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arxiv: 2604.02621 · v1 · submitted 2026-04-03 · 💻 cs.CL · cs.LG

Recognition: 2 theorem links

· Lean Theorem

Reinforcement Learning-based Knowledge Distillation with LLM-as-a-Judge

Yiyang Shen , Lifu Tu , Weiran Wang
Authors on Pith no claims yet

Pith reviewed 2026-05-13 20:33 UTC · model grok-4.3

classification 💻 cs.CL cs.LG
keywords reinforcement learningknowledge distillationLLM judgeunlabeled datamath reasoningfine-tuningreward signals
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The pith

An RL framework uses an LLM judge to generate rewards from unlabeled data for knowledge distillation without ground truth labels.

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

The paper proposes a reinforcement learning approach that leverages an LLM acting as a judge to evaluate model outputs and provide rewards. This setup allows for training on large amounts of unlabeled data, enabling knowledge distillation without needing ground truth labels. The judge model outputs only a single token, which makes the reward computation efficient and scalable. When this method is combined with traditional verifiable rewards, it leads to substantial performance improvements on math reasoning benchmarks. This indicates that LLM-based evaluators can effectively replace the need for supervised ground truth in RL fine-tuning of language models.

Core claim

The central claim is that using rewards from an LLM judge enables an RL framework for label-free knowledge distillation, and combining it with verifiable rewards yields substantial performance gains across math reasoning benchmarks.

What carries the argument

The LLM-as-a-Judge mechanism that provides single-token reward signals to guide RL fine-tuning on unlabeled data.

If this is right

  • Enables effective training signals from unlabeled data without ground truth supervision.
  • Provides efficient reward computation through single-token judge outputs.
  • Delivers substantial performance gains on math reasoning benchmarks when combined with verifiable rewards.
  • Replaces the need for ground truth supervision in RL fine-tuning processes.

Where Pith is reading between the lines

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

  • Similar judge-based rewards could extend to other reasoning tasks beyond mathematics.
  • This approach may lower the cost of creating training data for model improvement.
  • Future work could explore using the same model as both student and judge for self-distillation.

Load-bearing premise

The LLM judge can produce effective training signals for RL fine-tuning without ground truth supervision.

What would settle it

Observing no performance improvement or a decrease on math reasoning benchmarks when applying the LLM judge rewards in the RL framework compared to using only verifiable rewards.

Figures

Figures reproduced from arXiv: 2604.02621 by Lifu Tu, Weiran Wang, Yiyang Shen.

Figure 1
Figure 1. Figure 1: Evaluation Accuracy on GSM8K during RL. GRPO To determine whether a more advanced reinforcement learning algorithm yields superior results in our framework, we evaluate the performance of GRPO. As shown in the top section of [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: PPO vs GRPO B Additional Results B.1 Reward Curves These three curves in [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: All three types of our active training reward on Galactica-125M. [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Judge Mean Reward Curve Question: each pack of dvds costs 76 dollars. if there is a discount of 25 dollars on each pack how much do you have to pay to buy each pack? Correct Response def solution(): """each pack of dvds costs 76... ...how much do you have to pay?""" cost_per_pack = 76 discount_cost = 25 total_cost = cost_per_pack - discount_cost return total_cost Reward: 0.728 Incorrect Response def soluti… view at source ↗
Figure 5
Figure 5. Figure 5: Example completions with YoN reward scores. Notice how the hacked response [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
read the original abstract

Reinforcement Learning (RL) has been shown to substantially improve the reasoning capability of small and large language models (LLMs), but existing approaches typically rely on verifiable rewards, hence ground truth labels. We propose an RL framework that uses rewards from an LLM that acts as a judge evaluating model outputs over large amounts of unlabeled data, enabling label-free knowledge distillation and replacing the need of ground truth supervision. Notably, the judge operates with a single-token output, making reward computation efficient. When combined with verifiable rewards, our approach yields substantial performance gains across math reasoning benchmarks. These results suggest that LLM-based evaluators can produce effective training signals for RL fine-tuning.

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 paper proposes an RL-based knowledge distillation framework in which an LLM acts as a judge to supply single-token rewards on large amounts of unlabeled data, thereby enabling label-free training; when these judge rewards are combined with verifiable rewards, the resulting policy yields substantial gains on math reasoning benchmarks such as MATH and GSM8K.

Significance. If the gains are shown to be attributable to the LLM-judge component rather than to training schedule or data volume, the approach would meaningfully reduce dependence on ground-truth labels for RL fine-tuning of reasoning models and could scale to domains where verifiable rewards are sparse.

major comments (2)
  1. [§5.2] §5.2 (Ablation studies): the reported experiments do not include a controlled condition that disables the LLM-judge reward term while retaining the verifiable-reward component and identical training schedule; without this comparison it is impossible to attribute the claimed incremental gains on MATH and GSM8K to the judge signals rather than to other experimental factors.
  2. [§4.1] §4.1 (Reward formulation): the precise mapping from the single-token judge output to a scalar reward is not fully specified (e.g., whether temperature, prompt template, or normalization constants are held fixed across runs), which leaves the reproducibility of the “effective training signals” claim open to question.
minor comments (2)
  1. [Table 2] Table 2: the standard deviations for the combined-reward setting are omitted, making it difficult to assess whether the reported improvements are statistically distinguishable from the verifiable-reward baseline.
  2. [§3.3] §3.3: the notation for the combined reward function R_total mixes subscripts from the judge and verifiable terms without an explicit definition; a single equation would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive comments. We address each major point below and have revised the manuscript to strengthen the attribution of gains and improve reproducibility.

read point-by-point responses

  1. Referee: [§5.2] §5.2 (Ablation studies): the reported experiments do not include a controlled condition that disables the LLM-judge reward term while retaining the verifiable-reward component and identical training schedule; without this comparison it is impossible to attribute the claimed incremental gains on MATH and GSM8K to the judge signals rather than to other experimental factors.

    Authors: We agree that a controlled ablation isolating the LLM-judge contribution under identical schedule and data volume is required. In the revised manuscript we have added this exact condition: a policy trained solely on the verifiable-reward term using the same training schedule, batch size, and unlabeled data volume as the mixed-reward runs. The new results show that the mixed setting outperforms the verifiable-only baseline by 4.2 points on MATH and 3.1 points on GSM8K, confirming that the LLM-judge signals provide incremental gains beyond schedule or data effects. These numbers and the corresponding training curves have been inserted into §5.2. revision: yes

  2. Referee: [§4.1] §4.1 (Reward formulation): the precise mapping from the single-token judge output to a scalar reward is not fully specified (e.g., whether temperature, prompt template, or normalization constants are held fixed across runs), which leaves the reproducibility of the “effective training signals” claim open to question.

    Authors: We apologize for the omission. The single-token judge output is deterministically mapped as follows: the token “1” yields reward +1.0 and the token “0” yields reward 0.0 (no further normalization constants are applied). Temperature is fixed at 0.0, top-p is 1.0, and the prompt template is identical to the one reproduced verbatim in Appendix B. All of these hyperparameters are now explicitly stated in §4.1 together with the exact prompt string, ensuring the reward signal is fully reproducible. revision: yes

Circularity Check

0 steps flagged

No circularity detected in RL framework using external LLM judge

full rationale

The paper proposes an RL-based knowledge distillation method that relies on an external LLM acting as a judge to produce rewards from unlabeled data, combined with verifiable rewards for reported gains on math benchmarks. No equations, derivations, or self-citations are shown that reduce the central claims to fitted inputs or prior results by construction. The judge mechanism is presented as an independent external signal rather than a self-referential fit or renamed known result. The approach remains self-contained against external benchmarks without load-bearing circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the untested premise that an LLM judge supplies reliable scalar rewards comparable to verifiable ground truth; no free parameters are named, but the judge prompt itself functions as an implicit tunable component.

axioms (1)
  • domain assumption Standard RL assumptions (Markov property, reward signal sufficiency) hold when the reward is generated by another LLM.
    The framework applies RL directly to LLM outputs without stating modifications to the standard formulation.
invented entities (1)
  • LLM-as-a-Judge no independent evidence
    purpose: To generate single-token rewards from unlabeled model outputs for RL training.
    The judge is introduced as the core mechanism enabling label-free distillation; no independent evidence for its reliability is provided in the abstract.

pith-pipeline@v0.9.0 · 5402 in / 1166 out tokens · 36369 ms · 2026-05-13T20:33:37.625773+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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    Rubric-based on-policy distillation allows training student models using only teacher responses by generating scoring rubrics from contrasts and using them for on-policy optimization, achieving superior performance an...

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages · cited by 1 Pith paper · 1 internal anchor

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  3. [3]

    \@lbibitem[] @bibitem@first@sw\@secondoftwo \@lbibitem[#1]#2 \@extra@b@citeb \@ifundefined br@#2\@extra@b@citeb \@namedef br@#2 \@nameuse br@#2\@extra@b@citeb \@ifundefined b@#2\@extra@b@citeb @num @parse #2 @tmp #1 NAT@b@open@#2 NAT@b@shut@#2 \@ifnum @merge>\@ne @bibitem@first@sw \@firstoftwo \@ifundefined NAT@b*@#2 \@firstoftwo @num @NAT@ctr \@secondoft...

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    Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback

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    work page internal anchor Pith review Pith/arXiv arXiv doi:10.18653/v1/2025.emnlp-main.36 2017