Authors Clarify Interpretability Role in Scientific ML

The arXiv paper by Conor Rowan and coauthors reframes interpretability in SciML by arguing that the field has mistakenly equated sparsity with interpretability. The authors propose an operational, philosophically informed definition that emphasizes understanding the underlying mechanism rather than producing compact mathematical expressions. The paper revises and synthesizes prior work from interpretable ML and symbolic regression to show where those ideas fail for physical science discovery.

The paper surveys existing definitions and methods from interpretable ML, equation discovery, and symbolic regression, and identifies core failure modes when these are applied to scientific problems. Key technical points include:

• •Interpretability is defined as the capacity to generate mechanistic explanations that integrate with prior scientific knowledge, not simply low parameter count or formulaic sparsity.
• •The paper argues sparsity is often unnecessary and does not by itself guarantee mechanistic clarity.
• •The paper highlights the role of prior knowledge and model inductive biases in whether interpretability is attainable, and it questions the possibility of interpretable scientific discovery when prior knowledge is lacking.

This paper matters because many practitioners treat symbolic regression and sparse discovery techniques as turnkey routes to scientific laws. The authors push back, reframing the research agenda: methodology should target mechanistic identifiability and epistemic integration. That shifts evaluation criteria away from compactness and toward reproducibility, causal interpretability, and compatibility with domain theory. For SciML tool builders, this implies reconsidering loss functions, priors, and benchmark tasks used to claim interpretability.

• •Reassess benchmarks that reward sparsity alone and adopt tests for mechanistic fidelity.
• •Incorporate stronger domain priors, experimental interventions, or causal assumptions when discovery is the goal.
• •Treat explainability modules as hypothesis generators requiring experimental validation, not final answers.

Expect follow-up work that develops quantitative metrics for mechanistic interpretability and benchmark datasets where prior knowledge is explicitly controlled. Progress will hinge on tighter integration between experimental design and model inductive bias.