---
title: "XNOR-Net — paper by Rastegari et al. (2016)"
description: "The authors propose two binary approximations of standard architectures, trained from scratch… 44 references, cited by 206 papers here."
authors: ["Mohammad Rastegari", "Vicente Ordonez", "Joseph Redmon", "Ali Farhadi"]
year: 2016
venue: "arXiv:1603.05279"
source: "https://arxiv.org/abs/1603.05279"
doi: "10.48550/arxiv.1603.05279"
arxiv: "1603.05279"
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/rastegari-2016-xnor-net-imagenet-classification-using/"
---
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# XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks

**Authors:** [Mohammad Rastegari](https://md.research.elamur.ai/free/en/authors/mohammad-rastegari/), [Vicente Ordonez](https://md.research.elamur.ai/free/en/authors/vicente-ordonez/), Joseph Redmon and [Ali Farhadi](https://md.research.elamur.ai/free/en/authors/ali-farhadi/) · **Year:** 2016 · **Venue:** [arXiv:1603.05279](https://md.research.elamur.ai/free/en/venues/lecture-notes-in-computer-science/) ([Lecture notes in computer science 2016](https://md.research.elamur.ai/free/en/venues/lecture-notes-in-computer-science/2016/)) · **Publisher:** [Springer Science+Business Media](https://md.research.elamur.ai/free/en/publishers/springer-science-business-media/) · **Licence:** [arXiv — non-exclusive license to distribute](http://arxiv.org/licenses/nonexclusive-distrib/1.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/1603.05279) · [PDF](https://arxiv.org/pdf/1603.05279) · [DOI 10.48550/arxiv.1603.05279](https://doi.org/10.48550/arxiv.1603.05279) · [arXiv 1603.05279](https://arxiv.org/abs/1603.05279) · [OpenAlex](https://openalex.org/W2300242332)

**Citations:** 4,196 citations (OpenAlex, 2026-10-14) · [206](https://md.research.elamur.ai/free/en/papers/rastegari-2016-xnor-net-imagenet-classification-using/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Modern CNNs demand far more memory and compute than phones or embedded hardware can supply. AlexNet, for example, needs about 249MB and roughly 1.5B high-precision operations per image. The authors propose two binary approximations of standard architectures, trained from scratch rather than compressed after pretraining. Binary-Weight-Networks (BWN) restrict filters to +1/−1 times a per-filter scaling factor, which cuts memory about 32× and turns convolutions into additions and subtractions. XNOR-Networks also binarize the inputs to convolutional layers, so convolutions reduce mostly to XNOR and bit-counting. That gives roughly 58× fewer high-precision operations and makes real-time inference on CPUs plausible. They evaluate on ImageNet (ILSVRC2012) with AlexNet, ResNet-18 and a GoogLenet variant. BWN AlexNet matches the full-precision model's accuracy, and both variants beat BinaryConnect and BinaryNet by more than 16% top-1. The work matters because it was the first evaluation of binarized networks at ImageNet scale, and it showed that extreme quantization need not destroy accuracy on hard tasks.

## Key points
- **Efficiency claims:** ~32× memory saving for both variants. Binary weights alone give ~2× speedup, while XNOR-Net gives ~58× fewer high-precision operations.
- **Comparison with prior binarization:** on ILSVRC2012 the method beats BinaryNet by 16.3% top-1, and it stays ahead of BC and BNN by roughly 17% across all training epochs.
- **ResNet-18 results (top-1/top-5):**
  - BWN: 60.8/83.0
  - XNOR-Net: 51.2/73.2
  - Full precision: 69.3/89.2
- **GoogLenet variant results (top-1/top-5):** BWN reaches 65.5/86.1 versus 71.3/90.0 for full precision. This variant has 21 plain convolutional layers and no branching.
- **Ablations:**
  - Computing α analytically gives 56.8 top-1, versus 46.2 when α is a learned layer.
  - Reordering the block from C-B-A-P to B-A-C-P lifts XNOR-Net top-1 from 30.3 to 44.2.
  - Dropping the input scaling β costs under 1% top-1.
  - Binary gradients cost only 1.4% top-1.

## Interesting ideas
- **Analytic scaling instead of learned scaling:** pairing binary values with a per-filter magnitude derived in closed form each training iteration worked much better than letting the network learn that scalar. The same move could help other extreme-quantization settings, such as compressing embedding or transformer weights for on-device NLP models.
- **Layer order as a quantization lever:** placing normalization and binarization before the convolution cut the information lost to quantization and gave a large accuracy jump. When compressing any architecture, block ordering is worth testing, not just bit-width.
- **Real-valued shadow weights:** full-precision weights are kept and updated during training, while binarized copies are used in the forward pass. This is a simple, general recipe for training models that must run in low precision at deployment.
- **Pruning cheap-to-remove components via ablation:** the input scaling factor contributed little accuracy, so it can be dropped for extra speed. Measuring each approximation component separately shows which ones are worth their cost.
- **Counting high-precision operations as the cost metric:** reporting savings this way, rather than only wall-clock time, gives a hardware-independent cost measure. It is useful for comparing compressed models across different deployment targets.

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

## Institutions

- [University of Washington](https://md.research.elamur.ai/free/en/universities/university-of-washington/) — University, Seattle, United States · 402 works · 212,763 citations
- [Allen Institute for Artificial Intelligence](https://md.research.elamur.ai/free/en/labs/allen-institute-for-artificial-intelligence/) — Research institute, Seattle, United States · 304 works · 106,137 citations

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## Cite

Cite as: Mohammad Rastegari, Vicente Ordonez, Joseph Redmon and Ali Farhadi. 2016. XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks. arXiv:1603.05279.

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

```bibtex
@misc{rastegari2016xnor,
  title = {{XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks}},
  author = {Mohammad Rastegari, Vicente Ordonez, Joseph Redmon and Ali Farhadi},
  year = {2016},
  doi = {10.48550/arxiv.1603.05279},
  eprint = {1603.05279},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.1603.05279}
}
```

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## References

44 references, 7 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. Krizhevsky, A., Sutskever, I., Hinton, G.E.: [Imagenet classification with deep convolutional neural networks](https://md.research.elamur.ai/free/en/papers/krizhevsky-2012-imagenet-classification-deep-convolutional/). In: Advances in neural information processing systems. (2012) 1097–1105 1, 10, 11, 12
2. Simonyan, K., Zisserman, A.: [Very deep convolutional networks for large-scale image recognition](https://md.research.elamur.ai/free/en/papers/simonyan-2014-very-deep-convolutional-networks-large/). arXiv preprint arXiv:1409.1556 (2014) 1
3. Szegedy, C., Liu, W., Jia, Y., Sermanet, P., Reed, S., Anguelov, D., Erhan, D., Vanhoucke, V., Rabinovich, A.: Going deeper with convolutions. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. (2015) 1–9 1, 4, 11, 13 [find](https://scholar.google.com/scholar?q=Szegedy%2C+C%2E%2C+Liu%2C+W%2E%2C+Jia%2C+Y%2E%2C+Sermanet%2C+P%2E%2C+Reed%2C+S%2E%2C+Anguelov%2C+D%2E%2C+Erhan%2C+D%2E%2C+Vanhoucke%2C+V%2E%2C+Rabinovich%2C+A%2E%3A+Going+deeper+with+convolutions%2E+In%3A+Proceedings+of+the+IEEE+Conference+on+Computer+Vision)
4. He, K., Zhang, X., Ren, S., Sun, J.: [Deep residual learning for image recognition](https://md.research.elamur.ai/free/en/papers/he-2015-deep-residual-learning-image-recognition/). CoRR (2015) 1, 4, 10, 11, 12
5. Girshick, R., Donahue, J., Darrell, T., Malik, J.: [Rich feature hierarchies for accurate object detection and semantic segmentation](https://md.research.elamur.ai/free/en/papers/girshick-2013-rich-feature-hierarchies-accurate-object/). In: Proceedings of the IEEE conference on computer vision and pattern recognition. (2014) 580–587 1
6. Girshick, R.: Fast r-cnn. In: Proceedings of the IEEE International Conference on Computer Vision. (2015) 1440–1448 1 [find](https://scholar.google.com/scholar?q=Girshick%2C+R%2E%3A+Fast+r%2Dcnn%2E+In%3A+Proceedings+of+the+IEEE+International+Conference+on+Computer+Vision%2E+%282015%29+1440%E2%80%931448+1)
7. Ren, S., He, K., Girshick, R., Sun, J.: [Faster r-cnn: Towards real-time object detection with region proposal networks](https://md.research.elamur.ai/free/en/papers/ren-2015-faster-r-cnn-towards-real/). In: Advances in Neural Information Processing Systems. (2015) 91–99 1
8. Oculus, V.: Oculus rift-virtual reality headset for 3d gaming. URL: [http://www.oculusvr](http://www.oculusvr). com (2012) 1 [↗](http://www.oculusvr)
9. Gottmer, M.: Merging reality and virtuality with microsoft hololens. (2015) 1 [find](https://scholar.google.com/scholar?q=Gottmer%2C+M%2E%3A+Merging+reality+and+virtuality+with+microsoft+hololens%2E+%282015%29+1)
10. Long, J., Shelhamer, E., Darrell, T.: Fully convolutional networks for semantic segmentation. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. (2015) 3431–3440 2 [find](https://scholar.google.com/scholar?q=Long%2C+J%2E%2C+Shelhamer%2C+E%2E%2C+Darrell%2C+T%2E%3A+Fully+convolutional+networks+for+semantic+segmentation%2E+In%3A+Proceedings+of+the+IEEE+Conference+on+Computer+Vision+and+Pattern+Recognition%2E+%282015%29+3431%E2%80%933440+2)
11. Courbariaux, M., Bengio, Y.: Binarynet: Training deep neural networks with weights and activations constrained to +1 or -1. CoRR (2016) 2, 3, 4, 6, 7, 10, 11, 12 [find](https://scholar.google.com/scholar?q=Courbariaux%2C+M%2E%2C+Bengio%2C+Y%2E%3A+Binarynet%3A+Training+deep+neural+networks+with+weights+and+activations+constrained+to+%2B1+or+%2D1%2E+CoRR+%282016%29+2%2C+3%2C+4%2C+6%2C+7%2C+10%2C+11%2C+12)
12. Denil, M., Shakibi, B., Dinh, L., de Freitas, N., et al.: Predicting parameters in deep learning. In: Advances in Neural Information Processing Systems. (2013) 2148–2156 3 [find](https://scholar.google.com/scholar?q=Denil%2C+M%2E%2C+Shakibi%2C+B%2E%2C+Dinh%2C+L%2E%2C+de+Freitas%2C+N%2E%2C+et+al%2E%3A+Predicting+parameters+in+deep+learning%2E+In%3A+Advances+in+Neural+Information+Processing+Systems%2E+%282013%29+2148%E2%80%932156+3)
13. Cybenko, G.: Approximation by superpositions of a sigmoidal function. Mathematics of control, signals and systems 2(4) (1989) 303–314 3 [find](https://scholar.google.com/scholar?q=Cybenko%2C+G%2E%3A+Approximation+by+superpositions+of+a+sigmoidal+function%2E+Mathematics+of+control%2C+signals+and+systems+2%284%29+%281989%29+303%E2%80%93314+3)
14. Seide, F., Li, G., Yu, D.: Conversational speech transcription using context-dependent deep neural networks. In: Interspeech. (2011) 437–440 3 [find](https://scholar.google.com/scholar?q=Seide%2C+F%2E%2C+Li%2C+G%2E%2C+Yu%2C+D%2E%3A+Conversational+speech+transcription+using+context%2Ddependent+deep+neural+networks%2E+In%3A+Interspeech%2E+%282011%29+437%E2%80%93440+3)
15. Dauphin, Y.N., Bengio, Y.: Big neural networks waste capacity. arXiv preprint arXiv:1301.3583 (2013) 3 — [arXiv:1301.3583](https://arxiv.org/abs/1301.3583) [find](https://scholar.google.com/scholar?q=Dauphin%2C+Y%2EN%2E%2C+Bengio%2C+Y%2E%3A+Big+neural+networks+waste+capacity%2E+arXiv+preprint+arXiv%3A1301%2E3583+%282013%29+3+%E2%80%94+%5BarXiv%3A1301%2E3583%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F1301%2E3583%29)
16. Ba, J., Caruana, R.: Do deep nets really need to be deep? In: Advances in neural information processing systems. (2014) 2654–2662 3 [find](https://scholar.google.com/scholar?q=Ba%2C+J%2E%2C+Caruana%2C+R%2E%3A+Do+deep+nets+really+need+to+be+deep%3F+In%3A+Advances+in+neural+information+processing+systems%2E+%282014%29+2654%E2%80%932662+3)
17. Hanson, S.J., Pratt, L.Y.: Comparing biases for minimal network construction with backpropagation. In: Advances in neural information processing systems. (1989) 177–185 3 [find](https://scholar.google.com/scholar?q=Hanson%2C+S%2EJ%2E%2C+Pratt%2C+L%2EY%2E%3A+Comparing+biases+for+minimal+network+construction+with+backpropagation%2E+In%3A+Advances+in+neural+information+processing+systems%2E+%281989%29+177%E2%80%93185+3)
18. LeCun, Y., Denker, J.S., Solla, S.A., Howard, R.E., Jackel, L.D.: Optimal brain damage. In: NIPs. Volume 89. (1989) 3 [find](https://scholar.google.com/scholar?q=LeCun%2C+Y%2E%2C+Denker%2C+J%2ES%2E%2C+Solla%2C+S%2EA%2E%2C+Howard%2C+R%2EE%2E%2C+Jackel%2C+L%2ED%2E%3A+Optimal+brain+damage%2E+In%3A+NIPs%2E+Volume+89%2E+%281989%29+3)
19. Hassibi, B., Stork, D.G.: Second order derivatives for network pruning: Optimal brain surgeon. Morgan Kaufmann (1993) 3 [find](https://scholar.google.com/scholar?q=Hassibi%2C+B%2E%2C+Stork%2C+D%2EG%2E%3A+Second+order+derivatives+for+network+pruning%3A+Optimal+brain+surgeon%2E+Morgan+Kaufmann+%281993%29+3)
20. Han, S., Pool, J., Tran, J., Dally, W.: Learning both weights and connections for efficient neural network. In: Advances in Neural Information Processing Systems. (2015) 1135–1143 3 [find](https://scholar.google.com/scholar?q=Han%2C+S%2E%2C+Pool%2C+J%2E%2C+Tran%2C+J%2E%2C+Dally%2C+W%2E%3A+Learning+both+weights+and+connections+for+efficient+neural+network%2E+In%3A+Advances+in+Neural+Information+Processing+Systems%2E+%282015%29+1135%E2%80%931143+3)
21. Van Nguyen, H., Zhou, K., Vemulapalli, R.: Cross-domain synthesis of medical images using efficient location-sensitive deep network. In: Medical Image Computing and Computer-Assisted Intervention–MICCAI 2015. Springer (2015) 677–684 3 [find](https://scholar.google.com/scholar?q=Van+Nguyen%2C+H%2E%2C+Zhou%2C+K%2E%2C+Vemulapalli%2C+R%2E%3A+Cross%2Ddomain+synthesis+of+medical+images+using+efficient+location%2Dsensitive+deep+network%2E+In%3A+Medical+Image+Computing+and+Computer%2DAssisted+Intervention%E2%80%93MICC)
22. Han, S., Mao, H., Dally, W.J.: Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding. arXiv preprint arXiv:1510.00149 (2015) 3 [find](https://scholar.google.com/scholar?q=Han%2C+S%2E%2C+Mao%2C+H%2E%2C+Dally%2C+W%2EJ%2E%3A+Deep+compression%3A+Compressing+deep+neural+networks+with+pruning%2C+trained+quantization+and+huffman+coding%2E+arXiv+preprint+arXiv%3A1510%2E00149+%282015%29+3)
23. Chen, W., Wilson, J.T., Tyree, S., Weinberger, K.Q., Chen, Y.: Compressing neural networks with the hashing trick. arXiv preprint arXiv:1504.04788 (2015) 3 — [arXiv:1504.04788](https://arxiv.org/abs/1504.04788) [find](https://scholar.google.com/scholar?q=Chen%2C+W%2E%2C+Wilson%2C+J%2ET%2E%2C+Tyree%2C+S%2E%2C+Weinberger%2C+K%2EQ%2E%2C+Chen%2C+Y%2E%3A+Compressing+neural+networks+with+the+hashing+trick%2E+arXiv+preprint+arXiv%3A1504%2E04788+%282015%29+3+%E2%80%94+%5BarXiv%3A1504%2E04788%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F1)
24. Denton, E.L., Zaremba, W., Bruna, J., LeCun, Y., Fergus, R.: Exploiting linear structure within convolutional networks for efficient evaluation. In: Advances in Neural Information Processing Systems. (2014) 1269–1277 3 [find](https://scholar.google.com/scholar?q=Denton%2C+E%2EL%2E%2C+Zaremba%2C+W%2E%2C+Bruna%2C+J%2E%2C+LeCun%2C+Y%2E%2C+Fergus%2C+R%2E%3A+Exploiting+linear+structure+within+convolutional+networks+for+efficient+evaluation%2E+In%3A+Advances+in+Neural+Information+Processing+Systems%2E+)
25. Jaderberg, M., Vedaldi, A., Zisserman, A.: Speeding up convolutional neural networks with low rank expansions. arXiv preprint arXiv:1405.3866 (2014) 3 [find](https://scholar.google.com/scholar?q=Jaderberg%2C+M%2E%2C+Vedaldi%2C+A%2E%2C+Zisserman%2C+A%2E%3A+Speeding+up+convolutional+neural+networks+with+low+rank+expansions%2E+arXiv+preprint+arXiv%3A1405%2E3866+%282014%29+3)
26. Lin, M., Chen, Q., Yan, S.: Network in network. arXiv preprint arXiv:1312.4400 (2013) 4 — [arXiv:1312.4400](https://arxiv.org/abs/1312.4400) [find](https://scholar.google.com/scholar?q=Lin%2C+M%2E%2C+Chen%2C+Q%2E%2C+Yan%2C+S%2E%3A+Network+in+network%2E+arXiv+preprint+arXiv%3A1312%2E4400+%282013%29+4+%E2%80%94+%5BarXiv%3A1312%2E4400%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F1312%2E4400%29)
27. Szegedy, C., Ioffe, S., Vanhoucke, V.: Inception-v4, inception-resnet and the impact of residual connections on learning. CoRR (2016) 4 [find](https://scholar.google.com/scholar?q=Szegedy%2C+C%2E%2C+Ioffe%2C+S%2E%2C+Vanhoucke%2C+V%2E%3A+Inception%2Dv4%2C+inception%2Dresnet+and+the+impact+of+residual+connections+on+learning%2E+CoRR+%282016%29+4)
28. Iandola, F.N., Moskewicz, M.W., Ashraf, K., Han, S., Dally, W.J., Keutzer, K.: Squeezenet: Alexnet-level accuracy with 50x fewer parameters and¡ 1mb model size. arXiv preprint arXiv:1602.07360 (2016) 4 [find](https://scholar.google.com/scholar?q=Iandola%2C+F%2EN%2E%2C+Moskewicz%2C+M%2EW%2E%2C+Ashraf%2C+K%2E%2C+Han%2C+S%2E%2C+Dally%2C+W%2EJ%2E%2C+Keutzer%2C+K%2E%3A+Squeezenet%3A+Alexnet%2Dlevel+accuracy+with+50x+fewer+parameters+and%C2%A1+1mb+model+size%2E+arXiv+preprint+arXiv%3A1602%2E07360+%282016%29+)
29. Gong, Y., Liu, L., Yang, M., Bourdev, L.: Compressing deep convolutional networks using vector quantization. arXiv preprint arXiv:1412.6115 (2014) 4 — [arXiv:1412.6115](https://arxiv.org/abs/1412.6115) [find](https://scholar.google.com/scholar?q=Gong%2C+Y%2E%2C+Liu%2C+L%2E%2C+Yang%2C+M%2E%2C+Bourdev%2C+L%2E%3A+Compressing+deep+convolutional+networks+using+vector+quantization%2E+arXiv+preprint+arXiv%3A1412%2E6115+%282014%29+4+%E2%80%94+%5BarXiv%3A1412%2E6115%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F1412%2E6115)
30. Arora, S., Bhaskara, A., Ge, R., Ma, T.: Provable bounds for learning some deep representations. arXiv preprint arXiv:1310.6343 (2013) 4 — [arXiv:1310.6343](https://arxiv.org/abs/1310.6343) [find](https://scholar.google.com/scholar?q=Arora%2C+S%2E%2C+Bhaskara%2C+A%2E%2C+Ge%2C+R%2E%2C+Ma%2C+T%2E%3A+Provable+bounds+for+learning+some+deep+representations%2E+arXiv+preprint+arXiv%3A1310%2E6343+%282013%29+4+%E2%80%94+%5BarXiv%3A1310%2E6343%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F1310%2E6343%29)
31. Vanhoucke, V., Senior, A., Mao, M.Z.: Improving the speed of neural networks on cpus. In: Proc. Deep Learning and Unsupervised Feature Learning NIPS Workshop. Volume 1. (2011) 4 [find](https://scholar.google.com/scholar?q=Vanhoucke%2C+V%2E%2C+Senior%2C+A%2E%2C+Mao%2C+M%2EZ%2E%3A+Improving+the+speed+of+neural+networks+on+cpus%2E+In%3A+Proc%2E+Deep+Learning+and+Unsupervised+Feature+Learning+NIPS+Workshop%2E+Volume+1%2E+%282011%29+4)
32. Hwang, K., Sung, W.: Fixed-point feedforward deep neural network design using weights+ 1, 0, and- 1. In: Signal Processing Systems (SiPS), 2014 IEEE Workshop on, IEEE (2014) 1–6 4 [find](https://scholar.google.com/scholar?q=Hwang%2C+K%2E%2C+Sung%2C+W%2E%3A+Fixed%2Dpoint+feedforward+deep+neural+network+design+using+weights%2B+1%2C+0%2C+and%2D+1%2E+In%3A+Signal+Processing+Systems+%28SiPS%29%2C+2014+IEEE+Workshop+on%2C+IEEE+%282014%29+1%E2%80%936+4)
33. Anwar, S., Hwang, K., Sung, W.: Fixed point optimization of deep convolutional neural networks for object recognition. In: Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on, IEEE (2015) 1131–1135 4 [find](https://scholar.google.com/scholar?q=Anwar%2C+S%2E%2C+Hwang%2C+K%2E%2C+Sung%2C+W%2E%3A+Fixed+point+optimization+of+deep+convolutional+neural+networks+for+object+recognition%2E+In%3A+Acoustics%2C+Speech+and+Signal+Processing+%28ICASSP%29%2C+2015+IEEE+International+Con)
34. Lin, Z., Courbariaux, M., Memisevic, R., Bengio, Y.: Neural networks with few multiplications. arXiv preprint arXiv:1510.03009 (2015) 4 — [arXiv:1510.03009](https://arxiv.org/abs/1510.03009) [find](https://scholar.google.com/scholar?q=Lin%2C+Z%2E%2C+Courbariaux%2C+M%2E%2C+Memisevic%2C+R%2E%2C+Bengio%2C+Y%2E%3A+Neural+networks+with+few+multiplications%2E+arXiv+preprint+arXiv%3A1510%2E03009+%282015%29+4+%E2%80%94+%5BarXiv%3A1510%2E03009%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F1510%2E03009%29)
35. Courbariaux, M., Bengio, Y., David, J.P.: Training deep neural networks with low precision multiplications. arXiv preprint arXiv:1412.7024 (2014) 4 — [arXiv:1412.7024](https://arxiv.org/abs/1412.7024) [find](https://scholar.google.com/scholar?q=Courbariaux%2C+M%2E%2C+Bengio%2C+Y%2E%2C+David%2C+J%2EP%2E%3A+Training+deep+neural+networks+with+low+precision+multiplications%2E+arXiv+preprint+arXiv%3A1412%2E7024+%282014%29+4+%E2%80%94+%5BarXiv%3A1412%2E7024%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F1412%2E7024%29)
36. Soudry, D., Hubara, I., Meir, R.: Expectation backpropagation: parameter-free training of multilayer neural networks with continuous or discrete weights. In: Advances in Neural Information Processing Systems. (2014) 963–971 4 [find](https://scholar.google.com/scholar?q=Soudry%2C+D%2E%2C+Hubara%2C+I%2E%2C+Meir%2C+R%2E%3A+Expectation+backpropagation%3A+parameter%2Dfree+training+of+multilayer+neural+networks+with+continuous+or+discrete+weights%2E+In%3A+Advances+in+Neural+Information+Processing+)
37. Esser, S.K., Appuswamy, R., Merolla, P., Arthur, J.V., Modha, D.S.: Backpropagation for energy-efficient neuromorphic computing. In: Advances in Neural Information Processing Systems. (2015) 1117–1125 4 [find](https://scholar.google.com/scholar?q=Esser%2C+S%2EK%2E%2C+Appuswamy%2C+R%2E%2C+Merolla%2C+P%2E%2C+Arthur%2C+J%2EV%2E%2C+Modha%2C+D%2ES%2E%3A+Backpropagation+for+energy%2Defficient+neuromorphic+computing%2E+In%3A+Advances+in+Neural+Information+Processing+Systems%2E+%282015%29+1117%E2%80%931125)
38. Courbariaux, M., Bengio, Y., David, J.P.: [Binaryconnect: Training deep neural networks with binary weights during propagations](https://md.research.elamur.ai/free/en/papers/courbariaux-2015-binaryconnect-training-deep-neural-networks/). In: Advances in Neural Information Processing Systems. (2015) 3105–3113 4, 6, 10, 11
39. Wan, L., Zeiler, M., Zhang, S., Cun, Y.L., Fergus, R.: Regularization of neural networks using dropconnect. In: Proceedings of the 30th International Conference on Machine Learning (ICML-13). (2013) 1058–1066 5 [find](https://scholar.google.com/scholar?q=Wan%2C+L%2E%2C+Zeiler%2C+M%2E%2C+Zhang%2C+S%2E%2C+Cun%2C+Y%2EL%2E%2C+Fergus%2C+R%2E%3A+Regularization+of+neural+networks+using+dropconnect%2E+In%3A+Proceedings+of+the+30th+International+Conference+on+Machine+Learning+%28ICML%2D13%29%2E+%282013%29+1)
40. Baldassi, C., Ingrosso, A., Lucibello, C., Saglietti, L., Zecchina, R.: Subdominant dense clusters allow for simple learning and high computational performance in neural networks with discrete synapses. Physical review letters 115(12) (2015) 128101 5 [find](https://scholar.google.com/scholar?q=Baldassi%2C+C%2E%2C+Ingrosso%2C+A%2E%2C+Lucibello%2C+C%2E%2C+Saglietti%2C+L%2E%2C+Zecchina%2C+R%2E%3A+Subdominant+dense+clusters+allow+for+simple+learning+and+high+computational+performance+in+neural+networks+with+discrete+synapse)
41. Kim, M., Smaragdis, P.: Bitwise neural networks. arXiv preprint arXiv:1601.06071 (2016) 5 — [arXiv:1601.06071](https://arxiv.org/abs/1601.06071) [find](https://scholar.google.com/scholar?q=Kim%2C+M%2E%2C+Smaragdis%2C+P%2E%3A+Bitwise+neural+networks%2E+arXiv+preprint+arXiv%3A1601%2E06071+%282016%29+5+%E2%80%94+%5BarXiv%3A1601%2E06071%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F1601%2E06071%29)
42. Kingma, D., Ba, J.: [Adam: A method for stochastic optimization](https://md.research.elamur.ai/free/en/papers/kingma-2014-adam-method-stochastic-optimization/). arXiv preprint arXiv:1412.6980 (2014) 6, 12
43. Ioffe, S., Szegedy, C.: Batch normalization: Accelerating deep network training by reducing internal covariate shift. arXiv preprint arXiv:1502.03167 (2015) 9, 11 [find](https://scholar.google.com/scholar?q=Ioffe%2C+S%2E%2C+Szegedy%2C+C%2E%3A+Batch+normalization%3A+Accelerating+deep+network+training+by+reducing+internal+covariate+shift%2E+arXiv+preprint+arXiv%3A1502%2E03167+%282015%29+9%2C+11)
44. Redmon, J.: Darknet: Open source neural networks in c. [http://pjreddie.com/darknet/](http://pjreddie.com/darknet/) (2013–2016) 13 [↗](http://pjreddie.com/darknet/)

*Updated 2 November 2026*