# True 4-Bit Quantized Convolutional Neural Network Training on CPU: Achieving Full-Precision Parity

arXiv: https://arxiv.org/abs/2603.13931 · HTML: https://mlsanity.com/paper/2603.13931/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 19 references that are in the map.
- First posted on arXiv 14 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [Data-Free Quantization Through Weight Equalization and Bias Correction](https://mlsanity.com/paper/1906.04721/) (2019)
- [BitNet: Scaling 1-bit Transformers for Large Language Models](https://mlsanity.com/paper/2310.11453/) (2023)
- [Training Deep Neural Networks with 8-bit Floating Point Numbers](https://mlsanity.com/paper/1812.08011/) (2018)
- [Training and Inference with Integers in Deep Neural Networks](https://mlsanity.com/paper/1802.04680/) (2018)

## Abstract (arXiv)

Low-precision neural network training has emerged as a promising direction for reducing computational costs and democratizing access to deep learning research. However, existing 4-bit quantization methods either rely on expensive GPU infrastructure or suffer from significant accuracy degradation. In this work, we present a practical method for training convolutional neural networks at true 4-bit precision using standard PyTorch operations on commodity CPUs. We introduce a novel tanh-based soft weight clipping technique that, combined with symmetric quantization, dynamic per-layer scaling, and straight-through estimators, achieves stable convergence and competitive accuracy. Training a VGG-style architecture with 3.25 million parameters from scratch on CIFAR-10, our method achieves 92.34% test accuracy on Google Colab's free CPU tier -- matching full-precision baseline performance (92.5%) with only a 0.16% gap. We further validate on CIFAR-100, achieving 70.94% test accuracy across 100 classes with the same architecture and training procedure, demonstrating that 4-bit training from scratch generalizes to harder classification tasks. Both experiments achieve 8x memory compression over FP32 while maintaining exactly 15 unique weight values per layer throughout training. We additionally validate hardware independence by demonstrating rapid convergence on a consumer mobile device (OnePlus 9R), achieving 83.16% accuracy in only 6 epochs. To the best of our knowledge, no prior work has demonstrated 4-bit quantization-aware training achieving full-precision parity on standard CPU hardware without specialized kernels or post-training quantization.