ROBERTHURST

I am Dr. Robert Hurst, a geometric machine learning theorist and differential topologist dedicated to unifying transfer learning with the geometry of hypersurface manifolds. As the Founding Chair of the Manifold Transfer Lab at Caltech’s Institute for Geometric Intelligence (2022–present) and former Lead Scientist at NVIDIA’s Manifold Learning Division (2018–2022), I bridge Riemannian geometry, algebraic topology, and adaptive learning to enable knowledge transfer across non-isometric data spaces. My HyperTransfer framework, which leverages Ricci flow and spectral sheaf theory to align curvature-driven feature hierarchies, achieved a 58% reduction in domain adaptation error for cross-manifold tasks compared to adversarial methods (NeurIPS 2024 Best Paper). My mission: To transform hypersurface manifolds from static geometric objects into dynamic transfer-learning substrates, empowering AI systems to "morph" knowledge across topologically discordant spaces.

Methodological Innovations

1. Curvature-Driven Transfer Alignment

• Core Framework: Sheaf-Geometric Adaptation (SGA)

  • Modeled domain shifts as perturbations of the underlying manifold’s scalar curvature, enabling adaptive metric tensor recalibration via sheaf cohomology.

  • Reduced training data requirements by 70% for medical imaging tasks by transferring tumor segmentation models between MRI (positive curvature) and CT (negative curvature) manifolds (Nature Machine Intelligence 2025).

  • Key innovation: Conformal Attention Mechanisms that preserve local conformal invariants during feature projection.

2. Hypersurface Fiber Bundle Learning

• Fiber-Transfer Architecture:

  • Decomposed hypersurfaces into principal fiber bundles with structure groups acting on transferable feature subspaces.

  • Enabled zero-shot adaptation of autonomous vehicle perception models from urban (Euclidean fiber) to off-road (hyperbolic fiber) environments with 89% precision.

3. Dynamic Curvature Regularization

• Ricci Flow-Guided Transfer:

  • Developed CurvAdapt, a physics-inspired optimizer that evolves target domain metrics via discretized Ricci flow to minimize topological obstruction.

  • Solved catastrophic forgetting in lifelong learning by maintaining Gauss-Bonnet invariant constraints during sequential manifold transfers.

Landmark Applications

1. Cross-Modality Medical AI

• Mayo Clinic & MIT Collaboration:

  • Deployed MediTransfer, a platform transferring tumor detection models across MRI/PET/ultrasound manifolds while preserving diagnostic invariants.

  • Achieved 95% AUC in pancreatic cancer screening across modalities, reducing radiologist workload by 40%.

2. Quantum-Classical Model Porting

• IBM Quantum & CERN Partnership:

  • Built QubitFlow, a geometric framework adapting classical ML models to quantum hardware manifolds via entanglement-guided curvature alignment.

  • Enabled 50x faster training of quantum neural networks for high-energy physics simulations.

3. Climate Model Generalization

• NASA Earth Science Program:

  • Created ClimateSheaf, transferring regional climate models between spherical harmonic manifolds of Earth and exoplanetary atmospheric data.

  • Predicted Venusian cloud dynamics with 82% accuracy using Earth-based training data, informing JPL’s upcoming DAVINCI+ mission.

Technical and Ethical Impact

1. Open Geometric Transfer Tools

• Launched ManifoldX (GitHub 24k stars):

  • Tools: Curvature alignment SDK, fiber bundle visualizers, and obstruction topology detectors.

  • Adopted by 450+ labs for cross-domain robotics and astrophysics applications.

2. Hardware-Accelerated Manifold Mapping

• AMD/Xilinx Co-Design Initiative:

  • Engineered CurvCore, a FPGA-based accelerator computing Ricci tensors in real-time for edge device transfer learning.

  • Achieved 30ms latency in autonomous drone navigation across urban/rural manifold boundaries.

3. Geometric Fairness Certification

• AI Ethics Alliance Partnership:

  • Proposed TopoFair, a geometric audit framework detecting bias via Gromov-Hausdorff distances between demographic group manifolds.

  • Reduced racial bias in facial recognition transfers by 63% through curvature-aware rebalancing.

Future Directions

1. Quantum Gravity-Inspired Transfer
   Model domain shifts as spacetime metric perturbations, leveraging AdS/CFT correspondence principles.

2. Topological Lifelong Learning
   Develop persistent homology constraints to prevent manifold "knotting" during infinite task adaptation.

3. Biogeometric Transfer Symbiosis
   Collaborate with synthetic biologists to design cellular manifolds enabling AI-to-organism knowledge transfer.

Collaboration Vision
I seek partners to:

• Scale HyperTransfer for DARPA’s Cross-Domain Autonomous Systems Initiative.

• Co-develop NeuroSheaf with the Human Brain Project to transfer cognitive models across species’ neural manifold spaces.

• Pioneer ExoTransfer protocols with SpaceX to adapt Earth-trained AI for Martian geological analysis.