Performance of Naiive Spectral Geometric Models in Histopathology AI.

There have been no systematic evaluations of purely spectral models for digital pathology tasks. We implemented and benchmarked four pipelines: binary classification on the BreaKHis dataset, multi-class region classification in glioblastoma, spatial transcriptomics, and denoising on Visium 10x. Across all tasks, extensive cross-validation and grouped splits showed that purely spectral models did not improve performance over CNN-only baselines, but offer useful complementary tools for interpretability and processing. Denoising showed strong performance that proves utility in data-scarce or heterogeneous image environments. Equivalence testing confirms that spectral and CNN model performances fall outside ±3% AUC. Fusion models between CNNs and spectral models show higher balanced accuracy. Spectral models failed to generalize across spatial transcriptomics tasks, with low correlation despite stable training loss. These findings represent a systematic negative result: despite their theoretical richness, spectral geometric features and SNO embeddings prove to be complementary features for WSI classification or segmentation. Reporting such outcomes is essential to establish empirical boundaries for spectral methods and to encourage future work on conditions or data modalities where these approaches may hold greater promise.