Performance of Naïve Spectral Geometric Models in Histopathology AI

Spectral geometric methods provide mathematically interpretable representations of tissue morphology, yet their standalone performance in histopathology artificial intelligence has not been systematically evaluated. This study benchmarks purely spectral pipelines across representative digital pathology and spatial omics tasks relative to convolutional baselines. Spectral features derived from graph Laplacians, heat kernel signatures, spectral wavelet energy, Slepian concentrations, fractal descriptors, and persistent homology were extracted from histopathology patches using fixed-grid graphs. Features were processed using spectral neural operators and gradient boosting. Four tasks were evaluated: binary breast cancer classification (BreaKHis), multi-class glioblastoma region-patch classification, spatial transcriptomics prediction (10× Visium), and spot-wise denoising. Cross-validation and leave-one-slide-out strategies were applied. Metrics included accuracy, sensitivity, specificity, area under the receiver operating characteristic curve (AUC), mean squared error, and Pearson correlation. Equivalence between spectral and CNN models was not established within the prespecified ±0.03 AUC margin. Purely spectral models achieved lower performance than convolutional baselines, with AUC differences of 0.12-0.23. The CNN→LGBM model achieved an accuracy of 0.83 ± 0.06, balanced accuracy of 0.73 ± 0.10, and AUC of 0.80 ± 0.13. Equivalence was not established within the prespecified margin. Fusion achieved balanced accuracy of 0.73 ± 0.08, equal to the CNN baseline mean balanced accuracy, without surpassing CNN AUC. Spatial transcriptomics prediction showed limited cross-slide generalization (Pearson correlation 0.06), whereas spot-wise denoising under sparse conditions showed competitive performance. Spectral geometric models do not outperform convolutional methods for classification or segmentation but provide complementary utility in denoising and sparse spatial settings.