhead	610.32 milliseconds per step	—	尚未评估
operation: Total additional overhead	0.375 megabytes	—	尚未评估
operation: Vanilla OPD update (reference)	573,669 milliseconds per step	—	尚未评估
operation: Vanilla OPD update (reference)	81,254.4 megabytes	—	尚未评估
	0.1064%	—	尚未评估
	0.0005%	—	尚未评估

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Under joint math-and-code multi-teacher distillation into Qwen3-4B, γOPD records TotalAvg 66.00, the highest table value; it leads HumanEval+ and LiveCodeBench among code tasks and exceeds the teacher on the paper's average math and code comparisons, but not every individual benchmark or metric.整组结论：等待复现0/65 项指标获得支持 · 0 项已有评估65项测量结果展开结果表

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每行是一项测量，分别显示论文报告、最近可用实测和累计证据状态。
指标与条件	论文报告	最近可用实测	证据判断
method: Student · dataset: AIME24	22.6%	—	尚未评估
method: Student · dataset: AIME25	20.83%	—	尚未评估
method: Student · dataset: AMC23	60.16%	—	尚未评估
method: Student · dataset: MATH500	67.4%	—	尚未评估
method: Student · dataset: HumanEval+	75.61%	—	尚未评估
method: Student · dataset: MBPP+	61.9%	—	尚未评估
method: Student · dataset: LiveCodeBench v6	17.14%	—	尚未评估
method: Student · dataset: TotalAvg	47.15%	—	尚未评估
method: Teacher · dataset: AIME24	57.4%	—	尚未评估
method: Teacher · dataset: AIME25	51.67%	—	尚未评估
method: Teacher · dataset: AMC23	93.52%	—	尚未评估
method: Teacher · dataset: MATH500	69.8%	—	尚未评估

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For Qwen3-4B-Math→Qwen3-1.7B mathematical distillation, every trained student remains below the teacher on the two reported averages, while γOPD gives the best trained-student average accuracy (56.51) and average pass rate (71.22).整组结论：等待复现0/102 项指标获得支持 · 0 项已有评估102项测量结果展开结果表

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每行是一项测量，分别显示论文报告、最近可用实测和累计证据状态。
指标与条件	论文报告	最近可用实测	证据判断
method: Student · dataset: AIME24	11.77%	—	尚未评估
method: Student · dataset: AIME24	46.67%	—	尚未评估
method: Student · dataset: AIME25	8.33%	—	尚未评估
method: Student · dataset: AIME25	20%	—	尚未评估
method: Student · dataset: AMC23	39.84%	—	尚未评估
method: Student · dataset: AMC23	90%	—	尚未评估
method: Student · dataset: MATH500	59.2%	—	尚未评估
method: Student · dataset: MATH500	72.8%	—	尚未评估
method: Student · dataset: Average	29.79%	—	尚未评估
method: Student · dataset: Average	57.37%	—	尚未评估
method: Teacher · dataset: AIME24	57.4%	—	尚未评估
method: Teacher · dataset: AIME24	76.67%	—	尚未评估

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On AIME24 and AIME25, temporal discounting alone raises average accuracy by 2.04 points over vanilla OPD; naive reward mixing adds only 0.05 point beyond discounting, while the full discounting-plus-mixing-plus-normalization configuration reaches 57.56 average accuracy, a 3.91-point gain. Mixing plus normalization without discounting gains 2.00 points, supporting complementary contributions.整组结论：等待复现0/19 项指标获得支持 · 0 项已有评估19项测量结果展开结果表

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每行是一项测量，分别显示论文报告、最近可用实测和累计证据状态。
指标与条件	论文报告	最近可用实测	证据判断
dataset: AIME24	56.46%	—	尚未评估
dataset: AIME25	50.83%	—	尚未评估
dataset: AIME24 and AIME25	53.65%	—	尚未评估
dataset: AIME24	58.29%	—	尚未评估
dataset: AIME25	53.08%	—	尚未评估
dataset: AIME24 and AIME25	55.69%	—	尚未评估
	2.04 percentage points	—	尚未评估
dataset: AIME24	58.81%	—	尚未评估
dataset: AIME25	52.67%	—	尚未评估
dataset: AIME24 and AIME25	55.74%	—	尚未评估
	2.09 percentage points	—	尚未评估
dataset: AIME24	57.55%	—	尚未评估

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定性结论

Without RBM in Qwen3-4B-Math→Qwen3-1.7B training, γ=1 produces much larger gradient norms, rapid policy-entropy collapse, and inferior AIME24 validation accuracy. Local OPD (γ=0) and discounted variants improve steadily, with γ=0.99 reported as best and better than γ=0.9.实验受阻，详见具体原因

The four gamma conditions require regenerated training trajectories, but the paper provides no numeric curve targets or safe complete categorical rule.

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For the displayed incorrect response, local A_t^(0) penalizes tokens only weakly related to the actual reasoning error, whereas A_t^(0.99) concentrates stronger negative credit on the erroneous formula derivation without excessively penalizing the final end-of-sequence token.实验受阻，详见具体原因

The exact illustrated response is retained in the ablation objective as qualitative source context; no scalar target is invented.

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In vanilla-distillation training curves, the paper reports that γOPD maintains the highest verifiable reward, stable absolute OPD advantage, and the smallest gradient-norm fluctuations; its response length becomes shorter and more stable than most baselines. TOPD is the exception on length because it truncates the distillation signal, and its verifiable reward remains mostly below zero.实验受阻，详见具体原因

The full training package retains these curve claims as source context, but automatic verification cannot safely bind them.

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For the displayed correct response, local A_t^(0) gives sparse supervision and noticeable negative credit to only a few tokens, whereas normalized A_t^(0.99) propagates later information, smooths the signal, assigns stronger positive credit to the key mathematical derivation, and mildly penalizes redundant text.实验受阻，详见具体原因

The exact illustrated response is retained in the ablation objective as qualitative source context; no scalar target is invented.

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其余结论4

The experiments use veRL with vLLM rollouts and FSDP actor training; OPD-based methods use one response per prompt, batch and PPO minibatch size 1024, maximum prompt length 2048, maximum response length 16384, RADAR with constant 1×10^-5 learning rate, temperature/top-p 1.0/1.0, and tensor parallel size 4. Math uses a DAPO-style boxed-answer verifier and code uses execution tests; binary outcomes map to ±1.随其他结论间接验证

This is protocol context rather than an independently testable result. Its reported settings are carried into each applicable training/evaluation objective, with missing revisions, seeds, stopping schedule, dtype, and multi-domain sampling ratio left explicit.

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γOPD assigns each token a discounted sum of its current and future teacher–student log-ratios; γ=0 recovers local token-level OPD and γ=1 recovers sequence-level return-to-go. Reward-Compatible Bounded Mixing response-normalizes and softsign-bounds that teacher term before adding a binary verifier reward, so the verifier reward fixes the update sign while teacher credit modulates token-level strength.随其他结论间接验证

This is method definition and algebraic context rather than an independently reported empirical result. Its equations are operational prerequisites for the planned reconstruction packages; hand checks cannot substitute for the represented empirical comparisons.

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Under a uniformly bounded second moment for local token advantages, the paper proves a remaining-horizon-squared upper bound for undiscounted sequence credit and a horizon-independent upper bound for fixed γ<1.随其他结论间接验证

The claim is a theorem under a stated moment assumption, not an empirical measurement. The fixed proof can be assessed mathematically; numerical examples would not reproduce it.

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Because of computational constraints, the experiments are limited to models smaller than 10B parameters; the paper leaves larger-scale evaluation and adaptive or entropy-aware discounting for future work.论文自述边界

This is a stated scope limitation and future-work boundary, not an empirical result requiring a reproduction package.

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