A3 : an Analytical Low-Rank Approximation Framework for Attention

TL;DR

The paper introduces A3, a low-rank approximation framework for Transformers that reduces model size and computation without runtime overhead, outperforming previous methods in language modeling tasks.

Contribution

A3 provides an analytical, layer-splitting approach to low-rank approximation that minimizes functional loss and improves compression efficiency over existing techniques.

Findings

A3 maintains superior performance compared to SoTAs under the same reduction budget.

LLaMA 3.1-70B with A3 achieves perplexity of 4.69 on WikiText-2.

A3 enables versatile applications including KV cache compression and quantization integration.

Abstract

Large language models have demonstrated remarkable performance; however, their massive parameter counts make deployment highly expensive. Low-rank approximation offers a promising compression solution, yet existing approaches have two main limitations: (1) They focus on minimizing the output error of individual linear layers, without considering the architectural characteristics of Transformers, and (2) they decompose a large weight matrix into two small low-rank matrices. Consequently, these methods often fall short compared to other compression techniques like pruning and quantization, and introduce runtime overhead such as the extra GEMM kernel launches and memory operations for decomposed small matrices. To address these limitations, we propose $A^3$, a post-training low-rank approximation framework. $A^3$ splits a Transformer layer into three functional components, namely $\texttt{QK}$, $\texttt{OV}$, and $\texttt{MLP}$ and provides analytical solutions that reduces the hidden dimension size inside each component while minimizing the component's functional loss. This approach directly reduces model sizes, KV cache sizes, and FLOPs without introducing any runtime overheads. Through extensive experiments, we show that $A^3$ maintains superior performance compared to SoTAs. For example, under the same reduction budget in computation and memory, our low-rank approximated LLaMA 3.1-70B achieves a perplexity of 4.69 on WikiText-2, outperforming the previous SoTA's 7.87 by 3.18. We also show versatile applications of $A^3$ in KV cache compression, integration with quantization, fine-tuning and mixed-rank assignments. We open-sourced our framework and code at https://github.com/DeepWok/a3.