  We introduce a method that dramatically reduces fine-tuning VRAM requirements
and rectifies quantization errors in quantized Large Language Models. First, we
develop an extremely memory-efficient fine-tuning (EMEF) method for quantized
models using Low-Rank Adaptation (LoRA), and drawing upon it, we construct an
error-correcting algorithm designed to minimize errors induced by the
quantization process. Our method reduces the memory requirements by up to 5.6
times, which enables fine-tuning a 7 billion parameter Large Language Model
(LLM) on consumer laptops. At the same time, we propose a Low-Rank Error
Correction (LREC) method that exploits the added LoRA layers to ameliorate the
gap between the quantized model and its float point counterpart. Our error
correction framework leads to a fully functional INT2 quantized LLM with the
capacity to generate coherent English text. To the best of our knowledge, this
is the first INT2 Large Language Model that has been able to reach such a
performance. The overhead of our method is merely a 1.05 times increase in
model size, which translates to an effective precision of INT2.1. Also, our
method readily generalizes to other quantization standards, such as INT3, INT4,
and INT8, restoring their lost performance, which marks a significant milestone
in the field of model quantization. The strategies delineated in this paper
hold promising implications for the future development and optimization of
quantized models, marking a pivotal shift in the landscape of low-resource
machine learning computations.
