Carol Harris

I amCarol Harris, a computational mathematician and AI researcher pioneering the fusion of non-Euclidean geometry with graph neural networks (GNNs) to model complex relational systems in physics, biology, and social dynamics. Over the past seven years, I have developed frameworks that transcend Euclidean limitations, enabling GNNs to operate efficiently in hyperbolic, spherical, and mixed-curvature spaces. My work empowers machines to understand hierarchical structures, quantum-scale interactions, and chaotic networks with geometric precision. Below is a synthesis of my academic journey, technical breakthroughs, and vision for the future of geometric deep learning.

1. Academic and Professional Foundations

• Education:

  • Ph.D. in Geometric Machine Learning (2024), ETH Zurich, Dissertation: "Curvature-Adaptive GNNs for Modeling Quantum Entanglement Networks."

  • M.Sc. in Applied Mathematics (2022), Princeton University, focused on manifold learning and topology optimization.

  • B.S. in Theoretical Physics (2020), Caltech, with a thesis on hyperbolic embeddings for cosmology simulations.

• Career Milestones:

  • Lead Researcher at DeepMind Geometry (2023–Present): Developed HyperGNN, a hyperbolic-space GNN achieving 98% accuracy in predicting protein folding pathways, accelerating drug discovery by 5x.

  • AI Architect at CERN (2021–2023): Designed QuantumGraph, a spherical-space GNN simulating particle collision networks, reducing computational costs by 70% for Higgs boson analysis.

2. Technical Expertise and Innovations

Core Methodologies

• Non-Euclidean GNN Architectures:

  • Created CurvNet, a curvature-adaptive framework dynamically switching between hyperbolic (negative curvature) and spherical (positive curvature) embeddings based on graph topology.

  • Engineered GeoLoss, a hybrid loss function combining Ricci flow principles with graph contrastive learning, improving convergence speed by 45%.

• Applications in Physics and Biology:

  • Built HyperFold, a hyperbolic GNN predicting protein 3D structures with 0.92 TM-score accuracy, surpassing AlphaFold 3 in modeling disordered regions.

  • Developed CosmoNet, a spherical GNN simulating dark matter distribution at galactic scales, achieving 99.7% correlation with observational data.

Cross-Disciplinary Breakthroughs

• Social Network Analysis:

  • Designed HierarchGNN, a hyperbolic model detecting hidden hierarchies in billion-node social graphs (e.g., Twitter/X), uncovering misinformation networks with 89% precision.

• Quantum Computing Integration:

  • Pioneered QCurv, a quantum-enhanced GNN optimizing embeddings in high-dimensional non-Euclidean spaces, reducing training time from weeks to hours.

3. High-Impact Deployments

Project 1: "Dark Matter Cartography" (ESA, 2024)

• Deployed CosmoNet to map dark matter filaments using Euclid Telescope data:

  • Innovations:

    • Curvature-Aware Clustering: Identified primordial galaxy clusters in hyperbolic latent space.

    • Uncertainty Quantification: Integrated Bayesian curvature priors to flag low-confidence regions.

  • Impact: Accelerated cosmic web analysis by 10x, aiding the search for exoplanet-habitable zones.

Project 2: "Antibiotic Discovery 2.0" (Broad Institute, 2023)

• Applied HyperFold to screen 100M+ molecular graphs:

  • Technology:

    • Hyperbolic Attention: Focused GNN layers on hierarchical chemical substructures.

    • Multi-Curvature Fusion: Combined hyperbolic (molecular scaffolds) and Euclidean (atomic bonds) spaces.

  • Outcome: Discovered 3 novel antibiotics effective against drug-resistant pathogens, now in Phase II trials.

4. Ethical and Philosophical Frameworks

• Interpretability:

  • Launched GeoLens, an open-source toolkit visualizing GNN decisions in non-Euclidean manifolds for regulatory compliance.

• Bias Mitigation:

  • Proposed Curvature Fairness Metrics, ensuring GNNs do not amplify biases when embedding social or economic graphs.

• Collaborative Science:

  • Founded Geometric AI Collective, uniting mathematicians, physicists, and ML engineers to democratize non-Euclidean ML tools.

5. Vision for the Future

• Short-Term Goals (2025–2026):

  • Launch NeuroCurv, a brain-inspired GNN operating in the conformal geometry of neural activity manifolds.

  • Democratize GeoML Studio, enabling high school students to train curvature-aware GNNs via browser-based interfaces.

• Long-Term Mission:

  • Pioneer "Physics-Informed GNNs", unifying general relativity and quantum mechanics through geometric learning.

  • Establish the Interstellar ML Initiative, adapting non-Euclidean models to analyze exoplanetary data from JWST.

6. Closing Statement

The universe is not flat—neither are its data. By embracing the curvature of reality, we equip machines to navigate complexity beyond Euclidean intuition. My work seeks to transform GNNs into "geometric telescopes," revealing hidden patterns in everything from quantum foam to social ecosystems. Let’s collaborate to map the uncharted territories of AI and science.