---
title: "DoReFa-Net — paper by Zhou et al. (2016) — summary and ideas"
description: "Large CNNs are costly to train and deploy. 93% accuracy. 29 references, cited by 140 papers here."
authors: ["Shuchang Zhou", "Yuxin Wu", "Zekun Ni", "Xinyu Zhou", "He Wen", "Yuheng Zou"]
year: 2016
venue: "arXiv:1606.06160"
source: "https://arxiv.org/abs/1606.06160"
doi: "10.48550/arxiv.1606.06160"
arxiv: "1606.06160"
licence: "arXiv — non-exclusive license to distribute"
licence_url: "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/zhou-2016-dorefa-net-training-low-bitwidth/"
---
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# DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients

**Authors:** Shuchang Zhou, [Yuxin Wu](https://md.research.elamur.ai/free/en/authors/yuxin-wu/), Zekun Ni, [Xinyu Zhou](https://md.research.elamur.ai/free/en/authors/xinyu-zhou/), He Wen and Yuheng Zou · **Year:** 2016 · **Venue:** arXiv:1606.06160 · **Licence:** [arXiv — non-exclusive license to distribute](http://arxiv.org/licenses/nonexclusive-distrib/1.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/1606.06160) · [PDF](https://arxiv.org/pdf/1606.06160) · [DOI 10.48550/arxiv.1606.06160](https://doi.org/10.48550/arxiv.1606.06160) · [arXiv 1606.06160](https://arxiv.org/abs/1606.06160) · [OpenAlex](https://openalex.org/W2469490737)

**Citations:** 1,622 citations (OpenAlex, 2026-10-14) · [140](https://md.research.elamur.ai/free/en/papers/zhou-2016-dorefa-net-training-low-bitwidth/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Large CNNs are costly to train and deploy. Earlier binarized models such as BNN and XNOR-Net reduced cost only in the forward pass. Their gradients stayed in full precision, so backpropagation still needed expensive floating-point convolutions. DoReFa-Net, from Megvii, generalizes binarization so that weights, activations and parameter gradients can each have an arbitrary low bitwidth. A dot product of low-bit fixed-point numbers can be split into bitwise AND and bitcount operations, with cost proportional to the product of the two bitwidths. This means bit convolution kernels on CPU, GPU, FPGA or ASIC could speed up both training and inference. Every quantizer is wrapped in a straight-through estimator. Weights are squashed with tanh, normalized by their maximum and rounded deterministically. Activations are bounded to [0, 1] and rounded. Gradients are rescaled per instance and quantized stochastically with added uniform noise. On SVHN and ImageNet the resulting networks come close to 32-bit baselines. An AlexNet variant with 1-bit weights, 2-bit activations and 6-bit gradients reaches 46.1% top-1. This suggests that cheap, energy-efficient low-bit training is feasible.

## Key points
- The AlexNet-derived DoReFa-Net with 1-bit weights, 2-bit activations and 6-bit gradients is trained from scratch. It achieves 46.1% single-crop top-1 accuracy on the ILSVRC12 validation set.
- The model is released in TensorFlow format in the tensorpack repository, together with a reference training implementation for SVHN.
- On SVHN, a configuration with 1-bit weights, 1-bit activations and 2-bit gradients reaches about 93% accuracy.
- Gradients are the most sensitive to bitwidth, activations are less sensitive, and weights are the least. The method's name was chosen to reflect this ordering.
- The authors state that no earlier work had quantized gradients below 8 bits while keeping accuracy comparable; prior low-precision training used convolutions with at least 10-bit numbers.
- Binary weights are scaled by one constant shared across all filters, rather than XNOR-Net's per-channel factors. This keeps bit kernels usable when gradients are convolved with weights. The authors could not reproduce XNOR-Net's activation binarization results.

## Interesting ideas
- **Straight-through estimator as a general tool:** the forward pass can apply any discrete operation, such as rounding or sampling, while the backward pass uses a hand-chosen surrogate gradient. This pattern could help in any pipeline with non-differentiable steps.
- **Bit-plane decomposition of dot products:** a multi-bit integer product becomes a weighted sum of 1-bit AND/bitcount products. Compute cost then scales directly with the bitwidths, which gives a tunable trade-off between precision and speed.
- **Different quantization for different tensors:** weights and activations can be rounded deterministically. Gradients, however, needed stochastic rounding plus uniform noise matched to the quantization step size. This is a useful lesson for anyone compressing gradients, for example to reduce communication in distributed training.
- **Normalize unbounded tensors before quantizing:** gradients are mapped into [0, 1] using a per-instance maximum, quantized, and then mapped back. Weights are first bounded with tanh. This is a simple recipe for quantizing values whose range is unknown in advance.
- **Check the whole pipeline when designing compression:** the authors dropped per-channel scaling because it would break bit kernels in the backward pass. This is a reminder that a compression scheme should be evaluated for training as well as inference, and that sweeping bitwidths separately for each component shows where precision really matters.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

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## Cite

Cite as: Shuchang Zhou, Yuxin Wu, Zekun Ni, Xinyu Zhou, He Wen and Yuheng Zou. 2016. DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients. arXiv:1606.06160.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{zhou2016dorefa,
  title = {{DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients}},
  author = {Shuchang Zhou, Yuxin Wu, Zekun Ni, Xinyu Zhou, He Wen and Yuheng Zou},
  year = {2016},
  doi = {10.48550/arxiv.1606.06160},
  eprint = {1606.06160},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.1606.06160}
}
```

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*Updated 2 November 2026*