EoRA: Training-free Compensation for Compressed LLM with Eigenspace
  Low-Rank Approximation
Authors: name: Shih-Yang Liu, name: Huck Yang, name: Chein-Yi Wang, name: Nai Chit Fung, name: Hongxu Yin, name: Charbel Sakr, name: Saurav Muralidharan, name: Kwang-Ting Cheng, name: Jan Kautz, name: Yu-Chiang Frank Wang, name: Pavlo Molchanov, name: Min-Hung Chen
Organization: NVIDIA

In this work, we re-formulate the model compression problem into the
customized compensation problem: Given a compressed model, we aim to introduce
residual low-rank paths to compensate for compression errors under customized
requirements from users (e.g., tasks, compression ratios), resulting in greater
flexibility in adjusting overall capacity without being constrained by specific
compression formats. However, naively applying SVD to derive residual paths
causes suboptimal utilization of the low-rank representation capacity. Instead,
we propose Training-free Eigenspace Low-Rank Approximation (EoRA), a method
that directly minimizes compression-induced errors without requiring
gradient-based training, achieving fast optimization in minutes using a small
amount of calibration data. EoRA projects compression errors into the
eigenspace of input activations, leveraging eigenvalues to effectively
prioritize the reconstruction of high-importance error components. Moreover,
EoRA can be seamlessly integrated with fine-tuning and quantization to further
improve effectiveness and efficiency. EoRA consistently outperforms previous
methods in compensating errors for compressed LLaMA2/3 models on various tasks,
such as language generation, commonsense reasoning, and math reasoning tasks
(e.g., 31.31%/12.88% and 9.69% improvements on ARC-Easy/ARC-Challenge and
MathQA when compensating LLaMA3-8B that is quantized to 4-bit and pruned to 2:4
sparsity). EoRA offers a scalable, training-free solution to compensate for
compression errors, making it a powerful tool to deploy LLMs in various
capacity and efficiency requirements.