Synthetic Consensus: Multi-Model Fusion

• Synthetic Consensus is a family of techniques that aggregates multiple candidate outputs to produce high-confidence decisions beyond simple majority voting.
• It employs methods like BERTScore for radiological diagnostics, consensus matrices in clustering, and iterative synthesis in LLM reasoning to ensure robust output.
• Applications range from diagnostic fusion and explainable AI to distributed optimization, requiring tailored aggregation rules for different modalities.

Searching arXiv for papers on synthetic consensus and related consensus-based fusion. Synthetic consensus denotes algorithmically constructed agreement from multiple outputs, models, or agents rather than reliance on a single prediction or partition. In the most explicit recent usage, it is a fusion strategy in which the outputs of multiple LLMs are compared and a diagnostic prediction is accepted only when there is strong semantic agreement between the models, an arrangement explicitly framed as analogous to seeking a second opinion in clinical practice (Siam et al., 16 Oct 2025). Across adjacent literatures, the same general idea appears as consensus matrices over stochastic clusterings, consensus functions over conflicting explanations, iterative agreement protocols among black-box reasoning models, and consensus scores that count how many detectors flag the same anomaly (Lancichinetti et al., 2012, Banegas-Luna et al., 2023, Ogunsina et al., 6 May 2025, Garg et al., 16 Mar 2026). This suggests that synthetic consensus is best understood not as a single algorithm, but as a family of procedures for synthesizing stable, high-confidence outputs from heterogeneous or stochastic sources.

1. Core idea and operational forms

Across the cited work, synthetic consensus is built from four recurring components: multiple candidate outputs, a comparison or aggregation operator, a decision rule, and a treatment of disagreement. In chest X-ray interpretation, the comparison operator is BERTScore applied to paired model outputs, and disagreement triggers manual review. In consensus clustering, the aggregation operator is a co-occurrence matrix over repeated partitions. In unsupervised anomaly analysis, the consensus score is the count of embedding models that flag a record as anomalous. In graph-based response synthesis, the shared and divergent content of multiple long-form responses is represented explicitly in a weighted DAG (Siam et al., 16 Oct 2025, Lancichinetti et al., 2012, Garg et al., 16 Mar 2026, Ghosh et al., 3 Oct 2025).

Two formulaic patterns recur. Output-level semantic agreement in diagnostic fusion is expressed as

$$\text{BERTScore}(P, R, F_1) = \frac{2 \cdot P \cdot R}{P + R}$$

with consensus defined by a threshold. Consensus clustering defines pairwise agreement as

$D_{ij} = \frac{\text{Number of partitions where nodes $i$and$j$ are clustered together}}{n_P}.$

Multi-embedding anomaly analysis instead uses a count-based score,

$S(r) = \sum_{m=1}^6 d_m(r),$

where each detector contributes a binary anomaly label (Siam et al., 16 Oct 2025, Lancichinetti et al., 2012, Garg et al., 16 Mar 2026).

Domain	Consensus object	Acceptance or synthesis rule
Chest X-ray interpretation	14-dimensional binary vectors from ChatGPT and Claude	Accept if BERTScore $\geq 95\%$; otherwise flag for manual review
Complex-network clustering	Pairwise co-clustering frequencies across $n_P$ partitions	Threshold the consensus matrix and re-cluster until partitions converge
Multi-model reasoning	Iteratively revised answers from black-box reasoning models	Stop when outputs are identical or semantically equivalent
Cross-protocol anomaly analysis	Binary anomaly flags from six embedding-model pipelines	Prioritize records with higher consensus score

A common misconception is that consensus is equivalent to simple majority voting. Several papers explicitly argue otherwise. The Hashgraph-inspired reasoning system is presented as going beyond simple majority voting by iteratively exchanging, cross-verifying, and merging knowledge from all models, while ConGrs uses alignment and synthesis over shared and divergent spans rather than selecting the modal response (Ogunsina et al., 6 May 2025, Ghosh et al., 3 Oct 2025).

2. Diagnostic fusion in radiology

In "Fusion-Augmented LLMs: Boosting Diagnostic Trustworthiness via Model Consensus" (Siam et al., 16 Oct 2025), synthetic consensus is defined as a fusion strategy where the outputs of multiple LLMs are compared and a diagnostic prediction is only accepted if there is strong semantic agreement between the models. The system uses ChatGPT (GPT-4) and Claude (3.7-sonnet) as black-box APIs with no fine-tuning, orchestrated through LangChain for parallel, modular inference and output comparison. Each model predicts, for each of 14 radiological findings, either a “1” or “0”, producing a 14-dimensional binary vector. If the outputs from both LLMs have a BERTScore $\geq 0.95$, the prediction is accepted as a consensus result; otherwise, the case is flagged for manual review. The paper states that the 95% threshold is empirically justified because the average agreement in tests was 95.75%, and sensitivity analysis found robustness for thresholds between 90% and 100%.

The experimental setting uses the CheXpert dataset of 224,316 chest radiographs across 14 pathology categories. In the unimodal image-only setup, 234 randomly selected radiologist-annotated studies were evaluated. ChatGPT achieved 62.8% accuracy and Claude 76.9%, while the consensus result reached 77.6% on the 170 of 234 cases, or 72.6%, where the models agreed at BERTScore $\geq 95\%$. McNemar’s test showed that consensus accuracy was significantly higher than ChatGPT alone, with $\chi^2 = 12.96, p < 0.001$, but not significantly improved over Claude, with $\chi^2 = 0.111, p = 0.74$. This is an important corrective to an overly strong reading of consensus: the method consistently outperformed the weaker model, but it did not automatically produce a statistically superior result to the strongest individual model in every condition.

The multimodal experiment used a separate subset of 50 randomly selected cases paired with both images and synthetic clinical notes. Those notes were generated from CheXpert’s ground-truth binary labels using a five-part template—Examination, Indication, Technique, Findings, Impression—modeled on MIMIC-CXR reports; positive findings were described in formal radiological language, negative findings used negated or normal statements, and phrase order and synonym variation were introduced for realism. The notes were embedded via BioClinicalBERT or OpenAI’s text-embedding-ada-002. On this cohort, performance improved to 84.0% for ChatGPT and 76.0% for Claude, while consensus accuracy reached 91.3% on 46 of 50 cases, or 92%, where the models agreed at the same threshold. On that same subset, the image-only baseline was 70% for ChatGPT and 74% for Claude. The paper attributes many disagreements to subtle or ambiguous findings, and notes that when both models are incorrect, the case is typically complex with co-occurring findings and is therefore likely to benefit from further expert review.

3. Language-model consensus, synthesis, and verification

Recent LLM work extends synthetic consensus from binary acceptance to iterative or structured response synthesis. The Hashgraph-inspired protocol for reliable multi-model reasoning treats each reasoning model as a black-box peer and organizes interaction through gossip-about-gossip communication and virtual voting (Ogunsina et al., 6 May 2025). Initial answers are denoted by

$O_i^0 = \text{Initial answer from } RM_i,$

and subsequent rounds are updated as

$D_{ij} = \frac{\text{Number of partitions where nodes $i$and$j$ are clustered together}}{n_P}.$0

Consensus is defined either by exact agreement, $D_{ij} = \frac{\text{Number of partitions where nodes $i$and$j$ are clustered together}}{n_P}.$1, or by semantic equivalence. The paper argues that this preserves minority but validated information better than majority voting, and presents robustness and fault-tolerance in Hashgraph terms, including the claim that the framework can tolerate up to $D_{ij} = \frac{\text{Number of partitions where nodes $i$and$j$ are clustered together}}{n_P}.$2 faulty or malicious reasoning models provided a supermajority behaves correctly. Its reported results are preliminary rather than empirical benchmarks; the paper explicitly describes expected rapid convergence, for example 1–3 rounds for fact-based queries.

"Sample, Align, Synthesize: Graph-Based Response Synthesis with ConGrs" (Ghosh et al., 3 Oct 2025) formalizes consensus at the level of long-form response structure. ConGrs are weighted DAGs built from multiple sampled responses using a light-weight lexical sequence alignment algorithm derived from Needleman–Wunsch and supplemented by targeted use of a secondary LM judge. Sequences of aligned tokens that appear in all responses become consensus nodes, while divergent regions are grouped into disagreement nodes through semantic-equivalence judgments. The resulting graph supports thresholded consensus decoding and guided self-verification. The reported effects are task-dependent but concrete: factual precision on two biography generation tasks improves by up to 31% over an average response, reliance on LM judges is reduced by more than 80% compared to other methods, abstention rate on refusal-based tasks is increased by up to 56%, and performance on MATH and AIME improves by up to 6 points of accuracy over self-verification and majority vote baselines.

Generative reproducibility work studies consensus as a verification primitive rather than an overview primitive. "Generative Artificial Intelligence Reproducibility and Consensus" (Kim et al., 2023) uses perceptual hashes for image generation and deterministic decoding for text. The paper reports that, with a majority vote between three independent verifiers, image-generated perceptual collisions can be detected with over 99.89% probability and less than 0.0267% chance of intra-class collision. For LLMs, greedy decoding or n-way beam search yielded 100% consensus across 5 LLMs, 4000 generations per model, and 4 machines. This literature shows that consensus may target either content quality or reproducibility, and that the appropriate mechanism depends sharply on the modality and the source of stochasticity.

4. Consensus over explanations and clusterings

In explainable machine learning, consensus is used to harmonize conflicting explanations rather than conflicting predictions. "Fighting the disagreement in Explainable Machine Learning with consensus" evaluates six consensus functions—Arithmetic Mean, Harmonic Mean, Geometric Mean, Voting, Ranking, and a proposed function—over five ML models and four synthetic datasets whose internal rules were known in advance (Banegas-Luna et al., 2023). The proposed function incorporates model accuracy, class probability for local methods, and normalization of attributions. The paper reports that Arithmetic Mean often identified all crucial features but failed to account for model accuracy, Harmonic Mean and Geometric Mean performed poorly and were unsuitable when attributions could be zero or negative, Voting remained susceptible to noise, Ranking lost quantitative information, and the proposed function outperformed all others by producing more consistent and accurate explanations.

WISCA extends this line of work to six ML models trained on six synthetic datasets with known ground truths (Banegas-Luna et al., 6 Jun 2025). Weighted Scaled Consensus Attributions normalizes attributions to $D_{ij} = \frac{\text{Number of partitions where nodes $i$and$j$ are clustered together}}{n_P}.$3, distinguishes global from local explanations, and weights local explanations by class probability or prediction error. The classification weighting factor is

$D_{ij} = \frac{\text{Number of partitions where nodes $i$and$j$ are clustered together}}{n_P}.$4

which emphasizes confident predictions. The paper reports that WISCA consistently aligned with the most reliable individual method, that in regression only WISCA reliably ranked all true features top for all models, and that Spearman correlation and Jensen–Shannon divergence showed the consensus attributions to be most similar to the best-performing individual interpretability method for a given setting. A recurrent conclusion in both studies is that consensus is not automatically “fair” merely because it aggregates multiple explainers; weighting, normalization, and model quality matter materially.

Consensus clustering provides a structurally different but conceptually allied use of synthetic consensus. In complex networks, stochastic community-detection runs are aggregated through a consensus matrix whose entries count how often node pairs co-occur in the same cluster; low-confidence edges are thresholded, isolated nodes are reattached to their strongest neighbor, and the method is rerun until the partitions converge (Lancichinetti et al., 2012). The paper reports substantially improved stability, much higher NMI between independent consensus partitions than between raw partitions, and applicability to temporal networks through overlapping windows and Jaccard-based matching of communities. More recent clustering work turns consensus into a model-selection criterion. DISCOTEC ranks clustering models by the distance between each model’s connectivity matrix and the ensemble consensus matrix, while IMPACC constructs consensus from tiny “minipatches” of both observations and features and adds adaptive sampling for observation uncertainty and feature importance (Ohl et al., 7 May 2025, Gan et al., 2021). In both cases, synthetic scenarios are used because known structure permits direct assessment of whether the consensus mechanism identifies the more faithful clustering.

5. Distributed, geometric, and on-demand formulations

A second major lineage treats consensus as a distributed optimization or dynamical systems problem. In distributed feature construction with ILP, each node builds local relational features and updates a local parameter vector while mixing with neighbors. The generic update is

$D_{ij} = \frac{\text{Number of partitions where nodes $i$and$j$ are clustered together}}{n_P}.$5

and for convex loss functions the authors state that all nodes converge to a consensus model (Dutta et al., 2014). The point of consensus here is not output validation but distributed agreement under feature heterogeneity and limited communication.

Riemannian consensus generalizes Euclidean averaging to manifold-valued data (Tron et al., 2012). The intrinsic cost is

$D_{ij} = \frac{\text{Number of partitions where nodes $i$and$j$ are clustered together}}{n_P}.$6

with local gradient

$D_{ij} = \frac{\text{Number of partitions where nodes $i$and$j$ are clustered together}}{n_P}.$7

and update

$D_{ij} = \frac{\text{Number of partitions where nodes $i$and$j$ are clustered together}}{n_P}.$8

The paper gives sufficient convergence conditions for manifolds with bounded curvature and emphasizes a key difference from Euclidean consensus: the Fréchet mean is not preserved by the iterations, and the consensus configuration reached may differ from the original Fréchet mean.

"Consensus Driven by the Geometric Mean" replaces arithmetic-mean dynamics with three nonlinear protocols—polynomial, entropic, and scaling-invariant—and proves exponential convergence to consensus for positive initial conditions (Mangesius et al., 2015). For the entropic protocol,

$D_{ij} = \frac{\text{Number of partitions where nodes $i$and$j$ are clustered together}}{n_P}.$9

and the limiting consensus value is the weighted geometric mean of the initial condition. The paper also proposes a variational characterization of the geometric mean as the solution of a nonlinear constrained optimization problem involving free energy. This work broadens the notion of consensus from simple arithmetic averaging to a family of metric- and geometry-dependent aggregation rules.

"Consensus on Demand" offers a different generalization: consensus is invoked only when conflicts arise (Sliwinski et al., 2022). The protocol combines broadcast-based processing with selective a posteriori consensus and tolerates Byzantine participants only when they are less than a one-fifth minority, stated as the optimal threshold. With $S(r) = \sum_{m=1}^6 d_m(r),$0, a transaction can be accepted on the fast path if acknowledgements satisfy

$S(r) = \sum_{m=1}^6 d_m(r),$1

and the slow path invokes consensus only for conflicting slots. This is synthetic consensus in a literal systems sense: the system behaves as though global agreement exists, but performs the heavier consensus machinery only where the local evidence of conflict requires it.

6. Synthetic benchmarks, anomaly triage, social robustness, and limitations

Synthetic consensus is often evaluated on synthetic artifacts because known ground truth permits controlled stress-testing. In cross-protocol mobile-core anomaly analysis, synthetic anomalies are created by swapping one field group at a time between fused SS7, Diameter, and GTP records so that per-message validity is preserved while the fused view becomes contradictory (Garg et al., 16 Mar 2026). On 219,294 fused records, 44.15% were flagged by at least one model, but only 0.97% reached full agreement across all six. Higher consensus was strongly associated with synthetic records: for thresholds $S(r) = \sum_{m=1}^6 d_m(r),$2 to $S(r) = \sum_{m=1}^6 d_m(r),$3, the odds that a flagged record was synthetic were in the hundreds, and for $S(r) = \sum_{m=1}^6 d_m(r),$4 all flagged records were synthetic, with extremely small p-values. The paper therefore presents consensus not as a final detector, but as a prioritization mechanism that drastically narrows analyst workload.

Synthetic settings are also used to study when consensus becomes fragile. In a two-state majority-vote model on Barabási–Albert scale-free networks, the visibility parameter $S(r) = \sum_{m=1}^6 d_m(r),$5 determines whether an agent considers a neighbor’s opinion at a given interaction; reduced visibility creates temporary synthetic influence groups (Porciúncula et al., 2024). The paper reports that lower $S(r) = \sum_{m=1}^6 d_m(r),$6 reduces the critical noise $S(r) = \sum_{m=1}^6 d_m(r),$7 and therefore undermines consensus robustness, whereas higher network connectivity increases $S(r) = \sum_{m=1}^6 d_m(r),$8. This use of the adjective “synthetic” is different from synthetic consensus as model fusion, but it is closely related: algorithmically constructed interaction structure can change whether consensus forms at all.

Several literatures identify sharp limits on what consensus can establish. In synthetic data privacy, a Delphi-based framework with 13 privacy experts concluded that current similarity metrics fail to measure identity disclosure and that their use is discouraged, while membership and attribute disclosure should be assessed through metrics tied to adversarial models and quasi-identifiers rather than raw record similarity (Pilgram et al., 6 Mar 2025). The paper also states that for differentially private synthetic data, a privacy budget other than close to zero was not considered interpretable. This is relevant because some consensus pipelines rely on similarity, distance, or co-occurrence statistics; the privacy framework warns that such measures are not interchangeable with disclosure risk.

A broader misconception is that higher agreement always implies correctness. The literature is more qualified. In radiology, consensus did not significantly improve over Claude in the unimodal setting even though it exceeded ChatGPT and improved trustworthiness under the paper’s acceptance criterion (Siam et al., 16 Oct 2025). In ensemble clustering, DISCOTEC is attracted to whichever hub dominates, so if the majority of models are poor, consensus is less meaningful (Ohl et al., 7 May 2025). In explanation aggregation, classical means can amplify scale bias or unreliable models (Banegas-Luna et al., 2023, Banegas-Luna et al., 6 Jun 2025). The consistent implication is that synthetic consensus is most effective when disagreement is interpretable, aggregation is matched to the structure of the outputs, and abstention or manual review remains available for the residual cases that consensus does not resolve.