New Paper: AI Interpretability Must Be Defined by Symmetries

A new preprint from researchers including Pietro Barbiero, Mateo Espinosa Zarlenga, and others challenges the foundations of AI interpretability. The paper, submitted in January 2026 and updated in June, argues that current definitions of interpretability are 'fundamentally ill-posed' because they fail to describe how interpretability can be formally tested or designed for. To remedy this, the authors propose that actionable definitions must be formulated in terms of four specific symmetries: inference equivariance, information invariance, concept-closure invariance, and structural invariance. These symmetries, they claim, allow interpretable models to be defined as a subclass of probabilistic models, providing a mathematically rigorous foundation.

Under this probabilistic view, the symmetries yield a unified formulation of key interpretability tasks—such as alignment, interventions, and counterfactuals—as forms of Bayesian inversion. This not only clarifies the relationship between different interpretability methods but also offers a formal framework to verify compliance with safety standards and regulations. The paper has been submitted to arXiv and spans fields including AI, machine learning, and neural and evolutionary computing. If adopted, this symmetry-based approach could reshape how researchers design and evaluate interpretable AI systems, moving from vague desiderata to testable conditions.