[論文レビュー] Understanding and Unifying Fourteen Attribution Methods with Taylor Interactions

Huiqi Deng, Na Zou+6 more|arXiv (Cornell University)|Mar 2, 2023

Multi-Criteria Decision Making被引用数 18

ひとこと要約

本論文は、テイラー相互作用フレームワークの下で14の入力寄与法を統合し、各寄与が独立効果と相互作用効果の重み付き配分であることを示し、忠実性原理を提案する。

ABSTRACT

Various attribution methods have been developed to explain deep neural networks (DNNs) by inferring the attribution/importance/contribution score of each input variable to the final output. However, existing attribution methods are often built upon different heuristics. There remains a lack of a unified theoretical understanding of why these methods are effective and how they are related. To this end, for the first time, we formulate core mechanisms of fourteen attribution methods, which were designed on different heuristics, into the same mathematical system, i.e., the system of Taylor interactions. Specifically, we prove that attribution scores estimated by fourteen attribution methods can all be reformulated as the weighted sum of two types of effects, i.e., independent effects of each individual input variable and interaction effects between input variables. The essential difference among the fourteen attribution methods mainly lies in the weights of allocating different effects. Based on the above findings, we propose three principles for a fair allocation of effects to evaluate the faithfulness of the fourteen attribution methods.

研究の動機と目的

• DNNの寄与方法に対する統一的な理論的理解の必要性を動機づける。
• ネットワーク出力を独立効果と相互作用効果に分解する、Taylor 相互作用ベースの系を定式化する。
• 既存の14の寄与方法がこの統一フレームワーク内で再定式化できることを示す。
• 入力変数への効果の割り当ての忠実さを評価する公正性原理を提案する。

提案手法

• DNN 出力をベースラインの周りでの Taylor 展開として定式化する: f(x) = f(b) + sum of independent effects phi(kappa) and interaction effects I(kappa).
• 適切な Taylor 項の総和として、generic independent effects psi(i) および generic interaction effects J(S) を定義する。
• Harsanyi dividend H(S) が general な相互作用効果 J(S) に等しいことを証明する。
• 各寄与 a_i が独立効果と相互作用効果の加重和として表現できることを示す: a_i = sum_j w_{i,j} psi(j) + sum_S w_{i,S} J(S).
• 14 の寄与方法をこのフレームワークへ統一的に対応づけるマッピングを提供し、各方法の配分ウェイトの明示的な式を示す。

実験結果

リサーチクエスチョン

• RQ1 Can fourteen attribution methods be theoretically unified under a single Taylor interaction framework?
• RQ2 How do independent and interaction effects contribute to input attributions, and how do different methods allocate these effects?
• RQ3 What principles ensure faithful allocation of independent and interaction effects to input variables?
• RQ4 How can existing attribution methods be expressed as reallocations of Taylor independent and interaction effects?
• RQ5 What is the relationship between the Taylor framework and game-theoretic measures like the Harsanyi dividend?

主な発見

• All fourteen attribution methods can be reformulated as allocations of Taylor independent effects and Taylor interaction effects.
• The generic interaction effect J(S) is equivalent to the Harsanyi dividend H(S).
• Three fidelity principles are proposed to evaluate fair allocation of independent and interaction effects to input variables.
• Several classic methods (e.g., Shapley value, Integrated Gradients, DeepLIFT Rescale) satisfy the fidelity principles.
• A comprehensive mapping table shows how each method fits the unified paradigm by specifying the allocation weights to independent and interaction components.