Neural QBAFs: Explaining Neural Networks Under LRP-Based Argumentation Frameworks

Abstract

In recent years, there have been many attempts to combine XAI with the field of symbolic AI in order to generate explanations for neural networks that are more interpretable and better align with human reasoning, with one prominent candidate for this synergy being the sub-field of computational argumentation. One method is to represent neural networks with quantitative bipolar argumentation frameworks (QBAFs) equipped with a particular semantics. The resulting QBAF can then be viewed as an explanation for the associated neural network. In this paper, we explore a novel LRP-based semantics under a new QBAF variant, namely neural QBAFs (nQBAFs). Since an nQBAF of a neural network is typically large, the nQBAF must be simplified before being used as an explanation. Our empirical evaluation indicates that the manner of this simplification is all important for the quality of the resulting explanation.

Appendix: Lemmas for Dialectical Properties Proofs

Lemma 1

Any attacking argument has a negative strength.

$\forall a \in A [\exists x \in \mathcal {P}(A)[a \in Att(x)] \rightarrow \sigma (a) < 0]$

Proof

Take arbitrary $a \in A$. Assume there exists some $x \in \mathcal {P}(A)$ such that $a \in Att(x)$. Since $a \in Att(x)$, $(a, x) \in Att$ so $c_-(a, x)$ is true, meaning $R_{\rho (a) \leftarrow \rho (x)} < 0$. As $\sigma (a) = R_{\rho (a) \leftarrow \rho (x)}$ by Definition 7, then $\sigma (a) < 0$.    $\square$

Lemma 2

Any supporting argument has a positive strength.

$\forall a \in A [\exists x \in \mathcal {P}(A)[a \in Supp(x)] \rightarrow \sigma (a) > 0]$

Proof

Take arbitrary $a \in A$. Assume there exists some $x \in \mathcal {P}(A)$ such that $a \in Supp(x)$. Since $a \in Supp(x)$, $(a, x) \in Supp$ so $c_+(a, x)$ is true, meaning $R_{\rho (a) \leftarrow \rho (x)} > 0$. As $\sigma (a) = R_{\rho (a) \leftarrow \rho (x)}$ by Definition 7, then $\sigma (a) > 0$.    $\square$

Lemma 3

Any argument that neither supports nor attacks any group and does not represent an output node has zero strength.

$\forall a \in A [\forall x \in \mathcal {P}(A)[(a, x) \notin Supp \wedge (a, x) \notin Att] \wedge \rho (a) \notin V_{d+1} \rightarrow \sigma (a) = 0]$

Proof

This proposition follows immediately from Definition 7.    $\square$