Reliability, Faithfulness, and the Limits of Post-hoc Explanations of Opaque Scientific Models

We review the concepts of interpretability and explainability as they apply to machine learning in physics. We define interpretability as concerning the structural transparency of a model (the ability to understand or approximate its inner workings) and explainability as concerning the scientific content of a model (the ability to map it onto domain knowledge). We discuss the trade-offs each entails (interpretability vs. expressivity; explainability vs. adaptability), the contexts in which each is needed, and the intrinsic and post-hoc tools available for achieving them. Throughout, we emphasize that machine-learned models are subject to the same scientific questions as classical models, differing only in scale, and that interpretability and explainability are best understood as deliberate modeling choices rather than inherent properties. We also emphasize the importance of task specification and intervention plans as a core aspect of model design.

Modern Machine Learning (ML) and Artificial Intelligence (AI) models, especially large language models (LLMs), are increasingly used to generate scientific hypotheses and mechanistic explanations from observational data. This position paper argues that in the high-dimensional proxy regimes where modern ML excels, mechanistic learning is generically underdetermined: many incompatible mechanisms induce essentially the same observational relationships on the support of the data, so predictive success and coherent explanations are insufficient evidence of mechanism discovery. This underdetermination becomes uniquely hazardous with large language models (LLMs), which tend to collapse large equivalence classes of explanations into a single fluent narrative. This paper proposes concrete standards for ``mechanistic ML,'' and argues these norms are necessary if LLM-centered workflows are to support science rather than merely simulate it.

Multiple machine learning models can achieve near-equivalent predictive performance on the same task, yet provide divergent feature-based explanations. This is called the Rashomon effect of (explainable) machine learning, and it raises the question of which explanations, if any, are trustworthy. We propose a framework based on metamorphic testing that assesses explanation faithfulness without requiring ground-truth labels by exploring attributed feature importance from post-hoc explanation methods. Five metamorphic relations formalize expected consistency properties between model behavior and feature attributions. We apply this general framework to two tabular regression datasets and two post-hoc explainers (SHAP and LIME) to demonstrate the approach. The framework offers a practical, model-agnostic tool for selecting accurate models with reliable and trustworthy explanations.