The Geometry of Saturation: Effective Rank Predicts When Labels Stop Helping in Few-Shot Classification
Read the original on arXiv Machine Learning →arXiv:2606. 24903v2 Announce Type: replace Abstract: Few-shot label acquisition lacks a label-free signal for when additional labels cease to improve accuracy: existing stopping criteria either require a held-out validation set (violating the few-shot premise) or rely on theoretically ungrounded heuristics, so we introduce the spectral saturation index $S(K)=\mathrm{erank}(\hat{\Sigma}_W^{(K)})/K$, the exponential spectral entropy of the pooled within-class covariance normalized by per-class support size $K$, which measures the exploration rate per label and falls below a fixed threshold $\tau=0.
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