# Compression for Better: A General and Stable Lossless Compression Framework

arXiv: https://arxiv.org/abs/2412.06868 · HTML: https://mlsanity.com/paper/2412.06868/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 21 references that are in the map.
- First posted on arXiv 9 Dec 2024.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [SWAG: A Large-Scale Adversarial Dataset for Grounded Commonsense Inference](https://mlsanity.com/paper/1808.05326/) (2018)
- [HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks](https://mlsanity.com/paper/1911.03852/) (2019)
- [Language model compression with weighted low-rank factorization](https://mlsanity.com/paper/2207.00112/) (2022)
- [Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications](https://mlsanity.com/paper/1511.06530/) (2015)
- [Convolutional neural networks with low-rank regularization](https://mlsanity.com/paper/1511.06067/) (2015)
- [AutoQ: Automated Kernel-Wise Neural Network Quantization](https://mlsanity.com/paper/1902.05690/) (2019)
- [Learning Low-rank Deep Neural Networks via Singular Vector Orthogonality Regularization and Singular Value Sparsification](https://mlsanity.com/paper/2004.09031/) (2020)
- [Post-training 4-bit quantization of convolution networks for rapid-deployment](https://mlsanity.com/paper/1810.05723/) (2018)
- [Trained Rank Pruning for Efficient Deep Neural Networks](https://mlsanity.com/paper/1812.02402/) (2018)

## Built on by (most cited first, 4 of 4)

- [SED-MVS: Segmentation-Driven and Edge-Aligned Deformation Multi-View Stereo with Depth Restoration and Occlusion Constraint](https://mlsanity.com/paper/2503.13721/) (2025)
- [A Qualitative Test-Risk Mechanism for Scaling Behavior in Normalized Residual Networks](https://mlsanity.com/paper/2605.08297/) (2026)
- [Rethinking Parameter Sharing as Graph Coloring for Structured Compression](https://mlsanity.com/paper/2511.06786/) (2025)
- [HeRo-Q: A General Framework for Stable Low Bit Quantization via Hessian Conditioning](https://mlsanity.com/paper/2601.21626/) (2026)

## Abstract (arXiv)

This work focus on how to stabilize and lossless model compression, aiming to reduce model complexity and enhance efficiency without sacrificing performance due to compression errors. A key challenge is effectively leveraging compression errors and defining the boundaries for lossless compression to minimize model loss. i.e., compression for better. Currently, there is no systematic approach to determining this error boundary or understanding its specific impact on model performance. We propose a general LossLess Compression theoretical framework (LLC), which further delineates the compression neighborhood and higher-order analysis boundaries through the total differential, thereby specifying the error range within which a model can be compressed without loss. To verify the effectiveness of LLC, we apply various compression techniques, including quantization and decomposition. Specifically, for quantization, we reformulate the classic quantization search problem as a grouped knapsack problem within the lossless neighborhood, achieving lossless quantization while improving computational efficiency. For decomposition, LLC addresses the approximation problem under low-rank constraints, automatically determining the rank for each layer and producing lossless low-rank models. We conduct extensive experiments on multiple neural network architectures on different datasets. The results show that without fancy tricks, LLC can effectively achieve lossless model compression. Our code will be made publicly.