Spatial Supervision Without Attribution Optimization: Improving Post-Hoc Class Activation Maps via Box-Guided Evidence Routing

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Post-hoc class activation maps (CAMs) are a standard tool for inspecting the evidence behind an image classifier's predictions, yet nothing in ordinary training encourages these maps to be spatially appropriate. We study whether inexpensive spatial supervision can improve a classifier's own predicted-class Grad-CAM without ever optimizing an attribution map. Box-Guided Evidence Routing (BGER) trains a lightweight gate on the final feature map under box or mask supervision and routes classification through the gated features, while Grad-CAM is computed separately at the pre-gate representation, so the evaluated map never enters the training objective. With a BCE routing loss, BGER raises MaxBoxAccV2 from $0.584$ to $0.715$ on CUB-200-2011 and from $0.757$ to $0.832$ on Stanford Dogs at comparable accuracy. Matched controls attribute most of the ResNet-50 gain to the spatial supervision reshaping the backbone rather than to routing itself: when classification bypasses the gate, most of the improvement remains, and detaching gradients through the gate leaves the ResNet-50 result nearly unchanged. The same detachment preserves most of the gain in two DenseNet-121 chest X-ray settings but removes the apparent gain on Swin-T, and directly supervising the CAM reaches stronger localization at a larger accuracy cost. Overall, spatial supervision can improve separately evaluated post-hoc CAMs, but both the mechanism and the size of the benefit depend on the architecture and the evaluation setting.