A neuro-symbolic glaucoma framework crosses hospitals: graph reasoning and fuzzy rules each hold up alone, but together they cost 8.1 AUC points

Glaucoma screening models lose accuracy across hospitals and cameras; this neuro-symbolic framework puts graph reasoning over anatomical structures and four clinical fuzzy rules into one trainable network and tests both together on strictly held-out cross-hospital data. Most published glaucoma detection systems report results on a single source with no real cross-hospital performance, and prior neuro-symbolic glaucoma work used hand-coded cup-to-disc thresholds without multi-centre cross-hospital evaluation. The cross-hospital set is 485 RIM-ONE images from the University of Santiago de Compostela hospital and a Nidek AFC-210 camera, never used in training, validation or model selection; the training side is 12,134 images from seven datasets split 75%/12.5%/12.5% into 9,100 training, 1,517 validation and 1,517 test images.

Anatomical graph reasoning alone raises in-distribution discrimination, symbolic rules alone do not hurt cross-hospital performance, but stacking the two drops cross-hospital AUC below the plain EfficientNet-B4 baseline. The EfficientNet-B4-only baseline scores 0.9472 in-distribution and 0.6970 cross-hospital; adding the graph attention network raises in-distribution AUC to 0.9612 with 0.6915 cross-hospital, while adding the symbolic module gives 0.6997 cross-hospital, not significantly different from baseline. The full framework scores 0.6155 cross-hospital (95% CI 0.562–0.669), 8.1 points below baseline, with p=0.002 versus baseline, p=0.004 versus the graph configuration and p=0.001 versus the symbolic configuration; across three random seeds the graph-containing configurations score lower cross-hospital than those without it.

The network builds six anatomical nodes from multi-scale fundus features, learns relationships among them with graph attention layers, and constrains classification probabilities with four fuzzy logic rules, all without segmentation masks. Segmentation-driven pipelines need pixel-level disc and cup annotations to compute cup-to-disc ratio, whereas this pipeline trains on classification labels alone and learns its cup-to-disc thresholds from data rather than fixing them by hand. The six nodes correspond to optic disc, optic cup, rim, retinal nerve fiber layer, vessel density and global context, projected from different EfficientNet-B4 feature levels and used as anatomy-motivated architectural labels rather than verified segmented regions; the full model trains in about 8 hours on a single RTX 3080 Ti and graph-containing configurations infer at about 22 ms per image.

The cross-hospital conclusion covers only the transition from EyePACS/Canon CR-2 acquisition to the Nidek AFC-210 at the University of Santiago de Compostela hospital; generalisation to other devices, sites and populations has not been evaluated, and in-distribution AUC should be read as an upper bound on internal generalisation because five datasets lacked patient identifiers and were split at image level.

Agreement between the cup-to-disc proxy and expert measurements on held-out images is weak and inconsistent across datasets, with a Spearman interval of 0.186–0.791 on DRISHTI-GS and no detected association on REFUGE2, so the proxy is treated as a latent ordinal score rather than an anatomically calibrated value; latent representations for rim, nerve fiber layer and vessel are not yet validated against segmentation ground truth, and the gradient-interference mechanism offered to explain the cross-hospital drop is consistent with the ablation pattern but has not been measured directly.