  Large Language Models (LLMs) are reshaping the research landscape in
artificial intelligence, particularly as model parameters scale up
significantly, unlocking remarkable capabilities across various domains.
Nevertheless, the scalability of model parameters faces constraints due to
limitations in GPU memory and computational speed. To address these
constraints, various weight compression methods have emerged, such as Pruning
and Quantization. Given the low-rank nature of weight matrices in language
models, the reduction of weights through matrix decomposition undoubtedly holds
significant potential and promise. In this paper, drawing upon the intrinsic
structure of LLMs, we propose a novel approach termed Data-free Joint Rank-k
Approximation for compressing the parameter matrices. Significantly, our method
is characterized by without necessitating additional involvement of any corpus,
while simultaneously preserving orthogonality in conjunction with pruning and
quantization methods. We achieve a model pruning of 80% parameters while
retaining 93.43% of the original performance without any calibration data.
Additionally, we explore the fundamental properties of the weight matrix of
LLMs undergone Rank-k Approximation and conduct comprehensive experiments to
elucidate our hypothesis.
