Hyperbolic–topological signal fusion with Ricci-Adaptive geometry for hierarchy-aware pan-cancer histopathology classification

Accurate classification of histopathological images in pan-cancer settings remains a challenging biomedical signal processing problem because heterogeneous tissue morphologies coexist with inherently hierarchical diagnostic labels. Conventional deep learning models typically operate in Euclidean feature spaces and assume flat class structures, thereby overlooking both the topological organization of tissue architecture and the taxonomy of cancer subtypes. To address these limitations, this study proposes a novel framework, HyperPath-Net, which unifies topological signal analysis, hyperbolic representation learning, and curvature-aware feature fusion within a single end-to-end architecture. The proposed method introduces a Persistent Topological Signature (PTS) module that captures global morphological organization through persistence diagrams derived from nuclear spatial distributions. These descriptors are integrated with convolutional texture features via a Ricci-Adaptive Routing (RAR) mechanism, which dynamically modulates feature contributions using a scalar curvature proxy estimated from the image intensity surface. The proxy is an approximation inspired by Ricci curvature, not an exact computation, and the module name should be read as such throughout. The fused representation is projected onto a Poincaré ball to enable hierarchy-preserving embedding, where a geodesic-margin classifier and hierarchical Busemann loss jointly enforce organ-level structure and subtype discrimination. Extensive experiments on a large-scale multi-organ histopathology dataset of 130,000 image tiles across 26 cancer subtypes show that the proposed framework achieves state-of-the-art performance, with 99.47% classification accuracy and 99.44% macro-F1 score, outperforming both convolutional and transformer-based baselines. Ablation and sensitivity analyses confirm that topological encoding and hyperbolic geometry provide complementary discriminative power, while curvature-adaptive fusion enhances robustness to morphological variability. These accuracies should be read with one caveat: strict slide-level separation could be confirmed for 61.8% of the tiles, and the remaining 38.2% were split at the tile level after perceptual-hash duplicate removal, so residual correlation between tiles of the same specimen cannot be excluded, and the absolute figures may be optimistic. From a signal processing perspective, the proposed approach establishes a unified paradigm that integrates spatial-frequency texture features, topological invariants, and non-Euclidean geometric embeddings. This synergy enables compact, interpretable, and hierarchy-consistent representations, offering a promising direction for scalable, clinically meaningful decision-support systems in digital pathology.