Fairy2i: Training Complex LLMs from Real LLMs with All Parameters in $\{\pm 1, \pm i\}$
This work addresses the efficiency gap for deploying LLMs on commodity hardware by enabling quantization of pre-trained models without retraining, though it builds incrementally on existing complex-valued approaches.
The authors tackled the problem of large language models' massive memory and computational demands by developing Fairy2i, a framework that transforms pre-trained real-valued LLMs into complex-valued equivalents with extremely low-bit quantization, restoring LLaMA-2 7B performance at 2-bit precision to nearly full-precision levels and outperforming state-of-the-art real-valued binary and ternary methods.
Large language models (LLMs) have revolutionized artificial intelligence, yet their massive memory and computational demands necessitate aggressive quantization, increasingly pushing representations toward the theoretical limit of a single bit. While complex-valued LLMs, such as iFairy, offer a superior chance for low-bit representation compared to real-valued counterparts, they require training from scratch, preventing the utilization of the vast ecosystem of pre-trained real-valued foundation models. Here we present Fairy2i, a universal framework that transforms pre-trained real-valued layers into an equivalent widely-linear complex form, enabling extremely low-bit quantization while reusing existing checkpoints. By proving a lossless mathematical equivalence between real and widely-linear maps, we convert standard Transformers into the complex domain and employ a phase-aware quantization scheme with a highly efficient codebook of fourth roots of unity. Furthermore, we introduce a recursive residual quantization mechanism that iteratively minimizes quantization error, allowing inference to proceed via efficient multiplication-free accumulation. We demonstrate that Fairy2i restores the performance of LLaMA-2 7B at an effective 2-bit precision to levels nearly comparable with full-precision baselines, significantly outperforming state-of-the-art real-valued binary and ternary quantization methods. This work bridges the gap between the representational efficiency of complex-valued arithmetic and the practical utility of pre-trained models, paving a new way for efficient inference on commodity hardware.