The Standard Interpretable Model: Design interpretable machine learning methods from elementary symmetries

arXiv:2606.12289v3 Announce Type: replace Abstract: As Artificial Intelligence models grow in complexity, interpretability has become an indispensable tool for understanding, debugging, and controlling their computations. However, interpretability lacks general theories to deductively design interpretable methods. This gap between theories and methods results in a fragmented literature and inconsistent evaluation protocols. To fill this gap, we introduce the Standard Interpretable Model (SIM), a general theory that enables the deductive design of interpretable methods from first principles. Specifically, the SIM summarises, in a set of premises, what interpretability is for a target entity. From these premises, the SIM systematically derives interpretability symmetries and corresponding constraints. One can then build interpretable models by either introducing constraints in the optimisation problem or by compiling constraints into an interpretable architecture. The most important finding, both theoretical and empirical, is that full expressivity and interpretability symmetries can coexist in the same model, showing that the trade-off between accuracy and interpretability is an artefact of model design. We demonstrate this on language models (LMs), where SIM-based LMs match the performance of equivalent opaque LMs without making any compromise on interpretability. Beyond this, the SIM shows how to improve the interpretability of existing pre-trained models, highlights underexplored research directions, and unifies a discipline that has long been fragmented, offering pedagogical grounding for interpretability curricula.