# A Scalable, Interpretable, Verifiable & Differentiable Logic Gate Convolutional Neural Network Architecture From Truth Tables

arXiv: https://arxiv.org/abs/2208.08609 · HTML: https://mlsanity.com/paper/2208.08609/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 116 references that are in the map.
- First posted on arXiv 18 Aug 2022.

## Builds on (most cited first, 30 of 53)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [On Evaluating Adversarial Robustness](https://mlsanity.com/paper/1902.06705/) (2019)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Certified Defenses against Adversarial Examples](https://mlsanity.com/paper/1801.09344/) (2018)
- [A Survey on Neural Network Interpretability](https://mlsanity.com/paper/2012.14261/) (2020)
- [Approximating CNNs with Bag-of-local-Features models works surprisingly well on ImageNet](https://mlsanity.com/paper/1904.00760/) (2019)
- [Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks](https://mlsanity.com/paper/1705.01320/) (2017)
- [Bi-Real Net: Enhancing the Performance of 1-bit CNNs With Improved Representational Capability and Advanced Training Algorithm](https://mlsanity.com/paper/1808.00278/) (2018)
- [Towards Stable and Efficient Training of Verifiably Robust Neural Networks](https://mlsanity.com/paper/1906.06316/) (2019)
- [Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers](https://mlsanity.com/paper/2011.13824/) (2020)
- [A guide to convolution arithmetic for deep learning](https://mlsanity.com/paper/1603.07285/) (2016)
- [Scaling provable adversarial defenses](https://mlsanity.com/paper/1805.12514/) (2018)
- [An approach to reachability analysis for feed-forward ReLU neural networks](https://mlsanity.com/paper/1706.07351/) (2017)
- [Maximum Resilience of Artificial Neural Networks](https://mlsanity.com/paper/1705.01040/) (2017)

## Built on by (most cited first, 4 of 4)

- [Convolutional Differentiable Logic Gate Networks](https://mlsanity.com/paper/2411.04732/) (2024)
- [eXpLogic: Explaining Logic Types and Patterns in DiffLogic Networks](https://mlsanity.com/paper/2503.09910/) (2025)
- [Learning Compact Boolean Networks](https://mlsanity.com/paper/2602.05830/) (2026)
- [Overcoming Kernel Redundancy for Scaling Logic Gate Networks](https://mlsanity.com/paper/2610.01069/) (2026)

## Abstract (arXiv)

We propose Truth Table net (TTnet), a novel Convolutional Neural Network (CNN) architecture that addresses, by design, the open challenges of interpretability, formal verification, and logic gate conversion. TTnet 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, TTnet 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 TTnet 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.