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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.\n  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 mod","title":"The Standard Interpretable Model: A general theory of interpretable machine learning to deductively design interpretable methods using Lagrangian mechanics","url":"https://arxiv.org/abs/2606.12289","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.12289v1 Announce Type: cross \nAbstract: 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.\n  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. 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