What Does the Rank Buy? A Spectral and Distributional Analysis of Low-Rank Adaptation

arXiv:2609.32002v2 Announce Type: replace Abstract: The rank $r$ in LoRA is widely treated as a capacity control: a smaller rank is assumed to yield a simpler model that generalizes better. We show that, under hard per-factor norm budgets---the idealization of the weight decay and norm control used in practice---this intuition breaks down. The reason is structural: under such budgets, the updates LoRA can reach are exactly the matrices of rank at most $r$ inside a nuclear-norm ball, and every complexity and displacement functional we analyze is maximized over this set by a rank-one update---so

This content is for informational purposes only and is not professional advice. Specifications, prices, plan tiers, and features change frequently and may differ from what is shown here; verify current details on the manufacturer's or company's official page before purchasing. Ratings are based on analysis of published documentation, not independent lab testing.