# SDQ-LLM: Sigma-Delta Quantization for 1-bit LLMs of any size

arXiv: https://arxiv.org/abs/2510.03275 · HTML: https://mlsanity.com/paper/2510.03275/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 25 references that are in the map.
- First posted on arXiv 27 Sep 2025.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [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)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [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)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [LLM-QAT: Data-Free Quantization Aware Training for Large Language Models](https://mlsanity.com/paper/2305.17888/) (2023)
- [The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits](https://mlsanity.com/paper/2402.17764/) (2024)
- [A Survey on Model Compression for Large Language Models](https://mlsanity.com/paper/2308.07633/) (2023)
- [BitNet: Scaling 1-bit Transformers for Large Language Models](https://mlsanity.com/paper/2310.11453/) (2023)
- [BiLLM: Pushing the Limit of Post-Training Quantization for LLMs](https://mlsanity.com/paper/2402.04291/) (2024)
- [PB-LLM: Partially Binarized Large Language Models](https://mlsanity.com/paper/2310.00034/) (2023)
- [OneBit: Towards Extremely Low-bit Large Language Models](https://mlsanity.com/paper/2402.11295/) (2024)
- [Layer-Wise Quantization: A Pragmatic and Effective Method for Quantizing LLMs Beyond Integer Bit-Levels](https://mlsanity.com/paper/2406.17415/) (2024)

## Built on by (most cited first, 1 of 1)

- [When Can Depth Replace Precision? A Resource Theory of Quantized Neural Computation](https://mlsanity.com/paper/2607.23390/) (2026)

## Abstract (arXiv)

Large language models (LLMs) face significant computational and memory challenges, making extremely low-bit quantization crucial for their efficient deployment. In this work, we introduce SDQ-LLM: Sigma-Delta Quantization for 1-bit LLMs of any size, a novel framework that enables extremely low-bit quantization of LLMs while preserving their linguistic reasoning capabilities. A distinctive feature of SDQ-LLM is the continuous adjustability of the Over-Sampling Ratio (OSR), enabling dynamic adaptation to memory or VRAM constraints by selecting fractional OSR (e.g. 2.5 times) for an optimal trade-off between model size and accuracy. SDQ-LLM uses upsampling combined with Sigma-Delta Quantizer to binarize or ternarize LLMs weights, encoding high-precision parameters into 1-bit or 1.58-bit representations, replacing the multiplication operations within linear layers with addition. This approach significantly enhances inference efficiency under extremely low-bit quantization. To further reduce the loss of quantization precision, we incorporate Hadamard-based weight smoothing prior to quantization, improving the stability and robustness of the weight representations. Furthermore, to fully leverage the continuity of the OSR and reduce precision loss, recognizing the correlation between quantization sensitivity and weight variance, we propose a fine-grained, layer- and linear-wise OSR allocation strategy, MultiOSR. This strategy distributes OSR both across layers and within each layer, based on weight variance and parameter scale. Finally, extensive experiments on OPT and LLaMA model families demonstrate that SDQ-LLM achieves a more efficient and high-precision performance even under highly aggressive low-OSR settings. Our code is available at https://github.com/Dreamlittlecat/LLM-Quant-Factory.