Analysis on distribution and clustering of weight

The study on architecture and parameter characteristics remains the hot topic in the research of large language models. In this paper we concern with the characteristics of weight which are used to analyze the correlations and differences between models. Two kinds of vectors-standard deviation vector and clustering vector-are proposed to describe features of models. In the first case, the weights are assumed to follow normal distribution. The standard deviation values of projection matrices are normalized to form Standard-Deviation Vector, representing the distribution characteristics of models. In the second case, the singular values from each weight projection matrix are extracted and grouped by K-Means algorithm. The grouped data with the same type matrix are combined as Clustering Vector to represent the correlation characteristics of models' weights. The study reveals that these two vectors can effectively distinguish between different models and clearly show the similarities among models of the same family. Moreover, after conducting LoRA fine-tuning with different datasets and models, it is found that the distribution of weights represented by standard deviation vector is directly influenced by the dataset, but the correlations between different weights represented by clustering vector remain unaffected and maintain a high consistency with the pre-trained model.