Actionable Interpretability Must Be Defined in Terms of Symmetries

TL;DR

This paper proposes that interpretability in AI should be defined through symmetries that enable formal testing, model design, and compliance verification, offering a unified probabilistic framework.

Contribution

It introduces a symmetry-based framework for defining and testing interpretability, unifying various interpretability concepts under a probabilistic model.

Findings

Identifies four key symmetries for interpretability: inference equivariance, information invariance, concept-closure invariance, structural invariance.

Formalizes interpretable models as a subclass of probabilistic models.

Provides a framework for verifying interpretability compliance with safety standards.

Abstract

This paper argues that interpretability research in Artificial Intelligence (AI) is fundamentally ill-posed as existing definitions of interpretability fail to describe how interpretability can be formally tested or designed for. We posit that actionable definitions of interpretability must be formulated in terms of *symmetries* that inform model design and lead to testable conditions. Under a probabilistic view, we hypothesise that four symmetries (inference equivariance, information invariance, concept-closure invariance, and structural invariance) suffice to (i) formalise interpretable models as a subclass of probabilistic models, (ii) yield a unified formulation of interpretable inference (e.g., alignment, interventions, and counterfactuals) as a form of Bayesian inversion, and (iii) provide a formal framework to verify compliance with safety standards and regulations.