Similarity-based Reproducibility Index (SRI)

• SRI is a composite metric that quantifies reproducibility using a continuous scale from 0 (non-reproducible) to 1 (perfect reproducibility).
• It integrates diverse similarity measures such as ranking similarity, numerical error metrics, and object-specific comparisons to capture incremental differences in outcomes.
• SRI is applied in fields like information retrieval, computational notebooks, and NLP to provide nuanced insights that transcend binary reproducibility assessments.

The Similarity-based Reproducibility Index (SRI) is a class of composite metrics that quantify the degree to which outcomes from repeat experiments, system reimplementations, or computational reruns replicate original results, based on similarity measures rather than strict equality. SRI provides a continuous, interpretable scale—typically in [0, 1]—which enables nuanced assessment of reproducibility across system-oriented experiments, computational environments, and scientific domains. It represents a methodological advance over binary reproducibility checks, making it broadly relevant for quantifying reproducibility in contexts such as information retrieval, computational notebooks, and statistical analysis.

1. Conceptual Foundations and Motivation

SRI arises from the need to move beyond binary criteria of reproducibility (“identical” vs. “not identical”) towards a continuous, similarity-based quantification that captures both minor and significant differences in experimental results. This approach is motivated by practical challenges: even when faithfully rerunning an experiment, outputs may differ due to random seeds, dependency versions, or platform idiosyncrasies, yet such differences do not necessarily undermine scientific reproducibility if the core outcomes remain similar.

Several research directions converge on this principle:

• In computational notebooks (e.g., Jupyter), outputs are re-executed and compared using similarity metrics tailored to the data type, yielding an SRI that reflects “how close” re-run results are to originals (Hossain et al., 28 Sep 2025).
• In information retrieval (IR), SRI is proposed to combine ranked list similarity, effectiveness scores, and statistical tests into a composite measure of system reproducibility (Breuer et al., 2020).
• In natural language processing and meta-science, frameworks like QRA++ lay groundwork for SRI by explicitly coupling reproducibility assessment with experimental and outcome similarity (Belz, 13 May 2025).

2. Core Methodologies and Metrics

SRI construction involves aggregating similarity measures appropriate to the data and context. These typically include:

• Ranking Similarity: Metrics such as Rank-Biased Overlap (RBO) or Kendall’s tau to compare ranked result lists from IR outputs. The RBO is defined as:

$\mathrm{RBO} = (1-p) \sum_{d=1}^\infty p^{d-1} A_d$

where $A_d$ is the proportion of overlap at depth $d$, and $p$ controls top-heaviness (Breuer et al., 2020).

• Numerical and Score-Level Similarity: For continuous data, RMSE quantifies topic-wise score differences:

$$\mathrm{RMSE} = \sqrt{ \frac{1}{n} \sum_{i=1}^n (m_i - m'_i)^2 }$$

and effect ratios (ER) express the reproducibility of observed improvements:

$$\mathrm{ER} = \frac{\overline{\Delta M'}}{\overline{\Delta M}}$$

• Object/Type-Specific Similarities: For computational notebooks, outputs like text, numerical arrays, images, or structured collections are compared with individualized metrics (e.g., Jaro–Winkler similarity for text, SSIM for images, shape and element-wise comparison for arrays) (Hossain et al., 28 Sep 2025).
• Statistical Consistency Assessments: Paired or unpaired t-tests are employed to determine if discrepancies are significant under null hypotheses of equivalence (Breuer et al., 2020).
• Aggregation and Normalization: These individual similarity scores are normalized (e.g., to [0, 1]) and aggregated with tunable weights to yield an overall index, as in:

$$\mathrm{SRI} = w_1 \cdot \mathrm{norm}(\mathrm{RBO}) + w_2 \cdot \mathrm{norm}\left(1 - \frac{\mathrm{RMSE}}{\mathrm{maxRMSE}}\right) + w_3 \cdot \mathrm{norm}(p\text{-value})$$

where $w_1, w_2, w_3$ sum to one (Breuer et al., 2020).

3. Applications and Contextual Deployment

SRI has been proposed and tested across diverse scientific contexts:

• System-Oriented Information Retrieval: SRI enables quantitative assessment of how faithfully a reproduced IR system matches the original, supporting both topic-wise and aggregate reproducibility analysis. The approach leverages reproducibility-oriented test collections that systematically vary system parameters to validate SRI’s sensitivity (Breuer et al., 2020).
• Computational Notebooks and Data Science Platforms: SRI compares output cells in sequential notebook reruns, employing object-sensitive similarity scores to capture differences in text streams, numerical arrays, and images. Scores and qualitative insights assist in identifying sources of irreproducibility such as randomness or library drift (Hossain et al., 28 Sep 2025).
• Natural Language Processing Benchmarks: SRI-inspired frameworks (such as QRA++) use statistical similarity, ranking consistency, and meta-data-aware comparisons to generate continuous-valued reproducibility metrics, supporting reproducibility meta-analysis across multiple studies and evaluation criteria (Belz, 13 May 2025).

4. Interpretation of SRI Scores

The value of SRI is anchored in its interpretability:

• Range [0, 1]: A score of 1 indicates perfect reproducibility; 0 denotes complete divergence.
• Nuanced Diagnostics: High values despite minor, irrelevant output variations (such as formatting) correctly communicate that scientific reproducibility is not impaired. Low values direct users to potentially impactful inconsistencies.
• Qualitative Insights: Alongside numeric SRI, output includes qualitative annotations (e.g., “differences are only in float formatting” or “array shapes differ”), facilitating practical debugging (Hossain et al., 28 Sep 2025).
• Granularity: SRI can be reported per output, per topic, per experiment, or for higher-level aggregation, supporting both detailed and summary reproducibility analysis (Belz, 13 May 2025).

5. Integration with Experimental Similarity and Benchmarking

A key advancement in newer frameworks is to “ground” the assessment of reproducibility in the degree of experimental similarity. QRA++, for instance, operationalizes the principle that expected reproducibility should be higher when the properties of compared experiments are more similar (e.g., identical evaluation data and test configurations), and SRI can adjust weighting to reflect this (Belz, 13 May 2025). This aligns evaluative expectations with methodological closeness, offering an interpretive context for SRI values.

SRI validation is critically dependent on reproducibility-oriented datasets—collections that span controlled variations in system, code, or configuration—against which SRI’s discriminative power can be assessed and fine-tuned (Breuer et al., 2020).

6. Challenges, Limitations, and Future Prospects

Despite its flexibility, SRI faces challenges in operational deployment:

• Heterogeneous Output Representations: Variability in data types, metadata, and display conventions may compromise robust comparison strategies, sometimes necessitating fallback or approximation techniques (Hossain et al., 28 Sep 2025).
• Tuning Tolerance Parameters: Determining appropriate thresholds for similarity (e.g., floating-point tolerances) is nontrivial; overly strict or lax criteria could respectively overstate or understate reproducibility failures.
• Weight Calibration: Aggregating distinct similarity measures into a single meaningful SRI requires careful weight selection, informed by empirical validation and possibly domain-specific considerations.
• Interpretability vs. Sensitivity: Communicating the significance of intermediate SRI values (e.g., 0.8) requires context-aware guidance, especially when combining different types of similarity evidence.

Nevertheless, SRI offers a rigorous, multidimensional, and continuous standard for evaluating reproducibility, with broad applicability across computational research, system benchmarking, and experimental reporting. Its use supports the development of more transparent, actionable, and nuanced reproducibility standards in science.