# Boolean Variation and Boolean Logic BackPropagation

arXiv: https://arxiv.org/abs/2311.07427 · HTML: https://mlsanity.com/paper/2311.07427/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 66 references that are in the map.
- First posted on arXiv 13 Nov 2023.

## Builds on (most cited first, 30 of 31)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [Efficient Processing of Deep Neural Networks: A Tutorial and Survey](https://mlsanity.com/paper/1703.09039/) (2017)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Deep Learning with Limited Numerical Precision](https://mlsanity.com/paper/1502.02551/) (2015)
- [A Survey of Model Compression and Acceleration for Deep Neural Networks](https://mlsanity.com/paper/1710.09282/) (2017)
- [LQ-Nets: Learned Quantization for Highly Accurate and Compact Deep Neural Networks](https://mlsanity.com/paper/1807.10029/) (2018)
- [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)
- [ReActNet: Towards Precise Binary Neural Network with Generalized Activation Functions](https://mlsanity.com/paper/2003.03488/) (2020)
- [Designing Energy-Efficient Convolutional Neural Networks using Energy-Aware Pruning](https://mlsanity.com/paper/1611.05128/) (2016)
- [AdderNet: Do We Really Need Multiplications in Deep Learning?](https://mlsanity.com/paper/1912.13200/) (2019)
- [Latent Weights Do Not Exist: Rethinking Binarized Neural Network Optimization](https://mlsanity.com/paper/1906.02107/) (2019)
- [A Statistical Framework for Low-bitwidth Training of Deep Neural Networks](https://mlsanity.com/paper/2010.14298/) (2020)
- [PokeBNN: A Binary Pursuit of Lightweight Accuracy](https://mlsanity.com/paper/2112.00133/) (2021)
- [Learnable Companding Quantization for Accurate Low-bit Neural Networks](https://mlsanity.com/paper/2103.07156/) (2021)
- [Subdominant Dense Clusters Allow for Simple Learning and High Computational Performance in Neural Networks with Discrete Synapses](https://mlsanity.com/paper/1509.05753/) (2015)
- [Interstellar: Using Halide's Scheduling Language to Analyze DNN Accelerators](https://mlsanity.com/paper/1809.04070/) (2018)
- [Circulant Binary Convolutional Networks: Enhancing the Performance of 1-bit DCNNs with Circulant Back Propagation](https://mlsanity.com/paper/1910.10853/) (2019)
- [F8Net: Fixed-Point 8-bit Only Multiplication for Network Quantization](https://mlsanity.com/paper/2202.05239/) (2022)
- [Accurate Neural Training with 4-bit Matrix Multiplications at Standard Formats](https://mlsanity.com/paper/2112.10769/) (2021)
- [Join the High Accuracy Club on ImageNet with A Binary Neural Network Ticket](https://mlsanity.com/paper/2211.12933/) (2022)
- [A Max-Sum algorithm for training discrete neural networks](https://mlsanity.com/paper/1505.05401/) (2015)
- [All-You-Can-Fit 8-Bit Flexible Floating-Point Format for Accurate and Memory-Efficient Inference of Deep Neural Networks](https://mlsanity.com/paper/2104.07329/) (2021)
- [Towards Efficient Full 8-bit Integer DNN Online Training on Resource-limited Devices without Batch Normalization](https://mlsanity.com/paper/2105.13890/) (2021)
- [Neural Network Training on In-memory-computing Hardware with Radix-4 Gradients](https://mlsanity.com/paper/2203.04821/) (2022)

## Built on by (most cited first, 2 of 2)

- [BOLD: Boolean Logic Deep Learning](https://mlsanity.com/paper/2405.16339/) (2024)
- [Boolean Logic as an Error feedback mechanism](https://mlsanity.com/paper/2401.16418/) (2024)

## Abstract (arXiv)

The notion of variation is introduced for the Boolean set and based on which Boolean logic backpropagation principle is developed. Using this concept, deep models can be built with weights and activations being Boolean numbers and operated with Boolean logic instead of real arithmetic. In particular, Boolean deep models can be trained directly in the Boolean domain without latent weights. No gradient but logic is synthesized and backpropagated through layers.