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npx versuz@latest install hiyenwong-ai-collection-collection-skills-holobrain-holograph-oscillatory-gnngit clone https://github.com/hiyenwong/ai_collection.gitcp ai_collection/SKILL.MD ~/.claude/skills/hiyenwong-ai-collection-collection-skills-holobrain-holograph-oscillatory-gnn/SKILL.md--- name: holobrain-holograph-oscillatory-gnn description: > HoloBrain and HoloGraph framework: modeling brain rhythms through coupled oscillatory synchronization and applying this principle to graph neural networks. Addresses GNN over-smoothing and enables reasoning on graphs through oscillatory dynamics. --- # HoloBrain & HoloGraph: Oscillatory Synchronization for Brain Modeling and GNNs **Paper:** arXiv:2602.00057 **Authors:** Tingting Dan, Jiaqi Ding, Guorong Wu **Categories:** q-bio.NC, cs.LG **Year:** 2026 ## Overview Two-part framework connecting neuroscience and machine learning through oscillatory synchronization: 1. HoloBrain: Models brain rhythms through interference of spontaneously synchronized neural oscillations 2. HoloGraph: Applies synchronization principle to GNNs, enabling oscillatory computation beyond heat diffusion ## Key Concepts ### Neural Oscillatory Synchronization - Brain rhythms emerge from synchronization of coupled neural oscillators - Phase relationships between oscillators encode abstract concepts - Synchronization patterns dynamically reconfigure for different cognitive functions ### HoloGraph: Oscillatory GNNs - Each node is an oscillator; edges define coupling strength - Information propagation through phase synchronization rather than feature diffusion - Addresses over-smoothing: oscillatory dynamics maintain distinct phase patterns even after many iterations ## Methodology ### HoloGraph Implementation 1. Replace conventional GNN message passing with oscillatory synchronization 2. Node states as complex numbers (amplitude + phase) 3. Information encoded in phase relationships 4. Synchronization dynamics enable iterative refinement 5. Readout maps final phase patterns to predictions ### Advantages over Traditional GNNs - No over-smoothing - Natural multi-scale representation - Biological plausibility - Enhanced reasoning capability ## Applications - Brain rhythm modeling - Graph classification - Molecular property prediction - Knowledge graph reasoning ## Key Insights 1. Shared mechanism: same oscillatory synchronization for brain rhythms and graph computation 2. Over-smoothing solution through oscillatory dynamics 3. Phase as richer representation 4. Biology inspires computation ## References - Dan, T., Ding, J., & Wu, G. (2026). HoloBrain & HoloGraph. arXiv:2602.00057.