# The Metagame of Interpretability and Meta-Attributions

arXiv: https://arxiv.org/abs/2605.06295 · HTML: https://mlsanity.com/paper/2605.06295/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 77 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 3 of 3)

- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [SigLIP 2: Multilingual Vision-Language Encoders with Improved Semantic Understanding, Localization, and Dense Features](https://mlsanity.com/paper/2502.14786/) (2025)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)

## Abstract (arXiv)

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.