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REVIEW 5 major objections 5 minor 2 cited by

Mars-PO: Multi-Agent Reasoning System Preference Optimization

T0 review · 5 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Mars-PO pools the best correct answers from several agents and pairs them with each agent's mistakes, lifting Llama3.1-8B-Instruct on MATH from 50.38% to 57.82%.

desk verdict A plausible multi-agent DPO variant with consistent reported gains, but the paper never states whether it trained on the GSM8K/MATH test splits—and that omission is decisive. read the letter →

arxiv 2411.19039 v1 pith:BOBY76GF submitted 2024-11-28 cs.AI

Xiaoxuan Lou , Chaojie Wang , Bo An This is my paper · ORCID
classification cs.AI
keywords mathematicalreasoningdirectpreferenceoptimizationmulti-agentLLMsystemhybridpositivesamplesrewardmodelscoringiterativetrainingGSM8KMATHbenchmark
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper sets out to show that a multi-agent twist on direct preference optimization (DPO) can push already instruction-tuned language models further on mathematical reasoning. For each problem, several agents generate many candidate solutions; the correct ones are pooled, scored by a reward model, and the highest-scoring correct solutions become a shared positive set, while each agent keeps its own wrong answers as negatives. Training each agent on these pairs with a DPO loss plus a next-token likelihood loss is reported to beat vanilla DPO, DPO with an extra NLL term, and supervised fine-tuning on the same positives. The headline result is Llama3.1-8B-Instruct improving from 50.38% to 57.82% on the MATH benchmark over three iterations.

What carries the argument

The load-bearing object is the hybrid positive sample set: correct answers sampled from all agents, scored by a reward model, and reduced to a shared high-quality subset. The paper pairs this shared positive set with each agent's own negative samples and optimizes $\mathcal{L} = \mathcal{L}_{\mathrm{DPO}} + \alpha \mathcal{L}_{\mathrm{NLL}}$ over three iterations of sampling and retraining. This construction is what converts multi-agent diversity into stronger preference pairs and is the claimed reason Mars-PO outperforms single-agent DPO and positive-sample SFT.

What would settle it

Run the full pipeline twice with everything fixed except the hybrid positive set: once with reward-model-selected correct answers and once with a same-size random sample of correct answers; if the MATH accuracy matches, reward-model selection is not what carries the result.

Watch

Extended reading notes

Core claim

The central discovery is that the quality and diversity of positive samples, not just the contrast with negatives, is what makes preference optimization work for mathematical reasoning. By merging correct outputs across agents and filtering them with a reward model, the authors construct what they call a hybrid positive sample set; pairing it with agent-specific negative samples avoids the degradation that vanilla DPO causes on already fine-tuned models. The paper reports consistent gains across all three agents on both GSM8K and MATH, with the largest gains on the weakest agent, and shows that supervised fine-tuning on the same positive samples without the contrastive negatives gives much smaller improvements.

Load-bearing premise

The method assumes the reward model reliably ranks the quality of correct solutions, so the highest-scoring correct answers across agents genuinely teach each agent better than its own correct answers.

Editorial extensions

If this is right

  • If the mechanism holds, improving math reasoning by preference optimization does not require step-level error annotations; final-answer correctness plus reward-model selection is enough.
  • Multi-agent alignment can amplify the weakest model in the group, since the largest reported gains are on Llama3.1-8B-Instruct, the weakest of the three agents.
  • Vanilla DPO should be expected to hurt already math-tuned models, while shared positives paired with agent-specific negatives should improve them.
  • Iterative retraining on freshly sampled responses continues to add accuracy, so the framework can be run as a loop rather than a one-shot post-training step.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural testable extension is to replace the 72-billion-parameter reward model with a smaller or process-based scorer; if the gains shrink, reward-model quality is the real driver rather than multi-agent pooling itself.
  • The method implicitly assumes the reward model's score tracks solution quality; a version using human-rated correct solutions could separate those two factors.
  • The same hybrid-positive, agent-specific-negative recipe could transfer to other verdictable generation tasks, such as code generation, where correctness can be checked and a scorer exists.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. Mars-PO proposes a multi-agent preference optimization framework for improving mathematical reasoning of instruction-tuned LLMs. The method (i) samples multiple responses per prompt from each of three agents (Qwen2.5-Math-7B-Instruct, DeepSeek-Math-7B-RL, Llama3.1-8B-Instruct), (ii) classifies responses by final-answer correctness, (iii) selects a hybrid positive set by scoring correct responses with an external reward model (Qwen2.5-Math-RM-72B), and (iv) trains each agent with DPO using the shared hybrid positives and agent-specific negatives, plus an NLL term, over three iterations. The authors report accuracy gains on GSM8K and MATH for all three agents, with the largest gain for Llama3.1-8B-Instruct on MATH (50.38% to 57.82%).

Significance. If the reported gains are reproducible and not an artifact of data leakage, the framework is a simple and potentially useful extension of DPO to multi-agent settings: sharing correct solutions across agents in preference pairs is a plausible way to transfer reasoning strengths, and the gains for DeepSeek-Math and Llama are nontrivial. The paper also includes a useful negative result for vanilla DPO (large degradation on these benchmarks) and an SFT-with-positive-samples baseline. However, the significance is currently limited by missing train/test split details, absent statistical uncertainty quantification, and a likely sign error in the NLL loss, all of which prevent a reader from verifying the central empirical claim.

major comments (5)
  1. [§3.1, §4.2, §4.4] The manuscript never states whether the training dataset D in §3.1 is the official train split of GSM8K/MATH or includes the evaluation problems. Since the method trains on the correct answers yi from D, any overlap between D and the test sets used to produce Table 1 would make all reported accuracy gains reflect memorization rather than improved reasoning. The authors must explicitly specify the train/test split, state how prompts were sampled, and ideally release code/data to allow verification. This is the most load-bearing issue: without this clarification, every quantitative conclusion in the paper is unverifiable.
  2. [Table 1, §5.1] No error bars, confidence intervals, or significance tests are reported. For Qwen2.5-Math-7B-Instruct, the Mars-PO iter1 gains are only +0.15 on GSM8K and +0.16 on MATH; on a benchmark with hundreds to thousands of problems, these differences are within the scale of one or two questions and are indistinguishable from sampling noise. The paper's claim of 'consistent' improvements across all agents is therefore not statistically supported for the strongest baseline model. The authors should report variance across seeds or a significance test, especially for small-magnitude gains.
  3. [§3.3, Eq. (4)] The NLL term is written as L_NLL = log Mtheta(cw, aw|xi) / (|cw| + |yw|). This is a positive (length-normalized) log-likelihood of the chosen response. Since the total loss is L = L_DPO + alpha * L_NLL and the objective is minimization, this term would minimize the likelihood of the chosen response, which is the opposite of the intended NLL regularization described in the text. A missing minus sign appears likely. The sign convention must be corrected and clarified, and the broken reference 'Equation ??' in §4.4 should be fixed.
  4. [§3.2, §4.1] The reward model Qwen2.5-Math-RM-72B belongs to the same model family as one of the three agents (Qwen2.5-Math-7B-Instruct). The paper does not analyze the composition of the hybrid positive sample set or ablate the reward model choice. If the reward model systematically favors Qwen-style solutions, the observed pattern of tiny gains for Qwen and larger gains for DeepSeek/Llama could stem from style transfer toward Qwen-like reasoning rather than from the claimed diversity-based benefit. The authors should report the distribution of selected positives across the three agents and add an ablation with a different reward model or no reward-model selection.
  5. [§3.3, §5.2] Eq. (3) uses Mk as the reference model in the DPO ratio, but the paper does not state whether Mk is frozen at its initial weights or updated across the three iterations. In iterative preference optimization, the choice of reference model changes the DPO objective; using the current policy as reference would break the standard DPO derivation. Please specify the reference-modelling procedure for each iteration and justify it.
minor comments (5)
  1. [Table 1] The header 'Postive SFT' is a typo and should read 'Positive SFT'.
  2. [§5.1, Table 1] The sentence 'Note that these are the results after the first iteration of training' is contradicted by Table 1, which reports iter1, iter2, and iter3 results. The authors should clarify whether the numbers discussed in §5.1 refer to iter1 only or to all iterations, and which iteration is used in the abstract's headline gain.
  3. [§1] The sentence 'To sum up, our main contribution are as follows' should be 'our main contributions are as follows'.
  4. [§5.1] The phrase 'as shown in in Table 1' contains a duplicated 'in'.
  5. [References] The paper cites Touvron et al. (2023) for Llama3.1-8B-Instruct, but the cited reference is the original Llama paper; the Llama3.1 technical report or a proper citation for the 8B Instruct model should be used.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: Mars-PO's empirical gains are not forced by its own construction; the reward-model entanglement and unstated data split are correctness concerns, not demonstrated circularity.

full rationale

The paper presents an empirical training pipeline rather than an equation-level derivation, and no load-bearing step reduces to its own inputs by construction. In Section 3.1–3.3, the hybrid positive sample set is selected by final-answer correctness (b_i^n = 1) and by scores from an external reward model, while negative samples are each agent's own incorrect outputs. The DPO loss (Eq. 3) and NLL term (Eq. 4) are optimized against these constructed preference pairs. Nothing in the construction consumes the reported GSM8K or MATH accuracies as an input; the Table 1 deltas are post-training measurements on benchmarks, not quantities reconstructed from the training set by definition. The only mild entanglement is Section 4.1, where Qwen2.5-Math-RM-72B, used to select positive samples, belongs to the same model family as one of the three agents; this could bias sample selection toward Qwen-style reasoning, but the reward model is an external fixed signal and does not force the reported improvements. The manuscript never states whether the GSM8K/MATH problems used to generate training responses are disjoint from the evaluation problems, and no code or data is released; if the sets overlap, every accuracy gain in Table 1 would be invalidated. That is a serious data-hygiene and reproducibility concern, but the paper provides no quote or equation exhibiting such overlap, so under the hard rules it cannot be counted as demonstrated circularity. No load-bearing self-citation or imported uniqueness theorem appears in the derivation chain.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The method has no closed-form derivation. Its ingredients are hyperparameters chosen by hand and assumptions about answer correctness, reward-model quality, and dataset hygiene. The central result depends on these choices, which are not validated with ablations, error bars, or multiple seeds.

free parameters (5)
  • beta (DPO temperature) = 0.1, then 0.2, then 0.4 across iterations
    Hand-set in Section 4.4 to amplify reward differences; no validation protocol or ablation is reported.
  • alpha (NLL coefficient) = 1.0
    Set in Section 4.4 without ablation; balances the DPO and NLL losses.
  • number of preference pairs per prompt = 15
    Selected in Section 4.4; the selection procedure, for example random or top-scoring, is not specified.
  • number of sampled responses N = 40 for GSM8K, 30 for MATH
    Chosen in Section 4.4; affects the size and diversity of positive and negative pools.
  • sampling temperature schedule = 0.8 for iteration 1, 1.2 for iterations 2 to 3
    Hand-picked in Section 4.4 to increase the number of incorrect generations in later iterations; no ablation is shown.
assumptions (4)
  • domain assumption Correctness of a response can be determined by exact match of the final answer, so b_i^n = 1 iff a_i^n = a_i.
    Used in Section 3.1 to split responses into positive and negative sets; this ignores partially correct reasoning chains.
  • domain assumption Qwen2.5-Math-RM-72B reward scores reliably rank solution quality, so taking the highest-scoring correct outputs yields the best hybrid positive set.
    Introduced in Section 3.2 and Section 4.1; the central selection step of the method depends on this assumption.
  • domain assumption DPO with the hybrid positive set and agent-specific negatives, regularized by the NLL term, improves each agent's reasoning without degrading base knowledge.
    Assumed in Section 3.3; DPO's general validity is cited from Rafailov et al. 2024, but its benefit for already-strong math models is the empirical claim under test.
  • domain assumption The training dataset D does not overlap with the GSM8K and MATH test sets used for evaluation.
    The paper never states which splits are used for training, and the evaluation is on the benchmark test sets, so this assumption is load-bearing.

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Cite this review

Pith. "Pith review of Mars-PO: Multi-Agent Reasoning System Preference Optimization." pith.science (2026). https://pith.science/paper/BOBY76GF

@misc{pith2026241119039,
  author       = {Pith},
  title        = {Pith review of: Mars-PO: Multi-Agent Reasoning System Preference Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BOBY76GF}},
  note         = {Machine review of arXiv:2411.19039}
}
read the original abstract

Mathematical reasoning is a fundamental capability for large language models (LLMs), yet achieving high performance in this domain remains a significant challenge. The auto-regressive generation process often makes LLMs susceptible to errors, hallucinations, and inconsistencies, particularly during multi-step reasoning. In this paper, we propose Mars-PO, a novel framework to improve the mathematical reasoning capabilities of LLMs through a multi-agent system. It combines high-quality outputs from multiple agents into a hybrid positive sample set and pairs them with agent-specific negative samples to construct robust preference pairs for training. By aligning agents with shared positive samples while addressing individual weaknesses, Mars-PO achieves substantial performance improvements on mathematical reasoning benchmarks. For example, it increases the accuracy on the MATH benchmark of the state-of-the-art instruction-tuned LLM, Llama3.1-8B-Instruct, from 50.38% to 57.82%. Experimental results further demonstrate that our method consistently outperforms other baselines, such as supervised fine-tuning, vanilla DPO, and its enhanced versions, highlighting the effectiveness of our approach.

Figures

Figures reproduced from arXiv: 2411.19039 by the authors.

Figure 1
Figure 1. Mars-PO Framework. Our preference optimization method consists of three steps: (i) Response Samples Generation: training prompts are fed into the multi-agent system to generate candidate responses, which are then classified as positive or negative for each agent based on answer correctness. (ii) Positive Pairs Construction: positive samples from all agents are evaluated by a reward model to distill a high-quality po… view at source ↗
Figure 2
Figure 2. Accuracy of iterative Mars-PO training on GSM8K and Math. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Accuracy comparison between vanilla DPO and Mars-PO. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

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Forward citations

Cited by 2 Pith papers

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  2. Artificial Intelligence for Mathematical Reasoning: An Integrated Survey of Language Models, Neuro-symbolic Systems, and Verified Discovery

    cs.AI 2026-06 unverdicted novelty 5.0 of 10

    An integrated survey organizing AI mathematical reasoning into informal, formal, discovery, and technique axes while cataloging benchmarks and assessing failure modes.

Reference graph

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