Cross-Model Evaluation

Updated 19 December 2025

Cross-model evaluation is a framework that systematically compares models using multiple criteria beyond basic metrics to assess predictive performance, fairness, and interpretability.
It employs diverse methodologies such as multi-criteria voting, consensus explanation metrics, ensemble averaging, and infrastructure-agnostic benchmarking to reconcile heterogeneous outputs.
Best practices include publishing complete rank matrices, rigorous statistical validation, and data-driven calibration to ensure transparency and balanced trade-offs in model selection.

Cross-model evaluation encompasses a broad set of formal frameworks, algorithms, and diagnostic methodologies for comparing multiple models—whether across architectures, training protocols, or criteria—in a systematic and interpretable fashion. The goal is to transcend naive metrics (e.g., accuracy, F₁-score) by aggregating diverse measures, reconciling heterogeneous outputs, and highlighting trade-offs along axes such as scientific credibility, theoretical elegance, practical utility, interpretability, fairness, and reliability. State-of-the-art approaches range from multi-criteria voting and geometric averaging, to deep infrastructure-agnostic benchmarking, bidirectional model-data reliability checks, cross-lingual selection algorithms, and scan-intensive data integration. This article surveys foundational frameworks, technical principles, quantitative methodologies, field-specific instantiations, and best practices in cross-model evaluation.

1. Multi-Criteria Frameworks and Voting-Based Aggregation

A paradigmatic approach, exemplified by Harman & Scheuerman’s model evaluation protocol, is the formalization of cross-model evaluation as multi-criteria comparison over a set $M = \{m_1, ..., m_N\}$ of candidate models and $C = \{c_1, ..., c_K\}$ of evaluation criteria—scientific, theoretical, and practical alike (Harman et al., 2024). Each model $m_i$ receives a score $s_{i,j}$ on each criterion $c_j$ , which is converted to an ordinal rank $r_{i,j}$ . Aggregation proceeds via computational social choice rules:

Condorcet Criterion: Pairwise comparison over models, declaring a unique Condorcet winner if one model strictly outranks all others over majority of criteria.
Borda Count: Each model earns $(N - r_{i,j} + 1)$ per criterion; total Borda scores determine ranking, with tiebreaks by high-priority criteria.
Plurality Rule: The model(s) with most first-place ranks are surface-level winners.

Weighted criteria ( $w_j$ ) and deterministic or averaged tie-breaking deliver further flexibility, and the framework is scalable to large $N$ , field-agnostic, and transparent when full rank and pairwise matrices are published. This promotes taxonomies that balance predictive accuracy with parsimony, falsifiability, ethical alignment, and process identifiability, re-elevating simple models in cognitive and decision sciences.

2. Consensus-Based Explanation and Agreement Metrics

In high-dimensional settings, especially deep learning (DL) for vision, cross-model evaluation increasingly targets explanations and interpretability. The cross-model consensus framework constructs feature-importance maps $w = \mathcal{I}(M, d)$ from an interpretation algorithm, aggregates these across a committee to yield consensus maps $c(d)$ by normalized averaging, and scores individual models by agreement with consensus via cosine (LIME) or RBF (SmoothGrad) similarity (Li et al., 2021).

Empirical results reveal:

Consensus maps outperform any single model’s explanation in semantic alignment with ground-truth segmentation (mAP: consensus > best individual).
Consensus-score $S_i$ correlates strongly with model accuracy and with independently judged interpretability.
Committee voting filters idiosyncratic artifacts, and consensus scores serve as cross-model, model-agnostic metrics.

Limitations include interpreter dependence, committee composition sensitivity, and reduced effectiveness on multi-object scenes. Extensions target multi-label tasks, pseudo-label generation, and dynamic committee selection.

3. Ensemble Averaging and Calibration in Physical Sciences

Blank et al. apply ensemble averaging to fusion-evaporation cross-section calculations by comparing five distinct reaction codes and combining predictions via geometric mean and empirical scale normalization (Blank et al., 2017). The formal protocol is:

Compute cross-section predictions $\sigma_m(E_i)$ for all models at each energy.
Aggregate via $\langle \sigma \rangle_{geom}(E_i)$ and rescale by a global factor (11.2) to fit experiment.
Use logarithmic deviation metrics and scale factors for global calibration and uncertainty quantification.
Best performers combine low adjustment factors and low deviation.

This ensemble approach mitigates individual model biases, supports data-driven calibration and uncertainty propagation, and generalizes to other reaction types.

4. Infrastructure-Agnostic Reasoning Benchmarks

In language modeling, cross-platform evaluation has emerged as a rigorous solution for model comparison across computational environments. Evaluations are performed over diverse platforms (HPC, cloud, university cluster) and model architectures, with a benchmark of 79 reasoning problems spanning eight STEM and social-science domains (Curtò et al., 30 Oct 2025).

Metrics:

Final-Score: Cosine semantic-similarity between predicted and gold answers.
Step-Accuracy: Cosine similarity for each step in the worked solution.
Consistency: Inter-run standard deviation.
Statistical significance: One-way ANOVA and pairwise Welch t-tests.

Findings include parameter-efficiency paradoxes (smaller but better-trained models outperforming large ones), consistent cross-infrastructure scores (<3% variance), and decoupled transparency/correctness, informing deployment in production, educational, or audit-critical contexts.

5. Cross-Model Fairness and Model Multiplicity

Ruggieri et al. extend cross-model evaluation to fairness, focusing on model multiplicity: the scenario where multiple predictors are equally optimal by utility but diverge on individual predictions (Sokol et al., 2022). Formal definitions include:

Disputable regions: Instances $x$ where $f_i(x) \neq f_j(x)$ for $f_i, f_j \in \mathcal{F}_\epsilon$ (fixed performance).
Cross-model individual fairness: A model is fair if its decision on all individuals matches all other equally performing models.
Fair-by-design ensemble: Assigns each $x$ the maximal label across $\mathcal{F}_\epsilon$ , which sacrifices specificity for recall.
Per-individual/group fairness metrics: Discrepancy fractions $\Delta_i$ , aggregated into group-level scores.

Empirical analysis demonstrates substantial ambiguity when relaxing from optimal accuracy, persistent discrepancies along protected attributes, and utility–fairness trade-offs often requiring reduction in model expressiveness or aggressive regularization.

6. Database-Level Cross-Model Query Optimization

In heterogeneous data management, QUEST constitutes a major advance for scan-intensive cross-model queries spanning relational, document, and graph models (Huang et al., 2023). The system flattens disparate data into a unified columnar layout, indexes with an O(n) Skip-Tree over recursive schema, and deploys pairwise bitset operations for aggressive pre-aggregation and pruning. This reduces intermediate result size (from $O(N)$ to $O(\sigma N)$ ), minimizes multi-hop traversal cost ( $O((\sigma N)\log d)$ ), and empirically achieves speedups up to 178.2x over multi-model database baselines.

7. Best Practices, Limitations, and Recommendations

Cross-model evaluation frameworks converge on key principles:

Publish complete rank and pairwise score matrices for transparency (Harman et al., 2024).
Pre-register taxonomies, weigh criteria by domain priorities, and conduct sensitivity analyses.
Apply ensemble methods for uncertainty quantification and calibration (Blank et al., 2017).
Use rigorous statistical validation and leverage stepwise semantic similarity for reasoning models (Curtò et al., 30 Oct 2025).
Always measure ambiguity and per-individual discrepancies when fairness is critical (Sokol et al., 2022).
Validate transfer models on gold-standard annotation, audit training provenance rigorously, and apply bidirectional checks between model outputs and reference labels (Dzafic et al., 19 Jul 2025).

Limitations include subjective criteria scoring, computational cost for large $N$ , tie sensitivity in dichotomous criteria, and challenges in extending frameworks to multi-class, regression, or high-expressivity models. Theoretical guarantees for cross-validation further reinforce its value in relative model selection, but not absolute risk estimation in nonparametric settings (Wager, 2019).

Taken together, the evolution of cross-model evaluation has enabled holistic, transparent, and robust comparisons across an increasingly diverse landscape of AI/ML models, foundational architectures, explanation strategies, and fairness-aware deployments.