Spectral Overfitting in Noisy Linear Probing of Pretrained Representations

Frozen pretrained features are often treated as a safe interface for downstream learning: only a small linear readout is trained, while the backbone is fixed. We show that this readout can still overfit noisy labels in a structured way. A label-blind PCA rank sweep reveals a sharp spectral pattern: under label noise, exposing all pretrained directions can hurt clean accuracy, and intermediate ranks often recover much of the lost performance. Rank-matched random projections help less, and measured between-class signal is strongly concentrated in leading PCs. The pattern appears across three ImageNet-pretrained backbones on CIFAR-10, with gains up to $36.0\pm0.8$ points over the default full-rank probe at 40\% noise. Tuned full-rank probes outperform validation-selected PCA probes, so we present the sweep as a diagnostic of spectral overfitting rather than a competitive noisy-label method.