  Large Language Models (LLMs) have significantly advanced natural language
processing tasks such as machine translation, text generation, and sentiment
analysis. However, their large size, often consisting of billions of
parameters, poses challenges for storage, computation, and deployment,
particularly in resource-constrained environments like mobile devices and edge
computing platforms. Additionally, the key-value (k-v) cache used to speed up
query processing requires substantial memory and storage, exacerbating these
challenges. Vector databases have emerged as a crucial technology to
efficiently manage and retrieve the high-dimensional vectors produced by LLMs,
facilitating faster data access and reducing computational demands.
  Effective compression and quantization techniques are essential to address
these challenges, as they reduce the memory footprint and computational
requirements without significantly compromising performance. Traditional
methods that uniformly map parameters to compressed spaces often fail to
account for the uneven distribution of parameters, leading to considerable
accuracy loss. Therefore, innovative approaches are needed to achieve better
compression ratios while preserving model performance.
  In this work, we propose HERA, a novel algorithm that employs heuristic
Element Replacement for compressing matrix. HERA systematically replaces
elements within the model using heuristic methods, which simplifies the
structure of the model and makes subsequent compression more effective. By
hierarchically segmenting, compressing, and reorganizing the matrix dataset,
our method can effectively reduce the quantization error to 12.3% of the
original at the same compression ratio.
