The advancements in Large Language Models (LLMs) have been hindered by their
substantial sizes, which necessitate LLM compression methods for practical
deployment. Singular Value Decomposition (SVD) offers a promising solution for
LLM compression. However, state-of-the-art SVD-based LLM compression methods
have two key limitations: truncating smaller singular values may lead to higher
compression loss, and the lack of update on the remaining model parameters
after SVD truncation. In this work, we propose SVD-LLM, a new SVD-based LLM
compression method that addresses the limitations of existing methods. SVD-LLM
incorporates a truncation-aware data whitening strategy to ensure a direct
mapping between singular values and compression loss. Moreover, SVD-LLM adopts
a layer-wise closed-form model parameter update strategy to compensate for
accuracy degradation caused by SVD truncation. We evaluate SVD-LLM on a total
of 11 datasets and seven models from three different LLM families at four
different scales. Our results demonstrate the superiority of SVD-LLM over
state-of-the-arts, especially at high model compression ratios. The source code
is available at this https URL

提出了一种新的基于奇异值分解的大型语言模型压缩方法 SVD-LLM，它解决了现有方法的限制，并在高模型压缩比下展现了优越性能。

SVD-LLM：大型语言模型压缩的截断感知奇异值分解

SVD-LLM: Truncation-aware Singular Value Decomposition for Large  Language Model Compression

In this work we derive the performance achievable by a network of distributed
agents that solve, adaptively and in the presence of communication constraints,
a regression problem. Agents employ the recently proposed ACTC
(adapt-compress-then-combine) diffusion strategy, where the signals exchanged
locally by neighboring agents are encoded with randomized differential
compression operators. We provide a detailed characterization of the
mean-square estimation error, which is shown to comprise a term related to the
error that agents would achieve without communication constraints, plus a term
arising from compression. The analysis reveals quantitative relationships
between the compression loss and fundamental attributes of the distributed
regression problem, in particular, the stochastic approximation error caused by
the gradient noise and the network topology (through the Perron eigenvector).
We show that knowledge of such relationships is critical to allocate optimally
the communication resources across the agents, taking into account their
individual attributes, such as the quality of their data or their degree of
centrality in the network topology. We devise an optimized allocation strategy
where the parameters necessary for the optimization can be learned online by
the agents. Illustrative examples show that a significant performance
improvement, as compared to a blind (i.e., uniform) resource allocation, can be
achieved by optimizing the allocation by means of the provided
mean-square-error formulas.

本文研究了分布式代理网络解决回归问题的性能及其在通信约束下的自适应能力，采用 ACTC 扩散策略，在邻居代理之间交换的信号中使用随机差分压缩算子进行编码。提供了均方估计误差的详细特征描述，揭示了压缩损失与分布式回归问题的基本属性之间的定量关系，以及优化资源分配的重要性，提出了在线学习的优化参数分配策略，并给出实例验证。