Why Does Train-Validation Separation Emerge? Update-Pressure Density Dynamics in Pretrained Backbones

원문 초록

During fine-tuning, training accuracy often continues to improve after validation accuracy levels off, widening the empirical gap. We propose a support-transfer account: early updates reuse broadly shared structure, while later fitting relies increasingly on narrower structure with less benefit for held-out examples. From fixed training probes, we normalize per-example gradient magnitudes and measure their pooled dispersion, $D_{\mathrm{den}}$, and their probe-count-weighted within-class dispersion, $D_{\mathrm{within}}^{\mathrm{wt}}$. A local model gives conditions for dispersion and directional cross-entropy separation to grow together, separating uniform logit scaling; additional decision-boundary conditions characterize accuracy-gap growth. A controlled five-level hierarchy tests the effect of sample-private support. A 240-branch intervention matrix crosses training-progress anchors, batch sizes, private shares, and gradient-differentiation doses. The negative gap dose response is clearer at later training stages and is retained across the four batch sizes. A further 48 branches replicate its direction across additional seeds at a fixed stage and batch. Both normalized readouts are positively associated with the accuracy gap in all 90 language fine-tuning runs across three backbones and six tasks. The same direction holds in all 20 vision runs across four datasets. Together, the controlled hierarchy, targeted intervention, and real-model trajectories support a connection between evolving gradient differentiation and train-validation separation.