The Metagame of Interpretability and Meta-Attributions
Abstract
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 φj → 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.
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BibTeX
@misc{baniecki2026metagame,
title = {{The Metagame of Interpretability and Meta-Attributions}},
author = {Hubert Baniecki and Przemyslaw Biecek and Fabian Fumagalli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.06295},
eprint = {2605.06295},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.06295},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Metagame of Interpretability and Meta-Attributions
AU - Hubert Baniecki
AU - Przemyslaw Biecek
AU - Fabian Fumagalli
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2605.06295
UR - https://arxiv.org/abs/2605.06295
AB - 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 ϕ_i 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 φ_j → 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.
ER -