Under restricted strong convexity and smoothness, every stable point of LoRA training is either a low-rank global minimum or a high-rank, large-magnitude spurious minimum, and practical initialization and weight decay bias toward the former.
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LoRA Training Provably Converges to a Low-Rank Global Minimum or It Fails Loudly (But it Probably Won't Fail)
Under restricted strong convexity and smoothness, every stable point of LoRA training is either a low-rank global minimum or a high-rank, large-magnitude spurious minimum, and practical initialization and weight decay bias toward the former.