# Sub-bit Neural Networks: Learning to Compress and Accelerate Binary Neural Networks

arXiv: https://arxiv.org/abs/2110.09195 · HTML: https://mlsanity.com/paper/2110.09195/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 42 references that are in the map.
- First posted on arXiv 18 Oct 2021.

## Builds on (most cited first, 30 of 38)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [Once-for-All: Train One Network and Specialize it for Efficient Deployment](https://mlsanity.com/paper/1908.09791/) (2019)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Slimmable Neural Networks](https://mlsanity.com/paper/1812.08928/) (2018)
- [LQ-Nets: Learned Quantization for Highly Accurate and Compact Deep Neural Networks](https://mlsanity.com/paper/1807.10029/) (2018)
- [Universally Slimmable Networks and Improved Training Techniques](https://mlsanity.com/paper/1903.05134/) (2019)
- [Incremental Network Quantization: Towards Lossless CNNs with Low-Precision Weights](https://mlsanity.com/paper/1702.03044/) (2017)
- [Trained Ternary Quantization](https://mlsanity.com/paper/1612.01064/) (2016)
- [Forward and Backward Information Retention for Accurate Binary Neural Networks](https://mlsanity.com/paper/1909.10788/) (2019)
- [Towards Accurate Binary Convolutional Neural Network](https://mlsanity.com/paper/1711.11294/) (2017)
- [Fixed Point Quantization of Deep Convolutional Networks](https://mlsanity.com/paper/1511.06393/) (2015)
- [XNOR-Net++: Improved Binary Neural Networks](https://mlsanity.com/paper/1909.13863/) (2019)
- [Inside-Outside Net: Detecting Objects in Context with Skip Pooling and Recurrent Neural Networks](https://mlsanity.com/paper/1512.04143/) (2015)
- [Rotated Binary Neural Network](https://mlsanity.com/paper/2009.13055/) (2020)

## Built on by (most cited first, 8 of 8)

- [STBLLM: Breaking the 1-Bit Barrier with Structured Binary LLMs](https://mlsanity.com/paper/2408.01803/) (2024)
- [Taming Binarized Neural Networks and Mixed-Integer Programs](https://mlsanity.com/paper/2310.04469/) (2023)
- [Compacting Binary Neural Networks by Sparse Kernel Selection](https://mlsanity.com/paper/2303.14470/) (2023)
- [How to train accurate BNNs for embedded systems?](https://mlsanity.com/paper/2206.12322/) (2022)
- [Binary domain generalization for sparsifying binary neural networks](https://mlsanity.com/paper/2306.13515/) (2023)
- [LOCALUT: Harnessing Capacity-Computation Tradeoffs for LUT-Based Inference in DRAM-PIM](https://mlsanity.com/paper/2604.04523/) (2026)
- [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)

In the low-bit quantization field, training Binary Neural Networks (BNNs) is the extreme solution to ease the deployment of deep models on resource-constrained devices, having the lowest storage cost and significantly cheaper bit-wise operations compared to 32-bit floating-point counterparts. In this paper, we introduce Sub-bit Neural Networks (SNNs), a new type of binary quantization design tailored to compress and accelerate BNNs. SNNs are inspired by an empirical observation, showing that binary kernels learnt at convolutional layers of a BNN model are likely to be distributed over kernel subsets. As a result, unlike existing methods that binarize weights one by one, SNNs are trained with a kernel-aware optimization framework, which exploits binary quantization in the fine-grained convolutional kernel space. Specifically, our method includes a random sampling step generating layer-specific subsets of the kernel space, and a refinement step learning to adjust these subsets of binary kernels via optimization. Experiments on visual recognition benchmarks and the hardware deployment on FPGA validate the great potentials of SNNs. For instance, on ImageNet, SNNs of ResNet-18/ResNet-34 with 0.56-bit weights achieve 3.13/3.33 times runtime speed-up and 1.8 times compression over conventional BNNs with moderate drops in recognition accuracy. Promising results are also obtained when applying SNNs to binarize both weights and activations. Our code is available at https://github.com/yikaiw/SNN.