The Standard Interpretable Model: A general theory of interpretable machine learning to deductively design interpretable methods using Lagrangian mechanics
For the interpretability research community, this work provides a unified theoretical framework to deductively design and evaluate interpretable methods, addressing fragmentation and inconsistent evaluation.
The paper introduces the Standard Interpretable Model (SIM), a general theory grounded in Lagrangian mechanics for deductively designing interpretable machine learning methods. It shows that SIM identifies and solves limitations of existing interpretability methods, highlights underexplored research directions, and informs the design of core programming interfaces.
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 grounded in Lagrangian mechanics that enables the deductive design of interpretable methods. Specifically, the SIM summarises, in a set of premises, what interpretability is for a target user. From these premises, the SIM systematically derives interpretability symmetries and corresponding constraints, which shape the landscape of a Lagrangian whose minima correspond to optimal interpretable models. To reach the minima, one can either update the parameter values of an opaque model to make it more interpretable or compile constraints into an interpretable architecture. We empirically show that the SIM identifies and solves limitations of existing methods (including traditional, concept-based, and mechanistic interpretability), highlights underexplored research directions, and informs the design of core programming interfaces. Beyond being a research method, the deductive nature of the SIM offers pedagogical grounding for interpretability curricula and may shift the scientific community's perspective of a discipline that has long been fragmented.