# FleXOR: Trainable Fractional Quantization

arXiv: https://arxiv.org/abs/2009.04126 · HTML: https://mlsanity.com/paper/2009.04126/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2020.

## Built on by (most cited first, 9 of 9)

- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Bitwidth Heterogeneous Federated Learning with Progressive Weight Dequantization](https://mlsanity.com/paper/2202.11453/) (2022)
- [Sub-bit Neural Networks: Learning to Compress and Accelerate Binary Neural Networks](https://mlsanity.com/paper/2110.09195/) (2021)
- [Compacting Binary Neural Networks by Sparse Kernel Selection](https://mlsanity.com/paper/2303.14470/) (2023)
- [ATHEENA: A Toolflow for Hardware Early-Exit Network Automation](https://mlsanity.com/paper/2304.08400/) (2023)
- [LegoNet: Memory Footprint Reduction Through Block Weight Clustering](https://mlsanity.com/paper/2603.06606/) (2026)
- [Q-Rater: Non-Convex Optimization for Post-Training Uniform Quantization](https://mlsanity.com/paper/2105.01868/) (2021)
- [MST-compression: Compressing and Accelerating Binary Neural Networks with Minimum Spanning Tree](https://mlsanity.com/paper/2308.13735/) (2023)
- [Tiled Bit Networks: Sub-Bit Neural Network Compression Through Reuse of Learnable Binary Vectors](https://mlsanity.com/paper/2407.12075/) (2024)

## Abstract (arXiv)

Quantization based on the binary codes is gaining attention because each quantized bit can be directly utilized for computations without dequantization using look-up tables. Previous attempts, however, only allow for integer numbers of quantization bits, which ends up restricting the search space for compression ratio and accuracy. In this paper, we propose an encryption algorithm/architecture to compress quantized weights so as to achieve fractional numbers of bits per weight. Decryption during inference is implemented by digital XOR-gate networks added into the neural network model while XOR gates are described by utilizing tanh(x) for backward propagation to enable gradient calculations. We perform experiments using MNIST, CIFAR-10, and ImageNet to show that inserting XOR gates learns quantization/encrypted bit decisions through training and obtains high accuracy even for fractional sub 1-bit weights. As a result, our proposed method yields smaller size and higher model accuracy compared to binary neural networks.