We propose $\mathcal{T}$ruth $\mathcal{T}$able net ($\mathcal{TT}$net), a novel Convolutional Neural Network (CNN) architecture that addresses, by design, the open challenges of interpretability, formal verification, and logic gate conversion. $\mathcal{TT}$net is built using CNNs' filters that are equivalent to tractable truth tables and that we call Learning Truth Table (LTT) blocks. The dual form of LTT blocks allows the truth tables to be easily trained with gradient descent and makes these CNNs easy to interpret, verify and infer. Specifically, $\mathcal{TT}$net is a deep CNN model that can be automatically represented, after post-training transformation, as a sum of Boolean decision trees, or as a sum of Disjunctive/Conjunctive Normal Form (DNF/CNF) formulas, or as a compact Boolean logic circuit. We demonstrate the effectiveness and scalability of $\mathcal{TT}$net on multiple datasets, showing comparable interpretability to decision trees, fast complete/sound formal verification, and scalable logic gate representation, all compared to state-of-the-art methods. We believe this work represents a step towards making CNNs more transparent and trustworthy for real-world critical applications.

翻译：我们提出$\mathcal{T}$ruth $\mathcal{T}$able net（$\mathcal{TT}$net），一种新型卷积神经网络（CNN）架构，其设计旨在解决可解释性、形式化验证和逻辑门转换等公开挑战。$\mathcal{TT}$net采用与可处理真值表等价的CNN滤波器构建，我们称其为学习真值表（LTT）模块。LTT模块的对偶形式使得真值表易于通过梯度下降训练，并使这些CNN易于解释、验证和推理。具体而言，$\mathcal{TT}$net是一种深度CNN模型，在训练后变换可自动表示为布尔决策树之和、析取/合取范式（DNF/CNF）公式之和或紧凑布尔逻辑电路。我们在多个数据集上展示了$\mathcal{TT}$net的有效性和可扩展性，与最先进方法相比，其均表现出与决策树相当的可解释性、快速完全/可靠的形式化验证以及可扩展的逻辑门表示。我们相信，这项工作是推动CNN在现实关键应用中更加透明可信的重要一步。