PLUMAGE: Probabilistic Low rank Unbiased Min Variance Gradient Estimator for Efficient Large Model Training

Abstract

Accelerator memory and networking constraints have emerged as dominant bottlenecks when training large language models LLMs with billions of parameters. Existing low rank gradient estimators such as GaLoRE and FLORA compress gradients and optimizer tensors by projecting weight gradients onto a rank r subspace, enabling LLM training on consumer hardware. Yet, these methods are either biased or subject to high estimator variance. Moreover, the optimizer state based on the first and second moments estimates expressed in the previous subspace becomes misaligned whenever the projection is updated, leading to instabilities during training. We propose PLUMAGE: Probabilistic Low rank Unbiased Minimum vAriance Gradient Estimator. PLUMAGE is a drop in replacement for existing low rank gradient estimators. It does not introduce new hyperparameters beyond the chosen rank r and the update interval. In addition, we resolve optimizer state misalignment issues to prevent spurious weight updates and enhance training stability. We empirically demonstrate that PLUMAGE shrinks the full rank optimization's gap over the pre training evaluation loss by 33% on average across models and the average training loss across the GLUE benchmark by 28% within a similar computational and memory footprint as GaloRE.