# Exact Backpropagation in Binary Weighted Networks with Group Weight Transformations

arXiv: https://arxiv.org/abs/2107.01400 · HTML: https://mlsanity.com/paper/2107.01400/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 43 references that are in the map.
- First posted on arXiv 3 Jul 2021.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [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)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [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)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [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)
- [Binary Neural Networks: A Survey](https://mlsanity.com/paper/2004.03333/) (2020)
- [Forward and Backward Information Retention for Accurate Binary Neural Networks](https://mlsanity.com/paper/1909.10788/) (2019)
- [Deep Learning with Low Precision by Half-wave Gaussian Quantization](https://mlsanity.com/paper/1702.00953/) (2017)
- [Training Binary Neural Networks with Real-to-Binary Convolutions](https://mlsanity.com/paper/2003.11535/) (2020)
- [XNOR-Net++: Improved Binary Neural Networks](https://mlsanity.com/paper/1909.13863/) (2019)
- [Training Quantized Nets: A Deeper Understanding](https://mlsanity.com/paper/1706.02379/) (2017)
- [ProxQuant: Quantized Neural Networks via Proximal Operators](https://mlsanity.com/paper/1810.00861/) (2018)
- [Loss-aware Binarization of Deep Networks](https://mlsanity.com/paper/1611.01600/) (2016)
- [Multi-Prize Lottery Ticket Hypothesis: Finding Accurate Binary Neural Networks by Pruning A Randomly Weighted Network](https://mlsanity.com/paper/2103.09377/) (2021)
- [From Hashing to CNNs: Training BinaryWeight Networks via Hashing](https://mlsanity.com/paper/1802.02733/) (2018)
- [Improved training of binary networks for human pose estimation and image recognition](https://mlsanity.com/paper/1904.05868/) (2019)
- [Learning Accurate Low-Bit Deep Neural Networks with Stochastic Quantization](https://mlsanity.com/paper/1708.01001/) (2017)
- [Self-Binarizing Networks](https://mlsanity.com/paper/1902.00730/) (2019)

## Built on by (most cited first, 1 of 1)

- [Relational Compression: A Framework for Relational Fidelity in Constrained Representations](https://mlsanity.com/paper/2609.31816/) (2026)

## Abstract (arXiv)

Quantization based model compression serves as high performing and fast approach for inference that yields models which are highly compressed when compared to their full-precision floating point counterparts. The most extreme quantization is a 1-bit representation of parameters such that they have only two possible values, typically -1(0) or +1, enabling efficient implementation of the ubiquitous dot product using only additions. The main contribution of this work is the introduction of a method to smooth the combinatorial problem of determining a binary vector of weights to minimize the expected loss for a given objective by means of empirical risk minimization with backpropagation. This is achieved by approximating a multivariate binary state over the weights utilizing a deterministic and differentiable transformation of real-valued, continuous parameters. The proposed method adds little overhead in training, can be readily applied without any substantial modifications to the original architecture, does not introduce additional saturating nonlinearities or auxiliary losses, and does not prohibit applying other methods for binarizing the activations. Contrary to common assertions made in the literature, it is demonstrated that binary weighted networks can train well with the same standard optimization techniques and similar hyperparameter settings as their full-precision counterparts, specifically momentum SGD with large learning rates and L2 regularization. To conclude experiments demonstrate the method performs remarkably well across a number of inductive image classification tasks with various architectures compared to their full-precision counterparts. The source code is publicly available at https://bitbucket.org/YanivShu/binaryweightednetworkspublic.