Where Networks Adapt and Where They Fail: Layer-Localised Diagnostics for Continual Learning

We ask two questions that continual learning methods leave unanswered: which layer is currently the active site of adaptation, and which individual predictions are unreliable after a task shift? We show both admit diagnostic answers from a single principle — activation-subspace consistency — measured at training time and inference time respectively. Gradient Direction Coherence (GDC), the mean pairwise cosine similarity of per-sample gradient directions within a mini-batch, identifies the adaptation boundary at the layer with minimum coherence. In plain feedforward CNNs this argmin is seed-stable (${\ell }^{\ast }=\text{block2}$, 5/5 seeds); under pervasive residual connections the gradient-space signal collapses predictably, a boundary condition the theory predicts. An exploratory activation-space variant shows a depth-correlated signal in ResNet-18 and ViT-small, reported as a preliminary finding rather than a resolution of the architectural restriction. Activation Projection Score (APS), computed in a single forward pass without label access, measures how well a sample's activations fit the training subspace at each layer. Across four configurations spanning plain CNNs, ResNet-18, and ViT-small ($n=5$ seeds each), APS at the deepest stage predicts per-sample correctness ($\rho =0.253\text{–}0.286$; below softmax confidence by 0.14–0.19 AUROC) and detects distribution shift (AUROC-OOD up to 0.990), and localises OOD detection to the final stage on a standard ImageNet-1k benchmark (ResNet-50, no fine-tuning; AUROC-OOD = 0.866). Against the Mahalanobis detector (Lee et al., 2018), APS wins at the deepest layer in CNN and ResNet architectures ($\Delta =+0.109,+0.160$, $p<0.001$, label-free) — where Mahalanobis degrades under ill-conditioned high-dimensional covariance estimation — and ties it at ceiling in ViT-small. We additionally document that naive lr-scaling from GDC yields no reliable retention improvement ($n=5$, $d=0.02$) and that the largest previously reported single-seed effect was a 5-SD outlier baseline artefact.