# GradFreeBits: Gradient Free Bit Allocation for Dynamic Low Precision Neural Networks

arXiv: https://arxiv.org/abs/2102.09298 · HTML: https://mlsanity.com/paper/2102.09298/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 47 references that are in the map.
- First posted on arXiv 18 Feb 2021.

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

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Big Transfer (BiT): General Visual Representation Learning](https://mlsanity.com/paper/1912.11370/) (2019)
- [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)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [LQ-Nets: Learned Quantization for Highly Accurate and Compact Deep Neural Networks](https://mlsanity.com/paper/1807.10029/) (2018)
- [HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks](https://mlsanity.com/paper/1911.03852/) (2019)
- [A Comprehensive Survey of Neural Architecture Search: Challenges and Solutions](https://mlsanity.com/paper/2006.02903/) (2020)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [Learning to Quantize Deep Networks by Optimizing Quantization Intervals with Task Loss](https://mlsanity.com/paper/1808.05779/) (2018)
- [Improving Neural Network Quantization without Retraining using Outlier Channel Splitting](https://mlsanity.com/paper/1901.09504/) (2019)
- [Additive Powers-of-Two Quantization: An Efficient Non-uniform Discretization for Neural Networks](https://mlsanity.com/paper/1909.13144/) (2019)
- [Mixed Precision Quantization of ConvNets via Differentiable Neural Architecture Search](https://mlsanity.com/paper/1812.00090/) (2018)
- [Trained Quantization Thresholds for Accurate and Efficient Fixed-Point Inference of Deep Neural Networks](https://mlsanity.com/paper/1903.08066/) (2019)
- [Rethinking Differentiable Search for Mixed-Precision Neural Networks](https://mlsanity.com/paper/2004.05795/) (2020)
- [Evolving Mario Levels in the Latent Space of a Deep Convolutional Generative Adversarial Network](https://mlsanity.com/paper/1805.00728/) (2018)
- [CMA-ES for Hyperparameter Optimization of Deep Neural Networks](https://mlsanity.com/paper/1604.07269/) (2016)
- [Network Sketching: Exploiting Binary Structure in Deep CNNs](https://mlsanity.com/paper/1706.02021/) (2017)
- [BISMO: A Scalable Bit-Serial Matrix Multiplication Overlay for Reconfigurable Computing](https://mlsanity.com/paper/1806.08862/) (2018)
- [Blended Coarse Gradient Descent for Full Quantization of Deep Neural Networks](https://mlsanity.com/paper/1808.05240/) (2018)
- [Efficient Bitwidth Search for Practical Mixed Precision Neural Network](https://mlsanity.com/paper/2003.07577/) (2020)

## Built on by (most cited first, 2 of 2)

- [Quantized Convolutional Neural Networks Through the Lens of Partial Differential Equations](https://mlsanity.com/paper/2109.00095/) (2021)
- [Massive Dimensions Reduction and Hybridization with Meta-heuristics in Deep Learning](https://mlsanity.com/paper/2408.07194/) (2024)

## Abstract (arXiv)

Quantized neural networks (QNNs) are among the main approaches for deploying deep neural networks on low resource edge devices. Training QNNs using different levels of precision throughout the network (dynamic quantization) typically achieves superior trade-offs between performance and computational load. However, optimizing the different precision levels of QNNs can be complicated, as the values of the bit allocations are discrete and difficult to differentiate for. Also, adequately accounting for the dependencies between the bit allocation of different layers is not straight-forward. To meet these challenges, in this work we propose GradFreeBits: a novel joint optimization scheme for training dynamic QNNs, which alternates between gradient-based optimization for the weights, and gradient-free optimization for the bit allocation. Our method achieves better or on par performance with current state of the art low precision neural networks on CIFAR10/100 and ImageNet classification. Furthermore, our approach can be extended to a variety of other applications involving neural networks used in conjunction with parameters which are difficult to optimize for.