# LogbQuant: Quantizing Language Models in Logarithmic Space

arXiv: https://arxiv.org/abs/2607.01127 · HTML: https://mlsanity.com/paper/2607.01127/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 44 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 29 of 29)

- [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)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [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)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [Data-Free Quantization Through Weight Equalization and Bias Correction](https://mlsanity.com/paper/1906.04721/) (2019)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [A Survey on Deep Neural Network Pruning-Taxonomy, Comparison, Analysis, and Recommendations](https://mlsanity.com/paper/2308.06767/) (2023)
- [FP8 Formats for Deep Learning](https://mlsanity.com/paper/2209.05433/) (2022)
- [Language model compression with weighted low-rank factorization](https://mlsanity.com/paper/2207.00112/) (2022)
- [RedPajama: an Open Dataset for Training Large Language Models](https://mlsanity.com/paper/2411.12372/) (2024)
- [Understanding and Overcoming the Challenges of Efficient Transformer Quantization](https://mlsanity.com/paper/2109.12948/) (2021)
- [AI and Memory Wall](https://mlsanity.com/paper/2403.14123/) (2024)
- [GPTAQ: Efficient Finetuning-Free Quantization for Asymmetric Calibration](https://mlsanity.com/paper/2504.02692/) (2025)
- [VPTQ: Extreme Low-bit Vector Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2409.17066/) (2024)
- [MoDeGPT: Modular Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2408.09632/) (2024)
- [SlimGPT: Layer-wise Structured Pruning for Large Language Models](https://mlsanity.com/paper/2412.18110/) (2024)
- [Power-of-Two Quantization for Low Bitwidth and Hardware Compliant Neural Networks](https://mlsanity.com/paper/2203.05025/) (2022)
- [ADALog: Adaptive Unsupervised Anomaly detection in Logs with Self-attention Masked Language Model](https://mlsanity.com/paper/2505.13496/) (2025)

## Abstract (arXiv)

Quantization has become an invaluable tool to reduce memory requirements and inference speed of modern language models, in particular to make them available for consumer setups and edge devices. While previous work has primarily focused on uniform quantization codebooks, such approaches are prone to suboptimal representations due to low-frequency high-magnitude weights. We introduce LogbQuant, a novel logarithmic quantization approach with adjustable bases, to adapt to common parameter distributions. We show that our method exhibits superior performance at 4-bit precision on several performance benchmarks compared to asymmetric linear quantization at tensor-wise granularity, while achieving moderate speedup and high memory savings, making it suitable for private use on consumer-grade GPUs.