# MSQ: Memory-Efficient Bit Sparsification Quantization

arXiv: https://arxiv.org/abs/2507.22349 · HTML: https://mlsanity.com/paper/2507.22349/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 32 references that are in the map.
- First posted on arXiv 30 Jul 2025.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [FBNet: Hardware-Aware Efficient ConvNet Design via Differentiable Neural Architecture Search](https://mlsanity.com/paper/1812.03443/) (2018)
- [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)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [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)
- [Quantization Networks](https://mlsanity.com/paper/1911.09464/) (2019)
- [Q-ViT: Accurate and Fully Quantized Low-bit Vision Transformer](https://mlsanity.com/paper/2210.06707/) (2022)
- [Winning the Lottery with Continuous Sparsification](https://mlsanity.com/paper/1912.04427/) (2019)
- [NoisyQuant: Noisy Bias-Enhanced Post-Training Activation Quantization for Vision Transformers](https://mlsanity.com/paper/2211.16056/) (2022)
- [DORY: Automatic End-to-End Deployment of Real-World DNNs on Low-Cost IoT MCUs](https://mlsanity.com/paper/2008.07127/) (2020)
- [Oscillation-free Quantization for Low-bit Vision Transformers](https://mlsanity.com/paper/2302.02210/) (2023)
- [SQuant: On-the-Fly Data-Free Quantization via Diagonal Hessian Approximation](https://mlsanity.com/paper/2202.07471/) (2022)
- [BSQ: Exploring Bit-Level Sparsity for Mixed-Precision Neural Network Quantization](https://mlsanity.com/paper/2102.10462/) (2021)
- [Mix-QViT: Mixed-Precision Vision Transformer Quantization Driven by Layer Importance and Quantization Sensitivity](https://mlsanity.com/paper/2501.06357/) (2025)
- [CSQ: Growing Mixed-Precision Quantization Scheme with Bi-level Continuous Sparsification](https://mlsanity.com/paper/2212.02770/) (2022)

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

- [GAMMA: Global Bit Allocation for Mixed-Precision Models under Arbitrary Budgets](https://mlsanity.com/paper/2605.18475/) (2026)
- [TASQ: Temporal-Adaptive Bit Sparsification Quantization for Diffusion Models](https://mlsanity.com/paper/2608.03057/) (2026)

## Abstract (arXiv)

As deep neural networks (DNNs) see increased deployment on mobile and edge devices, optimizing model efficiency has become crucial. Mixed-precision quantization is widely favored, as it offers a superior balance between efficiency and accuracy compared to uniform quantization. However, finding the optimal precision for each layer is challenging. Recent studies utilizing bit-level sparsity have shown promise, yet they often introduce substantial training complexity and high GPU memory requirements. In this paper, we propose Memory-Efficient Bit Sparsification Quantization (MSQ), a novel approach that addresses these limitations. MSQ applies a round-clamp quantizer to enable differentiable computation of the least significant bits (LSBs) from model weights. It further employs regularization to induce sparsity in these LSBs, enabling effective precision reduction without explicit bit-level parameter splitting. Additionally, MSQ incorporates Hessian information, allowing the simultaneous pruning of multiple LSBs to further enhance training efficiency. Experimental results show that MSQ achieves up to 8.00x reduction in trainable parameters and up to 86% reduction in training time compared to previous bit-level quantization, while maintaining competitive accuracy and compression rates. This makes it a practical solution for training efficient DNNs on resource-constrained devices.