For binary classification in the NTK regime, LoRA rank r=1 suffices and is often optimal under cross-entropy loss, reducing the prior sufficient condition from r>=12.
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In the high-dimensional proportional regime, a large gradient step on a two-layer network induces a target-dependent spiked Gaussian covariance on the features, yielding a data-adaptive kernel that amplifies target-aligned eigenvalues and mixes leading eigenfunctions.
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Rethinking the Rank Threshold for LoRA Fine-Tuning
For binary classification in the NTK regime, LoRA rank r=1 suffices and is often optimal under cross-entropy loss, reducing the prior sufficient condition from r>=12.
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How does feature learning reshape the function space?
In the high-dimensional proportional regime, a large gradient step on a two-layer network induces a target-dependent spiked Gaussian covariance on the features, yielding a data-adaptive kernel that amplifies target-aligned eigenvalues and mixes leading eigenfunctions.