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The paper claims that the success of LLM-based multi-agent systems is largely set in the first round of interaction: peak token-level entropy harms correctness across every architecture, and a single agent is the best choice in 43.3% of cas

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2026-08-03 04:40 UTC pith:IO25R27P

load-bearing objection Solid empirical study of MAS entropy dynamics whose descriptive findings survive scrutiny, but the abstract's causal language overstates what the evidence supports. the 4 major comments →

arxiv 2602.04234 v6 pith:IO25R27P submitted 2026-02-04 cs.MA cs.AI

When Does Multi-Agent Collaboration Help? An Entropy Perspective

Yuxuan Zhao , Sijia Chen , Ningxin Su This is my paper
classification cs.MA cs.AI
keywords multi-agent systemsentropyuncertainty quantificationlarge language modelsreasoningsingle-agent vs multi-agententropy judgerLLM collaboration
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to establish that the success or failure of LLM-based multi-agent systems can be explained by the entropy—the token-level uncertainty—of their early reasoning, rather than by the number of agents or the collaboration topology. It reports that a single agent matches or beats every multi-agent architecture in 26 of 30 model-benchmark combinations, and that the decisive signal is the first round of interaction: peak entropy is harmful, stable low entropy helps, and higher base-model entropy hurts the team. If correct, this gives practitioners a cheap, label-free diagnostic for when to deploy a team at all, and the paper's Entropy Judger uses exactly this signal to pick better answers from pass@k candidates.

Core claim

The paper's central claim is that MAS effectiveness is largely determined by early-round uncertainty dynamics, with peak entropy universally harmful across architectures. Across five open-source LLMs and six benchmarks, a single agent achieves the highest accuracy in 43.3% of cases, and in 86.7% of scenarios it matches or exceeds at least one MAS architecture. Three principles emerge: Certainty Preference (low, stable cross-agent entropy correlates with correctness), Base Uncertainty (lower base-model entropy directly benefits MAS performance), and Task Awareness (optimal entropy profiles shift with task difficulty and architecture). The paper further claims that the first round is decisive

What carries the argument

Hierarchical entropy features: 245 features computed from token-level Shannon entropy of every agent's output, aggregated at agent, round, sample, and system levels. These feed an ensemble of gradient-boosted tree classifiers trained to predict per-sample correctness from the entropy trace; feature-attribution analysis then identifies which entropy patterns push predictions toward success or failure. The Entropy Judger is this classifier used for label-free pass@k selection.

Load-bearing premise

The load-bearing premise is that the entropy measured during reasoning causes performance differences—not merely that it happens to correlate with them—so that increasing peak entropy or stabilizing entropy would change outcomes as the paper's SHAP directions suggest.

What would settle it

A reader could split the paper's released data by whether the base model already answered correctly and re-run the correlation between round-1 peak entropy and MAS correctness within each split; if the negative correlation vanishes when base-model correctness is held fixed, the 'peak entropy harms MAS' claim reduces to a proxy for problem difficulty rather than a causal mechanism.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Multi-agent collaboration should not be assumed superior; single-agent baselines are the reference point, and teams only pay off under specific early-uncertainty conditions.
  • First-round entropy peaks are a universal warning sign; adding more interaction rounds rarely recovers from initial misalignment and often degrades accuracy.
  • The Entropy Judger provides a label-free way to select high-quality outputs from multiple candidates, with consistent accuracy gains across architectures and tasks.
  • Base-model entropy is a strong predictor of team performance, so choosing a base model with lower reasoning uncertainty is a direct lever for MAS success.

Where Pith is reading between the lines

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

  • If the entropy signal is this informative, an adaptive router that runs a single agent when first-round entropy is low and only convenes a team when divergence is moderate could get most of the team's benefit at a fraction of the cost; the paper does not test this but its data make it a natural next step.
  • The paper's own appendix shows 83.4% of round-1 to round-2 transitions reduce entropy without improving accuracy, which suggests much of the observed convergence may be agents anchoring on each other—so Certainty Preference may be partly about suppressing disagreement rather than about finding the truth.
  • The RL-trained base model results imply that entropy's meaning is training-dependent: the same entropy value can signal productive exploration or noise depending on the model, so a single entropy threshold will not transfer across base models and selection rules should be recalibrated per model family.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper studies entropy dynamics in LLM-based multi-agent systems (MAS) built on five open-weight models across six benchmarks and four topologies. It extracts 245 hierarchical entropy features, trains an XGBoost/LightGBM ensemble (the Entropy Judger) to predict per-sample correctness, and uses SHAP analysis to derive three observations: certainty preference, base-model entropy as a limiting factor, and task/architecture-dependent entropy roles. It reports that a single agent achieves the best accuracy in 43.3% of cases, that first-round entropy dynamics dominate prediction, and that entropy-based pass@k selection improves accuracy. The appendices include extensive robustness checks (temperature, model scale, tool-calling tasks, RL-trained base models) and a causal-analysis appendix that explicitly acknowledges unresolved causal identification and reports an 83.4% 'possible anchoring' rate in round 1→2 transitions.

Significance. If the descriptive claims hold, the paper provides a useful, reproducible diagnostic for when MAS collaboration pays off and when it does not, based on openly available models and a large dataset (44,780 samples). Strengths include the favorable sample-to-feature ratio, stratified 5-fold CV, ablation studies, cross-method importance validation, and explicit checks at 14B scale, different temperatures, and a tool-calling agentic benchmark. The authors are also unusually honest in Appendices H and J about the limits of causal inference. However, the headline contributions are framed causally ('peak entropy directly harms', 'base entropy causally drives MAS performance') while the evidence is correlational, and a claimed algorithmic benefit (pass@k selection) is not quantified in the manuscript. The central descriptive findings are defensible, but the causal and universal claims need substantial reframing or additional evidence.

major comments (4)
  1. [Abstract, §4.3–4.4, Appendix J] The abstract and Section 4.4 state that peak entropy 'directly harms' correctness and that lower base-model entropy 'causally drive[s]' MAS performance. The evidence is SHAP-based correlation from a trained classifier, not causal identification. Appendix J itself says 'strict causal mechanisms... remain inherently challenging' and defers causal identification to future work. Appendix H.4 reports 83.4% of round-1→2 entropy-decrease transitions without accuracy gain ('possible anchoring'). The causal language must be removed or substantiated with within-problem interventions (e.g., same question decoded under high- vs low-entropy traces) or explicit counterfactual manipulations.
  2. [§5.5, Appendix F.5] The Entropy Judger's central practical contribution is pass@k selection, and the main text claims it 'consistently improves accuracy across all MAS configurations and tasks.' However, no quantitative result for this selection is reported anywhere in the main text or the appendix. Appendix F.5 only describes the protocol (choose argmax predicted correctness) and mentions baselines (Random, Oracle) without giving numbers. The claimed accuracy improvement is therefore unsupported as written. Please add a table/figure reporting pass@k selection accuracy against random and oracle baselines across configurations.
  3. [§5.2, Figure 4(d)] The claim that 'peak entropy is universally harmful across architectures' is overstated. Figure 4(d) shows an across-architecture reversal: the single-agent architecture has the highest values of round-1 peak/entropy-dispersion features yet the highest accuracy, while sequential (lowest accuracy) has the lowest feature averages. The text acknowledges that the entropy–performance relationship depends on 'architectural capacity to control uncertainty,' which is a conditional rather than universal claim. The headline 'universally harmful' should be replaced with a qualified statement such as 'harmful within each architecture after controlling for architectural capacity', or the figure should be reconciled explicitly with the universal claim.
  4. [§4.4, Figure 2] The 'Base Uncertainty' observation claims that lower base-model entropy 'directly benefits' MAS performance. The Gbase-H analysis measures base entropy from the same base model trajectory that also produces the base correct/incorrect label; base entropy is likely a proxy for base capability. The authors do include base correctness in Gbase-full, but the causal claim in §4.4 is based on Gbase-H alone. A partial-correlation analysis controlling for base correctness, or an intervention (e.g., temperature/contrastive decoding on the base model), is needed before 'directly benefits' can be defended. Otherwise the claim should be phrased as 'base-model entropy is a strong predictor correlated with MAS accuracy'.
minor comments (5)
  1. [Abstract vs. §4.4] The abstract uses 'causally drive' while the contribution list in Section 1 says 'strongly correlate with correctness.' This inconsistency should be resolved in favor of the more accurate correlational framing throughout.
  2. [Figure 1 caption] 'The basedenotes...' is a typo; also the caption does not mention that debate is excluded on HumanEval (Appendix B.1), which affects the interpretation of '30 scenarios' in §4.4.
  3. [§4.2] The text reports '254 features' and then '245 trainable features' after excluding 9 experimental identifiers. Clarify explicitly which 9 are excluded and why they are not counted among the 245 used in Table 1.
  4. [Appendix G] Global average ECE is 0.391, with LLaMA models above 0.5. This substantial miscalibration means low entropy does not reliably indicate correctness for these models; this should be mentioned in the main text wherever 'low entropy is beneficial' is claimed, not only in the appendix.
  5. [§5.2] The phrase 'single agents channel higher entropy into genuine exploration' is a mechanistic interpretation not directly supported by the data; suggest softening to 'single agents can tolerate higher entropy without accuracy loss' or provide direct evidence.

Circularity Check

0 steps flagged

No significant circularity: the entropy-based findings come from a fitted classifier with cross-validated evaluation, and the paper's own caveats concern causal validity, not definitional circularity.

full rationale

The paper's central pipeline is an empirical supervised-learning analysis: it extracts 245 entropy/computational features, fits XGBoost/LightGBM to per-sample correctness labels, and reports cross-validated accuracy (Table 1) plus SHAP-based feature correlations (Sections 4.3-4.4). These relations are learned from data rather than assumed into the conclusions; the sign/direction of the SHAP correlations could in principle have come out differently, so the findings are not equivalent to the input by construction. The Entropy Judger's pass@k selection is a practical use of the fitted predictor and is supported by held-out evaluation and generalization checks (Appendices D.7-D.8). The only load-bearing assumption is causal: the paper says peak entropy 'directly harms' correctness, while Appendix J concedes 'strict causal mechanisms... remain inherently challenging' and future work, and Appendix H.4 reports 83.4% possible anchoring. That is a validity/overclaim concern about the entropy-to-accuracy direction, not circularity: no equation defines the conclusion into the input, and there is no self-citation chain used to force the result. The one possible self-citation (Ye et al. 2025, if 'Chen, S.' is the current author) appears only in a limitations paragraph about heterogeneous MAS and is not load-bearing.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The paper's central claims are empirical rather than derivations. The main extra assumptions are: entropy is a valid uncertainty proxy; homogeneous open-source agents represent MAS generally; SHAP attributions on fitted tree ensembles license directional statements; and benchmark labels are reliable. No new physical entities are introduced. The main fitted quantity is the Entropy Judger's trained ensemble, from which the qualitative SHAP findings are drawn.

free parameters (3)
  • XGBoost/LightGBM trained model parameters (Entropy Judger)
    The classifier's internal parameters are fitted to per-sample correctness labels on 44,780 samples; all qualitative SHAP-based observations are summaries of this fitted model, so their 'predictions' are not parameter-free derivations.
  • XGBoost/LightGBM hyperparameters (max_depth=6, lr=0.1, n_estimators=100, reg_lambda=1.0, num_leaves=31, etc.)
    Hand-set standard hyperparameters; the SHAP feature rankings and derived qualitative claims can shift with these choices, though the paper does not tune them per dataset.
  • Class-balance weight scale_pos_weight = N_neg/N_pos
    Computed from training-fold class counts; used in XGBoost training and thus influences which features the model emphasizes.
axioms (4)
  • standard math Token-level Shannon entropy H(s) = -Σ_v p(v|s) log p(v|s) is computed from the full softmax and is a meaningful uncertainty signal for reasoning correctness.
    Defined in §3.2 and used throughout §4.2 to build all 245 features; the central analysis depends on this proxy carrying signal rather than noise.
  • domain assumption All agents in a MAS share the same base model (homogeneous agents), and small open-source LLaMA/Qwen results generalize to larger or proprietary systems.
    Experimental setup in Appendix B; 14B scaling is tested, but 27B+ and proprietary models are not, and homogeneity is acknowledged as a limitation in Appendix J.
  • domain assumption SHAP-value/feature correlation indicates directional influence of entropy on MAS correctness.
    Section B.4 uses Pearson correlation between feature values and SHAP attributions to assign signs; this is a property of the fitted model, not an independent causal fact, as Appendix J concedes.
  • domain assumption Benchmark ground truth via Math-Verify, exact string matching, and code execution is reliable.
    Appendix B.1; these labels are used to train the Entropy Judger and to define all correctness outcomes.

pith-pipeline@v1.3.0-alltime-deepseek · 54148 in / 14625 out tokens · 162603 ms · 2026-08-03T04:40:46.102293+00:00 · methodology

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read the original abstract

Multi-agent systems (MAS) have emerged as a prominent paradigm for leveraging large language models (LLMs) to tackle complex tasks. However, the mechanisms governing the effectiveness of MAS built upon publicly available LLMs, specifically the underlying rationales for their success or failure, remain largely unexplored. In this paper, we revisit MAS through the perspective of \textit{entropy}, considering both intra- and inter-agent dynamics by investigating entropy transitions during problem-solving across various topologies, six reasoning benchmarks, and two agentic tasks. By analyzing 245 features spanning token-, agent-, and round-level entropy, we counterintuitively find that a single agent outperforms MAS in approximately 43.3\% of cases, and that entropy dynamics are largely determined during the first round of interaction. Furthermore, we provide three key observations: 1) \textit{Certainty Preference}: peak entropy directly harms and stable entropy directly benefits MAS correctness; 2) \textit{Base Entropy}: base models with lower entropy during problem-solving causally drive MAS performance; and 3) \textit{Task Awareness}: entropy dynamics of MAS play varying roles across different tasks. Building on these insights, we introduce a simple yet effective algorithm, the \textit{Entropy Judger}, to select solutions from MAS's pass@$k$ results, leading to consistent accuracy improvements across all MAS configurations and tasks. Our source code is available at \href{https://github.com/AgenticFinLab/multiagent-entropy}{this https URL}.

Figures

Figures reproduced from arXiv: 2602.04234 by Ningxin Su, Sijia Chen, Yuxuan Zhao.

Figure 1
Figure 1. Figure 1: Accuracy comparison of SAS and MAS across models and datasets. For brevity, LLaMA-3.2-3B-Instruct and LLaMA-3.1-8B￾Instruct are denoted as L-3 and L-8, respectively; Qwen3-0.6B, Qwen3-4B, and Qwen3-8B are denoted as Q-0.6, Q-4, and Q-8. The base denotes the accuracy of a single Mbase on each dataset. 4.3. Mining Effectiveness of MAS MAS built on LLMs inherently exhibit uncertainty during individual reasoni… view at source ↗
Figure 2
Figure 2. Figure 2: Base model uncertainty limits MAS effectiveness. The left two subfigures show results for LLaMA; the right two for Qwen. (a) Relationship between feature values and SHAP values for the most important entropy features on Gbase-H, sorted by I¯j and annotated with ρj . (b) MAS performance across deciles of Mbase entropy: Mbase entropy is partitioned into ten equal-sized bins, and average MAS accuracy, aggrega… view at source ↗
Figure 3
Figure 3. Figure 3: MAS mainly fails on inter-agent misalignment. The left two subfigures show results for LLaMA; the right two for Qwen. (a) Same as [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Uncertainty in MAS exerts distinct effects depending on task difficulty and the coordination architecture. (a, c) Feature-SHAP relationships for top entropy features in GMAS, grouped by dataset (a) and architecture (c). (b, d) Corresponding box plots across all models, annotated with average MAS correctness per dataset (b) or per architecture (d). Structured Deliberation for Hard Problems. On AIME24/25, ro… view at source ↗
Figure 5
Figure 5. Figure 5: More rounds do not necessarily improve MAS performance. (a) Accuracy and token consumption for different MAS architectures with R = 2 and R = 5 on two benchmarks. (b) Evolution of three key entropy metrics across rounds. (c) The impact of two prominent entropy features, notable for their high importance (I¯) and strong correlation (|ρ|) with sample correctness. tion. Sequential systems are most fragile: an… view at source ↗
Figure 6
Figure 6. Figure 6: The role of uncertainty is reshaped in MAS built on Qwen2.5-7B-SimpleRL-Zoo. (a) The performance of different MAS architectures across datasets. (b) Relationship between base-model entropy and MAS accuracy. (c) Most predictive features in GMAS. 5.4. RL Training Inverts the Role of Uncertainty Few studies have investigated whether using a specialized, fine-tuned model as the base model can improve MAS perfo… view at source ↗
Figure 7
Figure 7. Figure 7: PCA variance explained for the 245-dimensional entropy feature space. The curve shows cumulative explained variance as a function of the number of principal components. Achieving 95% explained variance requires 43 components, indicating that information is distributed across many dimensions rather than concentrated in a few dominant directions [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Recursive feature elimination (RFE) performance curve. The optimal subset of 25 features achieves the highest accuracy (86.77%) and F1 (88.92%). Performance plateaus and slightly decreases as more features are added, indicating that the model does not overfit to the high-dimensional space. C.4.3. FEATURE ABLATION STUDY To assess whether each feature contributes unique predictive information, we perform rec… view at source ↗
Figure 9
Figure 9. Figure 9: Cross-method feature importance comparison across tree-based (Random Forest), logistic regression, chi-square, mutual information, and F-statistic methods. Despite fundamentally different mechanisms, the methods produce consistent top-feature rankings, validating the robustness of our feature importance findings. C.4.4. CROSS-METHOD FEATURE IMPORTANCE VALIDATION A potential concern with SHAP-based feature … view at source ↗
Figure 10
Figure 10. Figure 10: Top 20 features on Gbase-H for Qwen (a) and LLaMA (b), ranked by mean normalized importance I¯. Each panel is divided into four subplots: top-left shows feature importance from XGBoost and LightGBM; bottom-left shows mean SHAP impact S¯, representing the average contribution of each feature to model predictions; right column displays scatter plots of feature values versus SHAP values, with Pearson correla… view at source ↗
Figure 11
Figure 11. Figure 11: SHAP waterfall plots on Gbase-H for representative samples: Qwen and LLaMA, with LightGBM and XGBoost. Each bar shows the contribution of a feature to the predicted MAS correctness. perfect correlation and strongly positive S¯ confirm that base model correctness is the single most powerful predictor: MAS succeeds largely when the base model is already correct. D.2. Inter-Agent Misalignment Causes MAS Fail… view at source ↗
Figure 12
Figure 12. Figure 12: Top: Feature importance and SHAP analysis on Gbase-full for Qwen (a) and LLaMA (b). Both show that base model is finally correct achieves I¯ = 1.0 and ρ ≈ 0.96, vastly surpassing all other features with nearly linear correlation to MAS correctness. Bottom: Top 20 features on GMAS for MAS failure analysis: Qwen (c) and LLaMA (d). Qwen’s top predictor is entropy variance, while LLaMA is dominated by answer-… view at source ↗
Figure 13
Figure 13. Figure 13: SHAP waterfall plots on GMAS for representative MAS failure samples. Qwen (a-b) shows entropy dispersion features (variance, Q3 agent) as dominant contributors; LLaMA (c-d) reveals answer-level features (token count, answer entropy) driving failure predictions. shows consistent positive effects at both levels, confirming that moderate deliberation uncertainty benefits medium tasks. However, excessive earl… view at source ↗
Figure 14
Figure 14. Figure 14: Top 20 features on GMAS for mathematical reasoning tasks grouped by difficulty: (a) GSM8K (easy, |ρ| ≤ 0.15 for top features), (b) MATH500 (medium, positive ρ and S¯ for average entropy), (c-d) AIME2024/AIME2025 (hard, round-2 uncertainty harms performance). D.4. Architecture Determines Which Uncertainty Matters Section 5 establishes that architecture fundamentally shapes which entropy dimensions matter: … view at source ↗
Figure 15
Figure 15. Figure 15: Top 20 features on GMAS for (a) code generation (HumanEval) and (b) knowledge Q&A (MMLU). HumanEval shows negative ρ and S¯ for answer-level features; MMLU shows that more agents hurt performance (ρ < 0, S <¯ 0 for sample num agents). that initial divergence amplifies across rounds. However, exp total entropy (ρ = +0.68, S¯ = +0.005) shows consistent positive effects, confirming that cumulative entropy be… view at source ↗
Figure 16
Figure 16. Figure 16: Top 20 features on GMAS for multi-agent architectures: (a) Centralized (verbose answers harm performance), (b) Debate (cumulative entropy benefits once agents align), (c) Hybrid (extended deliberation helps), and (d) Sequential (answer-level entropy is the primary failure mode). (ρ = −0.73, S¯ = −0.012). Later Rounds Provide Diminishing Signal. The extended ranking confirms that later-round features provi… view at source ↗
Figure 17
Figure 17. Figure 17: Top 20 features for (a) SAS and (b) MAS with R = 5 rounds on GMAS, and for MAS using MRL-base on (c) GMAS and (d) Gbase-H. Early-round uncertainty dominates prediction in all cases. In (c), round-2 entropy shows positive ρ but negative S¯, suggesting moderate later-round uncertainty is optimal. In (d), increased entropy from base to MAS still harms performance. GMAS: Round-2 Entropy Shows Inverted Pattern… view at source ↗
Figure 18
Figure 18. Figure 18: MAS accuracy across temperatures τ ∈ {0.4, 0.6, 0.8} for all five architectures on MATH500. Accuracy remains remarkably stable: the maximum variation within any architecture is 3.2% (Single), and the multi-agent average varies by only 0.5%. McNemar’s test yields p > 0.37 for all 15 pairwise comparisons, confirming statistical invariance. Implications for RL-Trained Systems. The inverted pattern for round-… view at source ↗
Figure 19
Figure 19. Figure 19: Entropy distribution statistics across temperatures for all architectures. Absolute entropy values scale approximately 2× from τ = 0.4 to τ = 0.8 (mean entropy: Centralized 0.048 → 0.075 → 0.101), but the relative ordering of architectures is preserved: Centralized and Single consistently exhibit higher entropy than Sequential, Debate, and Hybrid across all temperatures. feature importance rankings remain… view at source ↗
Figure 20
Figure 20. Figure 20: Feature importance and SHAP analysis for Qwen3-14B across two feature groups. (a) On GMAS, round-1 entropy dominates with approximately 70% of top-20 features being entropy-related (LightGBM accuracy: 83.2%, F1: 90.3%). (b) On Gbase-H, base model answer length emerges as the top predictor, while answer token entropy change (ρ ≈ −0.84) signals that entropy increase from base to MAS predicts failure (accura… view at source ↗
Figure 21
Figure 21. Figure 21: Top 20 features on FinanceAgent across two feature groups: (a) MAS-only features (GMAS), where architecture (ρ ≈ 0.83) and step-level entropy dominate; (b) including base model entropy (Gbase-H), where architecture remains the top pre￾dictor (ρ ≈ 0.84) and step 0 mean entropy shows moderate negative correlation (ρ ≈ −0.56). On the full feature set (Gbase-full), base model is finally correct (ρ ≈ 0.96) dom… view at source ↗
Figure 22
Figure 22. Figure 22: Reliability diagrams for all five models across six datasets. Each subplot shows observed accuracy (blue bars) versus entropy-derived confidence (x-axis), with the red dashed diagonal indicating perfect calibration. Bars above (below) the diagonal indicate under-confidence (over-confidence). Bin sample counts are annotated above each bar. Qwen3-4B and Qwen3-8B achieve near-perfect calibration on GSM8K (EC… view at source ↗
Figure 23
Figure 23. Figure 23: Heatmap of the confidently wrong proportion across all model–dataset combinations. Each cell reports the fraction of samples where the model exhibits low entropy (high confidence) yet answers incorrectly. Darker red indicates higher overconfident error rates. Qwen3-4B and Qwen3-8B maintain confidently wrong rates below 10% on most datasets, while LLaMA models and competition-level tasks exhibit rates exce… view at source ↗
Figure 24
Figure 24. Figure 24: Three-way entropy comparison across all 30 model-dataset combinations. Each subplot shows violin plots of per-token entropy distributions for SAS (teal), MAS Round 1 (red), and MAS Round 2 (blue), with mean µ annotated above each violin and the Wilcoxon signed-rank p-value for SAS vs. MAS R1 in the subplot title. The systematic shift from SAS to MAS R1 demonstrates that role assignment alone constitutes a… view at source ↗
Figure 25
Figure 25. Figure 25: Left: Mean entropy change from MAS Round 1 to Round 2 (HR2 − HR1) across all modelarchitecture-dataset combinations. Blue cells indicate entropy decrease (consensus formation); red cells indicate entropy increase. Right: Mean accuracy change (MAS − SAS) for the same combinations. Green cells indicate accuracy improvement; red cells indicate degradation. Cells that are blue on the left but red on the right… view at source ↗
Figure 26
Figure 26. Figure 26: Paired entropy scatter plots (MAS Round 1 vs. Round 2) across datasets. Each point represents a single sample; green circles (◦) denote correct answers and red crosses (×) denote incorrect answers. The dashed diagonal (y = x) separates entropy decrease (below) from entropy increase (above). The predominance of points below the diagonal confirms systematic entropy reduction, while the similar spatial distr… view at source ↗
Figure 27
Figure 27. Figure 27: Token-level entropy dynamics for Qwen3-0.6B across six datasets. High entropy persistence and frequent spikes characterize this smaller model, with entropy either remaining elevated or collapsing abruptly to zero in round 2. 48 [PITH_FULL_IMAGE:figures/full_fig_p048_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Token-level entropy dynamics for Qwen3-4B. Increased model capacity yields more stable entropy on easier tasks, while harder tasks still induce erratic uncertainty patterns. 49 [PITH_FULL_IMAGE:figures/full_fig_p049_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: Token-level entropy dynamics for Qwen3-8B. The largest Qwen model shows structured deliberation with controlled exploration in round 1 and smooth convergence in round 2. 50 [PITH_FULL_IMAGE:figures/full_fig_p050_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: Token-level entropy dynamics for LLaMA-3.2-3B-Instruct. LLaMA exhibits lower round-2 entropy compared to Qwen, often collapsing to near-zero, reflecting a more decisive but potentially overconfident reasoning style. 51 [PITH_FULL_IMAGE:figures/full_fig_p051_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: Token-level entropy dynamics for LLaMA-3.1-8B-Instruct. Scaling improves calibration, but the characteristic rapid entropy reduction in round 2 persists compared to Qwen models. 52 [PITH_FULL_IMAGE:figures/full_fig_p052_31.png] view at source ↗
Figure 32
Figure 32. Figure 32: Feature correlation heatmap for GMAS on LLaMA models. The lower triangle shows pairwise Pearson correlations; the upper-right inset lists the top 20 most strongly correlated feature pairs. 53 [PITH_FULL_IMAGE:figures/full_fig_p053_32.png] view at source ↗

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Works this paper leans on

31 extracted references · cited by 1 Pith paper

  1. [1]

    Architecture dominance: Architecture is the top predictor on both FinanceAgent Benchmark (ρ≈0.83 ) and the main benchmarks (Section 5), confirming that structural choices outweigh individual feature-level entropy in determining system performance

  2. [2]

    Initial uncertainty as failure signal: step 0 mean entropy on FinanceAgent Benchmark (ρ≈ −0.75) parallels the dominance of round-1 entropy features on mathematical tasks (Appendix D.5), extending the ”first-round decisive” principle to sub-round granularity

  3. [3]

    Base model correctness supremacy: The near-perfect correlation of base model is finally correct (ρ≈ 0.96) on FinanceAgent Benchmark matches the pattern observed across all six primary benchmarks (Appendix D.1)

  4. [4]

    This consistency suggests that the entropy signal captured by our framework reflects ageneralproperty of LLM uncertainty rather than task-specific patterns

    Entropy variance as failure predictor: Inter-agent entropy dispersion metrics maintain negative correlations on FinanceAgent Benchmark, consistent with the MAS failure analysis in Appendix D.2. This consistency suggests that the entropy signal captured by our framework reflects ageneralproperty of LLM uncertainty rather than task-specific patterns. Whethe...

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  9. [9]

    For each valid divisord=b+ 7, computeb=d−7and ensureb >9

  10. [10]

    Sum all valid integer values ofbobtained from step 5

  11. [11]

    only output the final answer without words, labels, and steps

    Computeb= 21,49; sum = 70 Analysis:Qwen performs deep reasoningwithinthe <think> block, independently deriving the complete solution before outputting a structured plan. Solver Agent. System Prompt You are the solver agent. Solve strictly according to the provided plans. Execute each step precisely and produce the final result. Output the final result int...

    2024

  12. [12]

    sample_mean_answer_token_entropy × sample_median_answer_token_entropy r = +0.991

  13. [13]

    base_model_min_answer_token_entropy × base_model_median_answer_token_entropy r = +0.989

  14. [14]

    sample_round_1_max_agent_std_entropy × sample_round_1_max_agent_variance_entropy r = +0.961

  15. [15]

    architecture × exp_infer_average_entropy r = -0.723

  16. [16]

    architecture × sample_total_entropy r = -0.683

  17. [17]

    architecture × sample_entropy_reduction_vs_base_total r = +0.678

  18. [18]

    architecture × sample_round_1_all_agents_total_entropy r = -0.677

  19. [19]

    architecture × round_1_total_token r = -0.652

  20. [20]

    base_model_min_answer_token_entropy × answer_token_entropy_change_direction r = +0.651

  21. [21]

    base_model_min_answer_token_entropy × base_model_vs_sample_final_answer_entropy_diffr = +0.651

  22. [22]

    base_model_min_answer_token_entropy × answer_token_entropy_change r = +0.645

  23. [23]

    architecture × sample_entropy_range r = -0.614

  24. [24]

    architecture × sample_max_entropy r = -0.614

  25. [25]

    architecture × sample_num_agents r = -0.612

  26. [26]

    architecture × exp_total_entropy r = -0.608

  27. [27]

    architecture × exp_total_token r = -0.588

  28. [28]

    base_model_is_finally_correct × is_finally_correct r = +0.554

  29. [29]

    exp_infer_average_entropy × sample_round_2_all_agents_total_entropy r = +0.536

  30. [30]

    architecture × sample_round_1_mean_agent_max_entropy r = -0.529

  31. [31]

    The lower triangle shows pairwise Pearson correlations; the upper-right inset lists the top 20 most strongly correlated feature pairs

    base_model_format_compliance × base_model_format_compliance_rate r = +0.521 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 Correlation Coefficient Figure 32.Feature correlation heatmap for GMAS on LLaMA models. The lower triangle shows pairwise Pearson correlations; the upper-right inset lists the top 20 most strongly correlated feature pairs. 53