Fairy$\pm i$: the First 2-bit Complex LLM with All Parameters in $\{\pm1, \pm i\}$

• URL: http://arxiv.org/abs/2508.05571v1
• Date: Thu, 07 Aug 2025 17:02:23 GMT
• Title: Fairy$\pm i$: the First 2-bit Complex LLM with All Parameters in $\{\pm1, \pm i\}$
• Authors: Feiyu Wang, Guoan Wang, Yihao Zhang, Shengfan Wang, Weitao Li, Bokai Huang, Shimao Chen, Zihan Jiang, Rui Xu, Tong Yang,
• Abstract summary: Quantization-Aware Training (QAT) integrates quantization into the training loop, enabling LLMs to learn robust low-bit representations.<n>We propose Fairy$pm i$, the first 2-bit quantization framework for complex-valued LLMs.<n>We map weights to the fourth roots of unity $pm1, pm i$, forming a perfectly symmetric and information-theoretically optimal 2-bit representation.
• Score: 12.184724224633609
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantization-Aware Training (QAT) integrates quantization into the training loop, enabling LLMs to learn robust low-bit representations, and is widely recognized as one of the most promising research directions. All current QAT research focuses on minimizing quantization error on full-precision models, where the full-precision accuracy acts as an upper bound (accuracy ceiling). No existing method has even attempted to surpass this ceiling. To break this ceiling, we propose a new paradigm: raising the ceiling (full-precision model), and then still quantizing it efficiently into 2 bits. We propose Fairy$\pm i$, the first 2-bit quantization framework for complex-valued LLMs. Specifically, our method leverages the representational advantages of the complex domain to boost full-precision accuracy. We map weights to the fourth roots of unity $\{\pm1, \pm i\}$, forming a perfectly symmetric and information-theoretically optimal 2-bit representation. Importantly, each quantized weight has either a zero real or imaginary part, enabling multiplication-free inference using only additions and element swaps. Experimental results show that Fairy$\pm i$ outperforms the ceiling of existing 2-bit quantization approaches in terms of both PPL and downstream tasks, while maintaining strict storage and compute efficiency. This work opens a new direction for building highly accurate and practical LLMs under extremely low-bit constraints.

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