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：我们提出了一种新颖的卷积神经网络架构——真值表网络（$\mathcal{TT}$net），该架构通过设计解决了可解释性、形式化验证和逻辑门转换等公开挑战。$\mathcal{TT}$net 采用与易处理真值表等价的 CNN 滤波器构建，这些滤波器被称为可学习真值表（LTT）模块。LTT 模块的对偶形式使得真值表能够通过梯度下降轻松训练，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，经过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证明了 $\mathcal{TT}$net 的有效性和可扩展性，展示了与决策树相当的可解释性、快速完备/可靠的形式化验证以及可扩展的逻辑门表示能力，均与当前最先进方法进行了对比。我们相信，这项工作朝着使 CNN 在现实关键应用中更加透明和可信迈出了重要一步。