# Differentiable Bit-Widths: Co-optimizing Pruning and Quantization via SVD for Ultra-Efficient LLM Compression

arXiv: https://arxiv.org/abs/2610.06026 · HTML: https://mlsanity.com/paper/2610.06026/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 43 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Builds on (most cited first, 30 of 33)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [A Survey on Model Compression for Large Language Models](https://mlsanity.com/paper/2308.07633/) (2023)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [Accelerating Sparse Deep Neural Networks](https://mlsanity.com/paper/2104.08378/) (2021)
- [LSQ+: Improving low-bit quantization through learnable offsets and better initialization](https://mlsanity.com/paper/2004.09576/) (2020)
- [RedPajama: an Open Dataset for Training Large Language Models](https://mlsanity.com/paper/2411.12372/) (2024)
- [ASVD: Activation-aware Singular Value Decomposition for Compressing Large Language Models](https://mlsanity.com/paper/2312.05821/) (2023)
- [BiLLM: Pushing the Limit of Post-Training Quantization for LLMs](https://mlsanity.com/paper/2402.04291/) (2024)
- [Bayesian Bits: Unifying Quantization and Pruning](https://mlsanity.com/paper/2005.07093/) (2020)
- [PB-LLM: Partially Binarized Large Language Models](https://mlsanity.com/paper/2310.00034/) (2023)
- [SliM-LLM: Salience-Driven Mixed-Precision Quantization for Large Language Models](https://mlsanity.com/paper/2405.14917/) (2024)
- [Streamlining Redundant Layers to Compress Large Language Models](https://mlsanity.com/paper/2403.19135/) (2024)

## Abstract (arXiv)

SVD-based pruning and quantization have recently emerged as a promising strategy for the ultra-efficient compression of large language models. In these methods, compression is performed in two stages: components are first truncated, and the remaining ones are subsequently quantized. Although this decoupled pipeline benefits from both pruning and quantization, it requires separate optimization for each stage and fails to fully exploit their balance, which can lead to suboptimal performance under aggressive compression. To address this limitation, we propose a new LLM compression method that co-optimizes pruning and quantization in a unified framework. Our key idea is a differentiable method for learning component-wise bit-widths, allowing less important components to be assigned 0-bit precision and pruned away. Notably, our method performs favorably against two-stage baselines, even when subjected to extreme quantization settings (1.61 bits) designed for ultra-efficiency. Code: https://github.com/MMAI-Laboratory/DBW.