The Metagame of Interpretability and Meta-Attributions

How can an arbitrary attribution method be generalized from first principles to capture interactions? We answer this with the metagame, a conceptual framework for quantifying second-order interaction effects of model explanations. We cast the attribution value φi of feature i as a cooperative game among the other features and compute its Shapley value, which measures how much feature j influences the attribution of i, yielding the directional meta-attribution varphij → i. By decomposing attribution itself rather than the model directly, meta-attributions extend any gradient- or attention-based method to interactions, uniting removal-based perturbations with model internals. Theoretically, we prove that meta-attributions sum to the first-order attribution they explain, a hierarchical decomposition that Shapley interactions and integrated Hessians turn out to perform implicitly. Empirically, we demonstrate that meta-attributions deliver insights across diverse interpretability applications: (i) quantifying token interactions in instruction-tuned language models, (ii) explaining cross-modal similarity in vision-language encoders, and (iii) interpreting text-to-image concepts in multimodal diffusion transformers.