  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.
