SubTrack++ : Gradient Subspace Tracking for Scalable LLM Training

Sahar Rajabi, Nayeema Nonta, Sirisha Rambhatla

Keywords: large language models, memory-efficient training, low-rank optimization, gradient projection

Abstract: Training large language models (LLMs) is highly resource-intensive due to their massive number of parameters and the overhead of optimizer states. While recent work has aimed to reduce memory consumption, such efforts often entail trade-offs among memory efficiency, training time, and model performance. Yet, true democratization of LLMs requires simultaneous progress across all three dimensions. To this end, we propose SubTrack++ that leverages Grassmannian gradient subspace tracking combined with projection-aware optimizers, enabling Adam’s internal statistics to adapt to subspace changes. Additionally, employing recovery scaling, a technique that restores information lost through low-rank projections, further enhances model performance. Our method demonstrates SOTA convergence by exploiting Grassmannian geometry, **reducing pre-training wall-time by up to 65% and fine-tuning time by 36%** compared to existing SOTA methods, while maintaining the same memory footprint. Code is at https://github.com/criticalml-uw/SubTrack.

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 16480