用逻辑语言查询神经网络，揭示模型内部的可解释性机制
Query Languages for Machine-Learning Models
- 用带求和的一阶逻辑及递归扩展表达神经网络查询
- 证明该逻辑能精准刻画神经网络的计算行为与表达能力
- 适合研究模型可解释性与形式化推理的学者
本文探讨两种用于加权有限结构的逻辑：带求和的一阶逻辑（FO(SUM)）及其递归扩展IFP(SUM)，其根源可追溯至Grädel、Gurevich与Meer在1990年代的奠基性工作。在与Standke、Steegmans及Van den Bussche的近期合作中，我们研究了这些逻辑作为机器学习模型（特别是神经网络）的查询语言的潜力，神经网络天然可表示为加权图。文中展示了若干可在这些逻辑中表达的神经网络查询示例，并讨论了其表达力与计算复杂性的基本结果。
原文摘要 · Abstract (English)
In this paper, I discuss two logics for weighted finite structures: first-order logic with summation (FO(SUM)) and its recursive extension IFP(SUM). These logics originate from foundational work by Grädel, Gurevich, and Meer in the 1990s. In recent joint work with Standke, Steegmans, and Van den Bussche, we have investigated these logics as query languages for machine learning models, specifically neural networks, which are naturally represented as weighted graphs. I present illustrative examples of queries to neural networks that can be expressed in these logics and discuss fundamental results on their expressiveness and computational complexity.
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