iFairy: the First 2-bit Complex LLM with All Parameters in $\{\pm1, \pm i\}$
Feiyu Wang, Guoan Wang, Yihao Zhang, Shengfan Wang, Weitao Li, Bokai Huang, Shimao Chen, Zihan Jiang, Rui Xu, Tong Yang
TL;DR
This work introduces iFairy, the first 2-bit complex-valued LLM that maps weights to the fourth roots of unity {±1, ±i} using PhaseQuant, enabling addition-only inference while raising the full-precision accuracy ceiling. By extending Transformer components into the complex domain (dual-channel embeddings, complex self-attention, and complex RoPE) and employing a 2-bit complex weight quantizer, iFairy achieves superior perplexity and downstream task performance relative to existing 2-bit baselines, approaching FP16 baselines. Comprehensive experiments across 700M and 1.3B parameter scales demonstrate improved training dynamics, language modeling, and transfer, with ablations confirming the value of the native complex-valued architecture and a fully complex-aware computation pattern. The work also analyzes weight distributions, norms, and embedding/LM-head structures, showing balanced codebook usage and stable magnitudes, and discusses limitations and future hardware-aware optimizations for practical deployment.
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.