RAG-GNN: Integrating Retrieved Knowledge with Graph Neural Networks for Precision Medicine

Network topology excels at structural predictions but fails to capture functional semantics encoded in biomedical literature. We present a retrieval-augmented generation (RAG) embedding framework that integrates graph neural network representations with dynamically retrieved literature-derived knowledge through contrastive learning. Benchmarking against ten embedding methods reveals task-specific complementarity: topology-focused methods achieve near-perfect link prediction (GCN: 0.983 AUROC), while RAG-GNN is the only method achieving positive silhouette scores for functional clustering (0.001 vs. negative scores for all baselines). Information-theoretic decomposition shows network topology contributes 77.3% of predictive information, while retrieved documents provide 8.6% unique information. Applied to cancer signaling networks (379 proteins, 3,498 interactions), the framework identifies DDR1 as a therapeutic target based on retrieved evidence of synthetic lethality with KRAS mutations. These results establish that topology-only and retrieval-augmented approaches serve complementary purposes: structural prediction tasks are solved by network topology alone, while functional interpretation uniquely benefits from retrieved knowledge.

Resonant Sparse Geometry Networks

We introduce Resonant Sparse Geometry Networks (RSGN), a brain-inspired architecture with self-organizing sparse hierarchical input-dependent connectivity. Unlike Transformer architectures that employ dense attention mechanisms with O(n^2) computational complexity, RSGN embeds computational nodes in learned hyperbolic space where connection strength decays with geodesic distance, achieving dynamic sparsity that adapts to each input. The architecture operates on two distinct timescales: fast differentiable activation propagation optimized through gradient descent, and slow Hebbian-inspired structural learning for connectivity adaptation through local correlation rules. We provide rigorous mathematical analysis demonstrating that RSGN achieves O(n*k) computational complexity, where k << n represents the average active neighborhood size. Experimental evaluation on hierarchical classification and long-range dependency tasks demonstrates that RSGN achieves 96.5% accuracy on long-range dependency tasks while using approximately 15x fewer parameters than standard Transformers. On challenging hierarchical classification with 20 classes, RSGN achieves 23.8% accuracy (compared to 5% random baseline) with only 41,672 parameters, nearly 10x fewer than the Transformer baselines which require 403,348 parameters to achieve 30.1% accuracy. Our ablation studies confirm the contribution of each architectural component, with Hebbian learning providing consistent improvements. These results suggest that brain-inspired principles of sparse, geometrically-organized computation offer a promising direction toward more efficient and biologically plausible neural architectures.

Attention mechanisms in neural networks

Attention mechanisms represent a fundamental paradigm shift in neural network architectures, enabling models to selectively focus on relevant portions of input sequences through learned weighting functions. This monograph provides a comprehensive and rigorous mathematical treatment of attention mechanisms, encompassing their theoretical foundations, computational properties, and practical implementations in contemporary deep learning systems. Applications in natural language processing, computer vision, and multimodal learning demonstrate the versatility of attention mechanisms. We examine language modeling with autoregressive transformers, bidirectional encoders for representation learning, sequence-to-sequence translation, Vision Transformers for image classification, and cross-modal attention for vision-language tasks. Empirical analysis reveals training characteristics, scaling laws that relate performance to model size and computation, attention pattern visualizations, and performance benchmarks across standard datasets. We discuss the interpretability of learned attention patterns and their relationship to linguistic and visual structures. The monograph concludes with a critical examination of current limitations, including computational scalability, data efficiency, systematic generalization, and interpretability challenges.