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REVIEW 6 major objections 5 minor 51 references

Evolution of Thought: Diverse and High-Quality Reasoning via Multi-Objective Optimization

T0 review · 6 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper argues that searching for reasoning paths in multimodal language models should optimize answer quality and diversity jointly, and shows that a genetic multi-objective algorithm (NSGA-II) with crossover, mutation, and…

desk verdict The core idea is real but the evidence is thinner than the abstract admits; the efficiency claim is contradicted by the paper's own Table 3. read the letter →

arxiv 2412.07779 v1 pith:SXGX6MAC submitted 2024-11-24 cs.NE cs.AI

Biqing Qi , Zhouyi Qian , Yiang Luo , Junqi Gao , Dong Li , Kaiyan Zhang , Bowen Zhou This is my paper · ORCID
classification cs.NEcs.AI
keywords EvolutionofThoughtmulti-objectiveoptimizationNSGA-IIreasoningpathsearchmultimodalLLManswerdiversitymathematicalParetofront
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 argues that reasoning in multimodal large language models can be improved by treating the search for good reasoning paths not as a single-objective optimization over answer quality but as a multi-objective problem that jointly maximizes quality and diversity. It introduces Evolution of Thought (EoT), which uses the NSGA-II genetic algorithm—crossover, mutation, and non-dominated sorting—to evolve a population of candidate answers along a Pareto front, and a Condensation-Aggregation mechanism that clusters and prunes redundant paths before summarizing a final answer. Experimental results on MathVista, Math-Vision, and GSM8K with three open vision-language models show gains in Pass@1 and Pass@K over Tree-of-Thoughts, Monte-Carlo Tree Self-Refine, and other baselines, at comparable or lower inference cost. If the claim holds, it suggests that explicit diversity pressure and information sharing between candidate solutions are practical levers for improving both accuracy and efficiency of model reasoning.

What carries the argument

The NSGA-II evolutionary loop is the engine: each candidate answer is scored by a quality metric $M_Q$ that compares against a reference answer generated by the same model, and a novelty metric $M_N$ combining normalized edit distance with semantic distance from Sentence BERT embeddings. Non-dominated sorting ranks solutions into Pareto layers and selects parents, then prompt-based crossover merges two parent answers and prompt-based mutation rewrites one parent to maintain diversity. The Condensation-Aggregation mechanism uses K-Medoids clustering on a joint distance matrix to discard the lowest-quality clusters and pass only cluster medoids to a final aggregation prompt, keeping the summarization context short.

What would settle it

Take a benchmark, compute the correlation between the model's $M_Q$ scores and ground-truth correctness; if it is near zero, EoT's selection is not optimizing for correctness. Alternatively, run EoT with reference answers that are deliberately wrong and see whether Pass@1 drops; if it does not, the quality score is not load-bearing.

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Extended reading notes

Core claim

The central claim is that the local optima and inefficiency of existing reasoning-path search methods stem from optimizing quality alone, and that balancing quality with a novelty objective, computed from edit distance and semantic similarity, steers the search onto a Pareto front that preserves diverse, high-quality candidates. This is operationalized through NSGA-II's non-dominated sorting, followed by crossover and mutation prompts that recombine and perturb parent answers, and a final condensation-aggregation stage that clusters candidates by distance, drops low-quality clusters, and asks the model to synthesize a refined answer. The paper reports that EoT outperforms single-objective tree-search baselines on three mathematical reasoning benchmarks across three base models, including on Pass@k diversity-based evaluation, and that the performance gain is not sensitive to population size or number of generations.

Load-bearing premise

The quality score the model gives each answer, compared with a reference answer it wrote itself, is a trustworthy measure of whether the answer is actually correct.

Editorial extensions

If this is right

  • Reasoning search methods for multimodal models can treat diversity as a first-class objective rather than a byproduct of sampling.
  • Population-based search with crossover and mutation is fully parallelizable, avoiding the sequential cost of tree search.
  • Reference-based scoring reduces the instability of direct self-scoring, enabling more consistent quality evaluation.
  • The clustering-based condensation step lets the model summarize a large candidate set without exceeding context length limits.

Reading between the lines

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

  • The framework could generalize to open-ended generation tasks where multiple valid answers exist, since it explicitly maintains a Pareto front of alternatives.
  • The novelty metric could be replaced or augmented with task-specific diversity measures, such as structural diversity in code generation or plan diversity in embodied tasks.
  • A testable extension is to feed an ensemble of reference answers instead of a single one, which may further stabilize the quality score and reduce reference bias.
  • If the correlation between $M_Q$ and true correctness is weak, the observed gains may instead come from the extra computation and aggregation, which a careful ablation could isolate.
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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

6 major / 5 minor

Summary. This paper proposes Evolution of Thought (EoT), a multi-objective reasoning framework for multimodal large language models. EoT represents candidate reasoning paths as a population and applies NSGA-II-style non-dominated sorting over two objectives: a reference-based quality score MQ(A)=f(pq,ps,Aref,A) and a novelty score MN(A) based on edit and semantic distances. Crossover and mutation operations generate offspring, and a Condensation-Aggregation (CA) mechanism clusters candidates, drops low-quality clusters, and prompts the model to aggregate the remaining candidates into a final answer. The authors report experiments on MathVista, Math-Vision, and GSM8K with Qwen2-VL, LLaVA-NeXT, and Phi-3.5-vision, comparing against IO, CoT, ToT, MCTSr, and other baselines, and claim superior performance and efficiency.

Significance. If the central claims could be supported, the paper would offer a useful new application of multi-objective evolutionary search to LLM and MLLM reasoning, and the CA mechanism is a sensible answer to the redundancy problem in population-based search. The manuscript is clearly organized and the ablation study covers the main hyperparameters. However, the evidence as presented is not yet sufficient: the quality objective is an unvalidated self-score, the efficiency claim is contradicted by the paper's own Table 3, and no statistical uncertainty is reported. The core idea is promising and the shortcomings are addressable, so the result is of potential interest to the evolutionary computation and LLM reasoning communities.

major comments (6)
  1. [Sec. 3.1, Eq. (1)] The quality objective MQ(A)=f(pq,ps,Aref,A) is computed by the same MLLM that generates Aref, and no evidence is given that this score tracks ground-truth correctness. Since non-dominated sorting, parent selection, and the CA cluster-dropping step all rely on MQ, the reported gains in Tables 1 and 2 could be produced by optimizing the model's self-consistency rather than reasoning accuracy. Please validate MQ (e.g., correlation or calibration against correctness) and include an ablation that replaces MQ with a trivial or random score to show that the quality signal, not merely population expansion, drives the improvements.
  2. [Sec. 4.3, Table 3] The efficiency claim in Section 4.3 is not supported by Table 3: EoT uses 2K+1 inference steps versus 2K for ToT, and EoT's time per answer is 15.23s versus 14.62s for ToT. The text states that EoT requires fewer reasoning steps and less time per step, but the table shows the opposite for ToT on both values. Please correct the claim, clarify whether 'time per step' is the intended metric, and provide token or cost measurements.
  3. [Sec. 3.2, Step 2] The described ranking procedure ('rank them according to the number of candidates they dominate... those with the same dominance count are placed in the same level') is not NSGA-II's non-dominated sorting, which partitions the population into Pareto fronts and uses crowding distance within fronts. As written, the algorithm is a dominance-count heuristic, and the claimed connection to NSGA-II and its diversity guarantees is inaccurate. Please clarify the exact ranking and whether crowding distance is used.
  4. [Tables 1 and 2] No error bars, multiple runs, or significance tests are reported. Many margins are small, for example Qwen2-VL Pass@8 on MathVista (EoT 67.50 vs MCTSr 66.75) and LLaVA-NeXT Pass@1 on MathVista (EoT 21.50 vs MAD 21.00), so single-run differences may be noise. Report repeated runs with means and confidence intervals, or paired significance tests, before claiming superiority.
  5. [Sec. 4.4, Fig. 3] Hyperparameters N, T, r, K, κ, and m are tuned on the same benchmarks used for the final comparison, with r=1:5 and K=3 reported as best on the challenging Math-Vision dataset. Without a separate validation split or a fixed default configuration, the reported results may be inflated by test-set selection. Please specify the selection protocol or validate on held-out tasks.
  6. [Sec. 4.2 and Table 1] The evaluation protocol for Table 1 is under-specified. Section 4.2 calls it Pass@1, but Table 1 includes methods that output a single answer, and for EoT it is not stated whether the reported value is the top-1 candidate after non-dominated sorting or the output of the CA aggregation. Please state explicitly how each number is obtained.
minor comments (5)
  1. [Sec. 3.1, Eq. (2)] The notation A/A to denote the set excluding A is easily confused with quotient notation; please replace it with A\A or an explicit subscript.
  2. [Sec. 3.1, Eq. (3)] Equation (3) includes a factor of 2 in the denominator, but the text says DSE is the semantic distance; the relation between this normalized cosine distance and the edit-distance term should be spelled out.
  3. [Table 1 and Fig. 3 caption] In Table 1, the Phi-3.5-vision CoT GSM8K improvement is 42.50, not 42.20; the Figure 3 caption reads 'Impact of and m' and is missing κ.
  4. [Algorithm 1, line 22] The line 'Expand the candidate set size: N × = 2' should be written as N ← 2N or similar; the printed notation is ambiguous.
  5. [Reproducibility] The manuscript does not mention code or data release; please include a reproducibility statement with exact prompts, model versions, and hyperparameter settings.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reported accuracy numbers are measured by exact match against ground truth, not by EoT's internal quality score, so the central performance claim is not equivalent to its own search objective.

full rationale

The central claim is an empirical benchmark result: EoT is compared to baselines using Pass@1 and Pass@k, defined as the probability that a ground-truth-correct answer appears among the top K generated answers (Section 4.1). The paper states 'An answer is considered correct if it matches the ground truth exactly' (Section 4), so the evaluation metric is external to the framework. The internal objective M(A)=(MQ(A), MN(A)) in Eq. (1) is a heuristic search signal; MQ(A)=f(pq,ps,Aref,A) uses a reference answer generated by the same MLLM, which is a self-referential proxy and a validity risk (if MQ does not track correctness, the evolutionary selection may optimize self-consistency rather than accuracy), but it is not circular: no equation in the paper makes Pass@1 or Pass@k equal to MQ or MN, and the reported numbers are not derived from the objective function. The hyperparameter ablations in Section 4.4 explore N, T, r, K, kappa, and m on the benchmark sets; even if some configurations were chosen using test results, this would be an overfitting/validity concern, not a by-construction equivalence between a fitted parameter and a prediction. The paper invokes NSGA-II [5,6] and baseline methods as external references; there are no load-bearing self-citations or imported uniqueness theorems. The condensation-aggregation step also uses MQ only to drop low-quality clusters before final aggregation, and the final answer is still evaluated against ground truth. Accordingly, no circular step is exhibited, and the derivation chain is self-contained with respect to circularity.

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

All tunable parameters are chosen by hand or selected on the same test benchmarks, and the central assumptions concern the validity of self-scoring and the transfer of evolutionary concepts to text. There are no new physical or conceptual entities beyond the framework itself.

free parameters (5)
  • Population size N = 3, 6, 9 in ablations; main-run value not stated
    EoT's Pass@K changes with N (Fig 3a), yet the main experiments do not report the N used.
  • Generations T = 1, 2, 3 in ablations; main-run value not stated
    The number of evolutionary rounds affects the search; Fig 3a shows only small fluctuation, but the main value is not given.
  • Crossover-to-mutation ratio r = Varied 1:5, 1:2, 1:1, 2:1, 5:1; 1:5 'best' on Math-Vision
    Selected after ablation on the same benchmarks (Section 4.4, Fig 3b), creating test-set dependence.
  • Parent set size K = Varied 3 to 6; K=3 'best' on Math-Vision
    Selected after ablation on the same benchmarks (Section 4.4, Fig 3c).
  • Cluster count κ and dropped clusters m = κ in {3,4,5,6}, m in {1,2,3}; main value not stated
    The CA mechanism's quality depends on these clustering parameters, adjusted per dataset in Fig 3d.
assumptions (5)
  • domain assumption The self-scored quality MQ(A) is a reliable proxy for answer correctness.
    Section 3.1 defines MQ by asking the same MLLM to score against a self-generated reference; no correlation with ground truth is shown.
  • domain assumption Edit distance plus Sentence-BERT semantic distance captures the diversity that helps reasoning.
    Equations (2) and (3) define novelty as textual and semantic distance; the paper offers no evidence that this diversity is task-relevant.
  • domain assumption Prompt-based crossover and mutation produce valid offspring that retain parent strengths.
    Step 3 in Section 3.2 assumes the MLLM can merge two answers or rewrite one usefully; no operator-quality analysis is given.
  • domain assumption Non-dominated sorting and Pareto fronts transfer from numerical optimization to text reasoning paths.
    Section 3.2 applies NSGA-II to answer sets without evidence that Pareto-optimal text answers are more likely correct.
  • domain assumption The reported benchmark numbers are stable and representative.
    No dataset subset sizes, random seeds, or variance estimates are reported in Section 4.

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Cite this review

Pith. "Pith review of Evolution of Thought: Diverse and High-Quality Reasoning via Multi-Objective Optimization." pith.science (2026). https://pith.science/paper/SXGX6MAC

@misc{pith2026241207779,
  author       = {Pith},
  title        = {Pith review of: Evolution of Thought: Diverse and High-Quality Reasoning via Multi-Objective Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SXGX6MAC}},
  note         = {Machine review of arXiv:2412.07779}
}
read the original abstract

As multi-modal large language models (MLLMs) are increasingly applied to complex reasoning tasks, the diversity and quality of reasoning paths become crucial factors affecting their performance. Although current methods aim to enhance reasoning quality through path expansion, they often neglect the diversity of reasoning paths and effective information sharing, leading to local optima and inefficiency. To address these challenges, we propose Evolution of Thought (EoT), a multi-objective framework designed to improve reasoning by fostering both high-quality and diverse reasoning paths. Specifically, we introduce the Non-dominated Sorting Genetic Algorithm II for multi-objective optimization, utilizing crossover and mutation operators to promote greater diversity in reasoning solutions. Additionally, we propose a Condensation-Aggregation mechanism to cluster and eliminate redundant paths, facilitate improved information sharing among parent nodes, and ultimately enhance both the efficiency and quality of the reasoning process. Validation experiments on various vision-language and language reasoning tasks demonstrate that EoT achieves superior reasoning performance and efficiency compared to other competitive baselines. Our study provides a novel perspective on the design of heuristic reasoning frameworks for MLLMs.

Figures

Figures reproduced from arXiv: 2412.07779 by the authors.

Figure 1
Figure 1. Comparison of Evolution of Thoughts (EoT) with other [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. EoT Process Flow Diagram.Step 1 involves scoring using [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Abalation results on different N, T, r, K, κ, m parameters and datsets. Fig (a) shows pass@4 accuracy (%) on different candidate answers N and evolutionary generations T. Fig (b) and (c) show the pass@k (k = 1, 2, ..., 12) accuracy (%) curves under different crossover-to-mutation ratios r and selected candidate parents K. Fig (d) shows the average accuracy on three datasets under different clusters κ and drop cluste… view at source ↗

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    A many-objective evo- lutionary algorithm based on three states for solving many- objective optimization problem

    Jiale Zhao, Huijie Zhang, Huanhuan Yu, Hansheng Fei, Xi- angdang Huang, and Qiuling Yang. A many-objective evo- lutionary algorithm based on three states for solving many- objective optimization problem. Scientific Reports , 14(1): 19140, 2024. 2

    2024

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    Pareto deep long-tailed recognition: A conflict-averse solution

    Zhipeng Zhou, Liu Liu, Peilin Zhao, and Wei Gong. Pareto deep long-tailed recognition: A conflict-averse solution. In International Conference on Learning Representations ,

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    We use the 7B parameter version, released in August 2024

    Qwen2VL: The latest multimodal model from the Qwen family. We use the 7B parameter version, released in August 2024

    2024

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    This model is trained with a more advanced language model, improving its perfor- mance and capabilities

    LLaV A-NeXT: We use the version based on LLaMA3- 8B, released in May 2024. This model is trained with a more advanced language model, improving its perfor- mance and capabilities

    2024

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    Phi3.5-vision: A lightweight multimodal model devel- oped by the Microsoft team with 4.5B parameters, re- leased in August 2024. The model weights used in our work are sourced from Hug- ging Face, and we deploy the models using the Transform- ers library, utilizing Flash-Atten...

    2024

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    The Answer is \boxed{{}}

    IO (Input-Output): We use a standard zero-shot input- output prompt, where the model will only response with “The Answer is \boxed{{}} ”

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    [Reasoning process]...[Verification]

    CoT (Chain-of-Thought): We apply prompting formats as “[Reasoning process]...[Verification]...” and “Let’s think step by step” to encourage the model to generate reasoning steps and validation steps

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    The process involves first providing feedback on the initial output, followed by re- fining the answer based on that feedback

    Self-Refine: Self-Refine improves model outputs through one refinement iteration, without requiring ex- tra training or supervision. The process involves first providing feedback on the initial output, followed by re- fining the answer based on that feedback. We use the second...

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    In each round, five answers are sampled, and the best answer is selected via voting for further reasoning

    ToT (Tree of Thoughts): ToT employs a greedy search strategy with two rounds of exploration. In each round, five answers are sampled, and the best answer is selected via voting for further reasoning. We adopt the original settings from [36]

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    We adopt the original settings from [38]

    MCTSr (Monte Carlo Tree Self-Refine): MCTSr com- bines Monte Carlo Tree Search with self-refine to en- hance decision-making and solve complex reasoning tasks. We adopt the original settings from [38]

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    We adopt the origi- nal settings from [30]

    SPP (Solo Performance Prompting) : SPP enables a single model to collaborate with itself through multiple personas in multi-turn interactions. We adopt the origi- nal settings from [30]

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    The Answer is \boxed{{}}

    MAD (Multi-Agent Debate) : MAD utilizes multiple agents engaged in debate, guided by a judge, to promote divergent thinking and address complex reasoning tasks. We adopt the original settings from [14]. All prompts are zero-shot, with the model required to end the response wit...

  43. [2024]

    Algorithm of EoT Here, we introduce the algorithmic description of EoT, with its workflow depicted in Algorithm 1

    5 Evolution of Thought: Diverse and High-Quality Reasoning via Multi-Objective Optimization Supplementary Material A. Algorithm of EoT Here, we introduce the algorithmic description of EoT, with its workflow depicted in Algorithm 1. Algorithm 1 EoT Search Algorithm 1: Input: U...

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.