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arxiv: 2605.22620 · v1 · pith:WLRYMFOBnew · submitted 2026-05-21 · 💻 cs.LG · cs.CL

Two is better than one: A Collapse-free Multi-Reward RLIF Training Framework

Shourov Joarder , Diganta Sikdar , Ahsan Habib Akash , Binod Bhattarai , Prashnna Gyawali This is my paper

Pith reviewed 2026-05-22 06:38 UTC · model grok-4.3

classification 💻 cs.LG cs.CL
keywords multi-reward reinforcement learninginternal feedbackcluster votingself-certaintyentropy regularizationLLM reasoningunsupervised trainingreward hacking prevention
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The pith

Combining cluster-voting and self-certainty rewards stabilizes unsupervised reinforcement learning for large language models.

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

This paper aims to show that a single internal reward signal often leads to problems like reward hacking and loss of exploration in training language models to reason. Instead, it introduces two different internal rewards that work at different levels: one checks consistency across possible answers by voting in clusters, and the other measures how certain the model is about each token in a response. These are balanced with a normalization step and a special regularization term that keeps the model from becoming too predictable too soon. If this works, it means language models can be trained to improve their reasoning over long sequences using only their own signals, without needing correct answers provided by humans. Experiments on math problems and code writing suggest the method holds up better than earlier unsupervised approaches and gets close to methods that do use external supervision.

Core claim

The paper claims that decomposing the training signal into an answer-level reward based on cluster voting and a completion-level reward based on token-wise self-certainty, then combining them with GDPO normalization and KL-Cov regularization, produces stable training that avoids entropy collapse and supports effective long-horizon reasoning in LLMs without any external ground-truth supervision.

What carries the argument

The central mechanism is the pairing of an answer-level cluster-voting reward with a completion-level token-wise self-certainty reward, stabilized through GDPO-based normalization and KL-Cov regularization.

If this is right

  • Training remains stable without entropy collapse or reward hacking over long horizons.
  • Performance on math reasoning and code generation tasks approaches that of supervised methods.
  • Reasoning structure is preserved better than with single-reward internal feedback approaches.
  • Scalable unsupervised improvement becomes feasible for complex reasoning tasks.

Where Pith is reading between the lines

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

  • Similar multi-signal combinations might help in other reinforcement learning domains beyond language models.
  • Testing the method on tasks requiring even longer reasoning chains could reveal limits of the complementarity.
  • The regularization technique may apply to preventing collapse in other training regimes that use model-generated feedback.

Load-bearing premise

The cluster-voting answer reward and the self-certainty completion reward provide enough different information that their normalized and regularized combination prevents both hacking and collapse.

What would settle it

Running the training and finding that the model still exhibits entropy collapse or starts producing repetitive low-quality outputs in later training stages despite the added regularization would show the approach does not fully solve the problem.

Figures

Figures reproduced from arXiv: 2605.22620 by Ahsan Habib Akash, Binod Bhattarai, Diganta Sikdar, Prashnna Gyawali, Shourov Joarder.

Figure 1
Figure 1. Figure 1: Given a prompt, we sample G completions from the rollout policy and compute two intrinsic [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Single- & multi-reward analysis (no KL-Cov) on Qwen2.5-1.5B. Left: GSM8K and [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: KL-Cov βcov sweep on the full multi-reward objective (Qwen2.5-1.5B). All three coefficients (βcov ∈ {0.0005, 0.05, 0.1}) maintain stable accuracy and completion length through step 280; the no-KL-Cov baseline (red) collapses around step 240. accuracy dropping to ∼1–2%. Additional results are provided in [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: INTUITOR + KL-Cov ablation on Qwen2.5-1.5B (steps 0–280). KL-Cov ( [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: GDPO-normalization ablation on Qwen2.5-1.5B with the full multi-reward + KL-Cov [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Logprob-space gradient norms per reward channel under each normalization variant. [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
read the original abstract

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning ability of LLMs, but often depends on external supervision from human annotations or gold-standard solutions. Reinforcement learning from internal feedback (RLIF) has recently emerged as a scalable unsupervised alternative, using signals extracted from the model itself. However, existing RLIF methods typically rely on a single internal reward, which can lead to reward hacking, entropy collapse, and degraded reasoning structure. We propose a multi-reward RLIF framework that decomposes the training signal into two complementary components: an answer-level reward based on cluster voting and a completion-level reward based on token-wise self-certainty. To combine these signals robustly, we apply GDPO-based normalization to reduce reward-scale imbalance. We further introduce KL-Cov regularization, which targets low-entropy token distributions responsible for disproportionate entropy reduction, preserving exploration and preventing late-stage collapse. Across mathematical reasoning and code-generation benchmarks, our method improves stability and robustness over prior unsupervised RL approaches, while achieving performance close to supervised RLVR methods. These results show that complementary internal rewards, combined with targeted regularization, can support stable long-horizon reasoning without relying on external ground-truth supervision. Code will be released soon.

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 a multi-reward RLIF framework for training LLMs on reasoning tasks without external ground-truth supervision. It decomposes the training signal into an answer-level cluster-voting reward and a completion-level token-wise self-certainty reward, combines them via GDPO-based normalization to address scale imbalance, and adds KL-Cov regularization targeting low-entropy tokens to prevent entropy collapse and reward hacking. Experiments on mathematical reasoning and code-generation benchmarks show improved stability and robustness relative to prior unsupervised RLIF methods, with performance approaching that of supervised RLVR approaches.

Significance. If the empirical results hold under the reported conditions, the work is significant for demonstrating a practical unsupervised alternative to RLVR that mitigates key failure modes (entropy collapse, hacking) through complementary internal signals and targeted regularization. The explicit focus on preserving exploration via covariance-based regularization on low-entropy distributions addresses a recurring issue in RLIF literature and could support more scalable long-horizon reasoning training.

major comments (2)
  1. §4 (Experiments) and associated tables: while benchmark gains on math and code tasks are reported along with stability improvements, the manuscript does not include error bars, statistical significance tests, or full ablation results isolating the contribution of cluster-voting versus self-certainty after GDPO normalization; this weakens the claim that the two rewards are demonstrably complementary across the full training trajectory.
  2. §3.2 (KL-Cov regularization): the formulation targets low-entropy token distributions via a covariance term, but the paper does not provide a derivation showing why this specific choice (as opposed to standard entropy bonuses or other variance penalties) is optimal or general; the coefficient is listed as a free hyperparameter, which could affect reproducibility of the collapse-prevention result.
minor comments (2)
  1. Notation for the two rewards and GDPO normalization should be introduced with explicit equations early in §3 to improve readability before the regularization discussion.
  2. The abstract claims 'performance close to supervised RLVR methods' but does not quantify the gap; adding a direct comparison table row or sentence in the results section would strengthen the claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and positive recommendation for minor revision. We address each major comment below and will update the manuscript accordingly to strengthen the empirical and methodological presentation.

read point-by-point responses

  1. Referee: §4 (Experiments) and associated tables: while benchmark gains on math and code tasks are reported along with stability improvements, the manuscript does not include error bars, statistical significance tests, or full ablation results isolating the contribution of cluster-voting versus self-certainty after GDPO normalization; this weakens the claim that the two rewards are demonstrably complementary across the full training trajectory.

    Authors: We agree that error bars and statistical significance tests would improve the presentation of results. In the revised version we will report standard deviations across multiple random seeds and include paired t-tests or similar significance assessments for key comparisons. For the ablations, the original experiments already include component-wise removals of each reward; we will expand these into a fuller set of post-GDPO ablations that track the individual and joint contributions of cluster-voting and self-certainty rewards at multiple training checkpoints, thereby more clearly demonstrating their complementarity over the full trajectory. revision: yes

  2. Referee: §3.2 (KL-Cov regularization): the formulation targets low-entropy token distributions via a covariance term, but the paper does not provide a derivation showing why this specific choice (as opposed to standard entropy bonuses or other variance penalties) is optimal or general; the coefficient is listed as a free hyperparameter, which could affect reproducibility of the collapse-prevention result.

    Authors: The KL-Cov term was introduced because empirical inspection showed that entropy collapse is driven disproportionately by a small subset of low-entropy tokens; the covariance formulation directly penalizes the joint reduction of KL and entropy on those tokens. While a complete theoretical optimality proof is not provided, we will add a detailed motivation section comparing KL-Cov to standard entropy bonuses and variance penalties, including the empirical rationale for the covariance choice. We will also report the exact coefficient values used in all experiments together with a brief sensitivity study to support reproducibility. revision: partial

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper constructs its multi-reward RLIF framework by defining an answer-level cluster-voting reward and a completion-level token-wise self-certainty reward directly from the model's internal outputs, then combines them via GDPO normalization and KL-Cov regularization explicitly targeting entropy collapse. These components are presented as independent design choices addressing reward hacking and stability, with benchmark improvements cited as external validation rather than derived tautologically from the inputs. No equation or step reduces by construction to a prior fit, self-citation load-bearing premise, or renamed empirical pattern; the derivation remains self-contained against the stated assumptions about complementarity of the two rewards.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that internal model signals can reliably proxy reasoning quality and on the introduction of a new regularization term whose strength is not quantified in the abstract.

free parameters (1)
  • KL-Cov regularization coefficient
    Controls the strength of the penalty applied to low-entropy token distributions; its specific value is not stated in the abstract.
axioms (1)
  • domain assumption Internal signals extracted from the model itself (cluster voting and token-wise self-certainty) constitute valid and complementary training rewards for reasoning tasks.
    This premise underpins the entire RLIF approach and the decision to combine the two reward types.

pith-pipeline@v0.9.0 · 5767 in / 1412 out tokens · 64726 ms · 2026-05-22T06:38:07.448764+00:00 · methodology

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Reference graph

Works this paper leans on

29 extracted references · 29 canonical work pages

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    Let’s break it down step-by-step . . . Step 1: Determine X. Let’s proceed step-by-step. Step 1: Determine X

    The complementary reward structure (cluster voting and self-certainty, with complementary policy gradients per) thusslowsconvergence to the degenerate fixed point, extending the usable training window by≈60steps versus INTUITOR, but does not, by itself, prevent collapse. (3) Multi-reward + KL-Cov is the only unsupervised configuration that remains robust ...

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    Let’s go through each step in detail

    Calculate the current age of Steve’s son’s wife. Let’s go through each step in detail. Step 1: Identify the current age of Steve.Steve is currently 60 years old. Step 2: Calculate the current age of Steve’s wife.Steve’s wife is 4 years older than Steve. Therefore, her age is: Age of Steve’s wife=Age of Steve+ 4 = 60 + 4 = 64years old. Step 3: Determine th...

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    Identify Martin’s weight

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    Divide the total weight by the number of friends to find the average weight. Let’s go through each step in detail. Step 1: Calculate Susan’s weight.Mark weighs 150 pounds. Susan weighs 20 pounds less than Mark. Therefore, we can calculate Susan’s weight as follows: Susan’s weight=Mark’s weight−20 = 150−20 = 130pounds. Step 2: Calculate Bob’s weight.Bob we...

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    Identify the age of Nani

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    Sum the ages of Nani, his brother, and his sister. Let’s go through each step in detail. Step 1: Identify the age of Nani.Nani is 8 years old. Step 2: Calculate the age of Nani’s brother.Nani’s brother is twice Nani’s age. So, we calculate: Age of Nani’s brother= 2×Age of Nani= 2×8 = 16years. Step 3: Calculate the age of Nani’s sister.Nani’s sister is 25%...

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    the first element,

    Return the first element of the sorted list. Let’s proceed step by step. Step 1: Sort the list.The given list is [1, 2, 2, 3, 4, 5] . When we sort this list, we get [1,2,2,3,4,5]. Step 2: Return the first element.The first element of the sorted list is1. Therefore, the output of the functionf([1, 2, 2, 3, 4, 5], 1)is1. So, the final answer is: 1 Multi-Rew...

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    Print the resulting string. Let’s proceed step by step. Step 1: Read the input string.We will use theinput()function to read the input string. Step 2: Remove the characters between the two |’s.We will use string slicing to remove the characters between the two|’s. Step 3: Print the resulting string.We will use theprint()function to output the result. Here...

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    Print the resulting string. Here is the Python code that implements these steps: # Read the input string S = input() # Find the positions of the two ’|’ left_index = S.find(’|’) right_index = S.rfind(’|’) # Remove the characters between the two ’|’ result = S[:left_index] + S[right_index + 1:] # Print the resulting string print(result) Let’s break down the code:

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