3D Weighted Geometric Graph Neural Networks for Sheep Facial Pain Assessment

Deep learning systems perform mainly within the 2D for a single image domain and take the face as a single-dimension representation, losing sight of the 3D anatomy of sheep and cross-landmark spatial relationships that are intrinsic to the clinically proven Sheep Pain Facial Expression Scale (SPFES). This paper presents the \textbf{3D Sheep Pain Facial Expression System (3D-SPFES)}, a novel, monocular depth-aware geometric graph neural network system that integrates each SPFES facial landmark, such as the ears, eyes, and nose, into 3D Euclidean space estimated from a single RGB camera by using VideoDepthAnything, thus preventing the need for specialized depth hardware. Each landmark node includes a feature vector containing its 3D spatial coordinates, estimated surface normal, and facial attribute class embedding. Edges linked to nodes are assigned weights based on an aggregate metric that combines both Euclidean distance and surface co-planarity in a 3D space. A Weighted Geometric Graph Neural Network (WG-GNN) studies this graph using $\mathcal{K} = 3$ geometry-aware message-passing layers enhanced by a scaled dot-product attention method that selectively enhances anatomically relevant inter-landmark messages. The resultant node embeddings are combined into $\mathcal{O} = 3$ pain-level clusters and integrated into a Normalized Pain Score (NPS) within the range of $[0, 100%]$ a confidence-weighted, SPFES-derived scoring method.

Curvature-Informed Potential Energy Surface for Protein-Ligand Binding Affinity Prediction

Accurate prediction of protein-ligand binding affinity is essential for structure-based drug discovery. Recent geometric deep learning methods have achieved promising performance by representing protein-ligand complexes as three-dimensional graphs. However, most existing approaches mainly rely on static interaction geometry from a single bound conformation, while neglecting molecular flexibility and binding-induced conformational changes. To address this limitation, we propose a curvature-informed potential energy surface (CPES) graph neural network for protein-ligand binding affinity prediction, which incorporates physics-informed curvature representations to model conformational flexibility. CPES first derives curvature spectral descriptors from the Hessian of the potential energy surface evaluated at equilibrium configurations, whose eigenvalues define the local principal curvatures of the potential energy surface. It then uses spectral cross-attention to compare the unbound ligand and protein with the bound complex, thereby capturing binding-induced changes in conformational dynamics. In parallel, hierarchical protein-ligand interaction representations are learned from static structural features through geometry-aware message passing, soft clustering, and bidirectional cross-attention. Finally, CPES fuses the curvature-informed dynamic representations with static interaction representations for affinity regression. Extensive evaluations on multiple benchmark datasets demonstrate that CPES achieves improved predictive performance and offers physical interpretability.

Curvature-Guided Geometric Representation for Protein-Ligand Binding Affinity Prediction

Protein-ligand binding affinity (PLA) prediction is critical in drug discovery. Despite the notable advancements in machine learning-based approaches, existing methods struggle to jointly characterize local geometric organization and globally coordinated cross-molecular interactions, limiting their ability to model complex binding mechanisms. Here, we propose RicciBind, a geometric representation framework that integrates curvature-guided hierarchical structure learning with optimal transport (OT)-based cross-domain alignment to model molecular interactions. Specifically, RicciBind leverages Ricci curvature to capture local interaction tightness within molecular structures, enhancing structural awareness and organizing atomic interactions into curvature-aware hierarchical representations. An OT-based cluster matching mechanism then aligns protein and ligand clusters across heterogeneous domains under geometric constraints, enabling globally consistent correspondences and revealing higher-order interaction patterns beyond local neighborhoods. By coupling curvature-guided structure encoding with OT-driven cross-domain alignment, RicciBind effectively models complex interaction semantics and substantially improves both the accuracy and interpretability of binding affinity prediction. Extensive experiments demonstrate that RicciBind achieved superior predictive performance and generalization across PLA benchmarks and virtual screening tasks. Ablation studies further confirmed the essential role of Ricci curvature in enhancing molecular interaction representations.

EpiFormer: Learning Antigen-Antibody Interactions for Epitope Prediction via Geometric Deep Learning

Antibodies neutralize foreign antigens by binding to specific surface regions called epitopes. Computational epitope prediction is critical for understanding immune recognition and guiding antibody engineering. However, existing methods face three fundamental challenges: antibody-aware models encode each chain independently and combine them only at a late stage, failing to capture co-dependent structural features that define binding interfaces, whereas severe class imbalance and scarcity of known antibody-antigen complexes render standard training objectives ineffective. We propose EpiFormer, a general encoder-decoder framework that addresses these challenges jointly. Our key design principle is interleaved cross-attention within GNN encoding layers, enabling bidirectional antigen-antibody information flow throughout representation learning rather than only at the output. This early-fusion principle is backbone-agnostic, providing consistent gains across GNN architectures from simple GCNs to equivariant models. We further show that sparsity-aware objectives are effective when paired with early-fusion architectures for the epitope prediction task. EpiFormer improves over the previous best method by over 40% in F1 score on standard benchmarks, demonstrating generalizability and cross-dataset transferability. Notably, EpiFormer discovers known biological principles as emergent behaviors of end-to-end training, where the learned cross-attention gates favor antigen-to-antibody information flow, consistent with the asymmetric roles of the two chains at the binding interface, and the model's preference for geometric over evolutionary features aligns with the established finding that epitope residues are not evolutionarily conserved. The source code is available at: https://github.com/mansoor181/epiformer.git