arXiv:2607.05872v1 Announce Type: new Abstract: Memory-efficient optimizers such as GaLore train large language models by projecting gradients onto a rank-r subspace recomputed every T steps, assuming this subspace is a slowly drifting object that can be tracked. We show that beyond a small reproducible core, there is no such object. Two estimates of the top-r subspace computed at the same step from disjoint minibatches disagree as much as estimates computed T steps apart (0.73 vs 0.74 of the maximal chordal distance sqrt(2r), at Pythia-160M with r=128): the apparent rotation at each refresh i
This research is published as memory-efficient optimizers, like GaLore, gain prominence for training large language models (LLMs), making their foundational assumptions critical to evaluate.
This finding challenges a core assumption behind memory-efficient optimizer designs, suggesting that current methods for tracking low-rank subspaces in LLM training might be fundamentally flawed or inefficient.
The understanding of how memory-efficient optimizers function is altered, potentially leading to revisions in their design or the development of entirely new approaches for large model training.
- · AI researchers focused on optimization theory
- · Developers of new, more robust memory-efficient training techniques
- · Cloud providers if more efficient training leads to lower compute costs
- · Existing memory-efficient optimizers relying on the 'slowly drifting subspace' a
- · Organizations heavily invested in current low-rank training methodologies withou
The current generation of memory-efficient optimizers may require significant re-evaluation or redesign to address the non-identifiability issue.
This could spur innovation in alternative memory-efficient training paradigms that do not rely on tracking unstable subspaces, potentially leading to faster or more stable LLM training.
Long-term, a better theoretical understanding of optimization dynamics could lead to entirely new architectures or training methodologies for future large AI models, impacting the broader compute supply chain.
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Read at arXiv cs.LG