PRAC: Principal-Random Subspace for LLM Activation Compression and Memory-Efficient Training

TL;DR

PRAC introduces a novel activation compression method for large language models that combines spectral decomposition and random sampling to significantly reduce memory usage while maintaining model performance.

Contribution

The paper proposes PRAC, a new spectral-based activation compression technique that achieves unbiased, low-variance estimates and substantial memory savings in LLM training.

Findings

Up to 36% memory reduction in training large models

Negligible performance degradation with PRAC

Minimal additional computational cost

Abstract

Activations have become the primary memory bottleneck in large-batch LLM training. However, existing compression methods fail to exploit the spectral structure of activations, resulting in slow convergence or limited compression. To address this, we bridge the relationship between the algorithm's fast convergence and the requirements for subspace projection, and show that an effective compression should yield an unbiased estimate of the original activation with low variance. We propose Principal-Random Subspace for LLM Activation Compression (PRAC), which novelly decomposes activations into two components: a principal subspace captured via SVD to retain dominant information, and a random subspace sampled from the orthogonal complement to approximate the tail. By introducing a precise scaling factor, we prove that PRAC yields an unbiased gradient estimator with minimum variance under certain conditions. Extensive experiments on pre-training and fine-tuning tasks demonstrate that PRAC achieves up to 36% total memory reduction with negligible performance degradation and minimal computational cost.