Attributions All the Way Down? The Metagame of Interpretability

TL;DR

This paper introduces the metagame framework to quantify second-order interaction effects of model explanations, providing hierarchical decomposition and empirical insights across various interpretability applications.

Contribution

It presents a novel metagame approach that measures directional influence among features in attribution methods, extending existing interaction indices with theoretical and empirical validation.

Findings

Hierarchical decomposition of attributions into meta-attributions.

Meta-attributions serve as directional extensions of interaction indices.

Empirical applications include token interactions, cross-modal similarity, and multimodal concept interpretation.

Abstract

We introduce the metagame, a conceptual framework for quantifying second-order interaction effects of model explanations. For any first-order attribution $\phi(f)$ explaining a model $f$, we measure the directional influence of feature $j$ on the attribution of feature $i$, denoted as meta-attribution $\varphi_{j \to i}(f)$, by treating the attribution method itself as a cooperative game and computing its Shapley value. Theoretically, we prove that attributions hierarchically decompose into meta-attributions, and establish these as directional extensions of existing interaction indices. Empirically, we demonstrate that the metagame delivers 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.