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

Recent activity

—Waiting for the model response
—Analysis environment started
—Analysis made new progress
—Research inventory and experiment plan prepared
—Waiting for experiment selection

ArkGraph

Explore ArkGraph and select the steps to run.

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

Public

Authors: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 Machine Learning (cs.LG)Artificial Intelligence Programming Languages

Reproduction results

All claims ↗

No reproduction results yet

The paper’s claims are available in Research claims.

Full research claim catalog

0 / 13 claims verified

the rest still being verified

Key metricsPaper-reported → reproduced · click a row to expand

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.Whole claim: Awaiting reproduction0/102 measurements supported · 0 assessed102measurementsExplore results

Experiment plan ready; no runs yet.

Measurement results

0/102 assessed

0 supported0 disputed or conflicting102 not assessed

The complete result group stays with its claim. Assessed rows come first; their judgments do not replace the whole-claim conclusion. Expand a row for conditions, sources, and evidence history.

Each row is a measurement with its reported value, latest available observation, and cumulative evidence state.
Metric and conditions	Reported	Latest observation	Evidence judgment
method: Student · dataset: AIME24	22.6%	—	Not assessed
method: Student · dataset: AIME24	60%	—	Not assessed
method: Student · dataset: AIME25	20.83%	—	Not assessed
method: Student · dataset: AIME25	33.33%	—	Not assessed
method: Student · dataset: AMC23	60.16%	—	Not assessed
method: Student · dataset: AMC23	92.5%	—	Not assessed
method: Student · dataset: MATH500	67.4%	—	Not assessed
method: Student · dataset: MATH500	72.6%	—	Not assessed
method: Student · dataset: Average	42.75%	—	Not assessed
method: Student · dataset: Average	64.61%	—	Not assessed
method: Teacher · dataset: AIME24	57.4%	—	Not assessed
method: Teacher · dataset: AIME24	76.67%	—	Not assessed

Open claim details

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.Whole claim: Awaiting reproduction0/12 measurements supported · 0 assessed12measurementsExplore results

Experiment plan ready; no runs yet.

Measurement results

0/12 assessed

0 supported0 disputed or conflicting12 not assessed

The complete result group stays with its claim. Assessed rows come first; their judgments do not replace the whole-claim conclusion. Expand a row for conditions, sources, and evidence history.

Each row is a measurement with its reported value, latest available observation, and cumulative evidence state.
Metric and conditions	Reported	Latest observation	Evidence judgment
operation: Discounted temporal credit	609.85 milliseconds per step	—	Not assessed
operation: Discounted temporal credit	0.063 megabytes	—	Not assessed
operation: Bounded advantage shaping	0.42 milliseconds per step	—	Not assessed
operation: Bounded advantage shaping	0.125 megabytes	—	Not assessed
operation: Verifier-reward mixing	0.04 milliseconds per step	—	Not assessed
operation: Verifier-reward mixing	0.188 megabytes	—	Not assessed
operation: Total additional overhead	610.32 milliseconds per step	—	Not assessed
operation: Total additional overhead	0.375 megabytes	—	Not assessed
operation: Vanilla OPD update (reference)	573,669 milliseconds per step	—	Not assessed
operation: Vanilla OPD update (reference)	81,254.4 megabytes	—	Not assessed
	0.1064%	—	Not assessed
	0.0005%	—	Not assessed

Open claim details

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.Whole claim: Awaiting reproduction0/65 measurements supported · 0 assessed65measurementsExplore results

Experiment plan ready; no runs yet.

Measurement results

0/65 assessed

0 supported0 disputed or conflicting65 not assessed

The complete result group stays with its claim. Assessed rows come first; their judgments do not replace the whole-claim conclusion. Expand a row for conditions, sources, and evidence history.

Each row is a measurement with its reported value, latest available observation, and cumulative evidence state.
Metric and conditions	Reported	Latest observation	Evidence judgment
method: Student · dataset: AIME24	22.6%	—	Not assessed
method: Student · dataset: AIME25	20.83%	—	Not assessed
method: Student · dataset: AMC23	60.16%	—	Not assessed
method: Student · dataset: MATH500	67.4%	—	Not assessed
method: Student · dataset: HumanEval+	75.61%	—	Not assessed
method: Student · dataset: MBPP+	61.9%	—	Not assessed
method: Student · dataset: LiveCodeBench v6	17.14%	—	Not assessed
method: Student · dataset: TotalAvg	47.15%	—	Not assessed
method: Teacher · dataset: AIME24	57.4%	—	Not assessed
method: Teacher · dataset: AIME25	51.67%	—	Not assessed
method: Teacher · dataset: AMC23	93.52%	—	Not assessed
method: Teacher · dataset: MATH500	69.8%	—	Not assessed

Open claim details

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).Whole claim: Awaiting reproduction0/102 measurements supported · 0 assessed102measurementsExplore results

Experiment plan ready; no runs yet.

Measurement results

0/102 assessed

0 supported0 disputed or conflicting102 not assessed

The complete result group stays with its claim. Assessed rows come first; their judgments do not replace the whole-claim conclusion. Expand a row for conditions, sources, and evidence history.

Each row is a measurement with its reported value, latest available observation, and cumulative evidence state.
Metric and conditions	Reported	Latest observation	Evidence judgment
method: Student · dataset: AIME24	11.77%	—	Not assessed
method: Student · dataset: AIME24	46.67%	—	Not assessed
method: Student · dataset: AIME25	8.33%	—	Not assessed
method: Student · dataset: AIME25	20%	—	Not assessed
method: Student · dataset: AMC23	39.84%	—	Not assessed
method: Student · dataset: AMC23	90%	—	Not assessed
method: Student · dataset: MATH500	59.2%	—	Not assessed
method: Student · dataset: MATH500	72.8%	—	Not assessed
method: Student · dataset: Average	29.79%	—	Not assessed
method: Student · dataset: Average	57.37%	—	Not assessed
method: Teacher · dataset: AIME24	57.4%	—	Not assessed
method: Teacher · dataset: AIME24	76.67%	—	Not assessed

Open claim details

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.Whole claim: Awaiting reproduction0/19 measurements supported · 0 assessed19measurementsExplore results

Experiment plan ready; no runs yet.

Measurement results

0/19 assessed

0 supported0 disputed or conflicting19 not assessed

The complete result group stays with its claim. Assessed rows come first; their judgments do not replace the whole-claim conclusion. Expand a row for conditions, sources, and evidence history.

Each row is a measurement with its reported value, latest available observation, and cumulative evidence state.
Metric and conditions	Reported	Latest observation	Evidence judgment
dataset: AIME24	56.46%	—	Not assessed
dataset: AIME25	50.83%	—	Not assessed
dataset: AIME24 and AIME25	53.65%	—	Not assessed
dataset: AIME24	58.29%	—	Not assessed
dataset: AIME25	53.08%	—	Not assessed
dataset: AIME24 and AIME25	55.69%	—	Not assessed
	2.04 percentage points	—	Not assessed
dataset: AIME24	58.81%	—	Not assessed
dataset: AIME25	52.67%	—	Not assessed
dataset: AIME24 and AIME25	55.74%	—	Not assessed
	2.09 percentage points	—	Not assessed
dataset: AIME24	57.55%	—	Not assessed

Open claim details

Qualitative findings

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.Experiment blocked; see the specific reason

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

Open claim details

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.Experiment blocked; see the specific reason

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

Open claim details

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.Experiment blocked; see the specific reason

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

Open claim details

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.Experiment blocked; see the specific reason

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

Open claim details

Other claims4

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.Covered by other claims

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.

Open claim details

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.Covered by other claims

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.

Open claim details

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.Covered by other claims

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.

Open claim details

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.Stated by the authors

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

Open claim details