Tissue graphs represent histology images as graphs over tissue-conforming superpixels, which keeps homogeneous tissue regions intact instead of cutting them into rectangular patches. To embed superpixels, current encoders crop them to bounding boxes and then pad, resize, or mask them, so background or fill values can leak into the node features. This matters in practice, and especially in medical imaging, where a prediction should depend on the tissue and not on an arbitrary preprocessing choice: on BACH, changing only the fill of the masked region shifts the accuracy of frozen encoders by up to 6 percentage points, larger than the differences among the four best encoders under mean fill, and the preferred fill differs between datasets, so it cannot be fixed once and for all. We present TAN (Tissue-Aware Network), a compact convolutional encoder (0.41M parameters) that processes each superpixel at its native shape and extent and excludes background from every operation, which makes its embeddings exactly invariant to the fill by construction. Under identical masks and an identical graph classifier, TAN's accuracy on BACH is not significantly different from that of the 303M-parameter foundation model UNI (81.1% vs. 80.7-82.6%, depending on the fill), with ~740x fewer parameters, ~1,190x fewer FLOPs, and no pretraining. On BRACS, TAN is close to a ResNet18 trained under the same protocol and trails the histopathology foundation models. An ablation with TAN's architecture but standard processing of fill-padded crops shows that masking keeps accuracy similar (nominally higher on BACH, lower on BRACS, within noise) at less than half the FLOPs.

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