Optimal Brain Decomposition for Accurate LLM Low-Rank Approximation
This work addresses the efficiency of LLM fine-tuning and inference for AI practitioners, but it is incremental as it builds on existing decomposition techniques with a novel optimization approach.
The paper tackled the problem of low-rank decomposition for Large Language Model fine-tuning and inference by proposing OBD-LLM, a method that uses second-order Hessian information and bi-directional whitening to achieve a closed-form optimal solution, resulting in 20-40% better performance than previous state-of-the-art methods.
Low-rank decomposition has emerged as an important problem in Large Language Model (LLM) fine-tuning and inference. Through Singular Value Decomposition (SVD), the weight matrix can be factorized into low-rank spaces optimally. Previously, a common practice was to decompose the weight in the activation-whitened space, and then achieve satisfying results. In this work, we propose Optimal Brain Decomposition LLM (OBD-LLM), which studies the decomposition problem in the model space by utilizing second-order Hessian information. Through a rigorous Kronecker-factorization of the Hessian, we show that the decomposition needs to consider both input and output information of the layer, and achieves much better decomposition results compared to input only method. Our loss-aware decomposition method involves a bi-directional whitening on the weight matrix. As a result, OBD-LLM is a closed-form solution for the optimal decomposition of weights in the language model. Remarkably, we achieve ~20-40\% better results than previous state-of-the-art decomposition methods, the SVD-LLM.