JoshuaMerritt

Greetings. I am Joshua Merritt, a machine learning theorist and computational mathematician specializing in invariance-driven few-shot learning. With a Ph.D. in Mathematical Machine Learning (MIT, 2025) and leadership of the Stanford-NeurIPS Invariance Initiative, my work pioneers frameworks that unify Lie group theory, topological data analysis, and meta-learning to conquer data scarcity challenges. My mission: "To arm AI systems with mathematical invariants—those universal truths that persist across domains—enabling robust learning even when examples are sparse as starlight."

Theoretical Framework

1. Invariance as Inductive Bias

My methodology formalizes invariant learning through:

Group-Theoretic Embeddings: Encoding symmetry structures (e.g., rotation/translation invariance in medical imaging) via Lie algebra representations.

Topological Persistence: Preserving homological features (connected components, voids) across few-shot domains using Čech complexes.

Invariant Risk Minimization++: Extending IRM with differential geometry constraints for non-linear support (manifold stability ≥98.7%).

2. Meta-Invariant Architecture

Developed INV-FSL, a meta-learning system integrating:

1. Cohomology-Aware Prototyping:

- Extracts equivalence classes using Hodge Laplacian eigenmaps.

2. Adversarial Invariance Certifier:

- Generates worst-case perturbations while maintaining key invariants.

3. Sheaf-Theoretic Adaptation:

- Aligns local data stalks to global semantic structures via sheaf cohomology.

Validated on 12 benchmarks (Mini-ImageNet → ISIC 2025 skin lesions: +29.4% accuracy).

Key Innovations

1. Differential Invariant Distillation

Derived Noether’s Learning Theorem:

"Every data-efficient learner implies a conserved quantity in feature space."

Applied to stabilize few-shot object detection under occlusions (COCO-FSL: mAP +17.2).

2. Hyperbolic Few-Shot Alignment

Mapped invariant relations to Poincaré disks:

Enabled 5-shot classification with 3.1× lower hyperbolic distortion than Euclidean baselines.

Revolutionized low-data astrophysical transient classification (ZTF → LSST domain shift).

3. Stochastic Invariant Mining

Trained G-invariant VAEs to disentangle:

Compact core invariants (e.g., molecular chirality in drug discovery).

Context-sensitive variations (lighting/pose in robotics).

Achieved 89% OOD robustness on NASA’s Mars terrain navigation with 3 training images.

Breakthrough Applications

1. Pandemic Pathogen Prediction

Collaborated with WHO on EpiINV:

Predicted Zoonotic spillover risks from 5 viral genome snippets.

Identified invariant epitope regions across 12 SARS-CoV-2 variants (Nature, 2026).

2. Exoplanet Atmospheric Retrieval

Deployed AstroINV for JWST data:

Classified atmospheric compositions with 3 spectral samples per planet.

Discovered methane invariance patterns hinting at biotic processes (TRAPPIST-1e).

3. Quantum Material Discovery

Partnered with CERN on QINV:

Predicted topological insulator properties from 2 HRTEM images.

Accelerated novel superconductors’ discovery by 40× (Science Robotics, 2025).

Methodological Contributions

Invariant Curriculum Meta-Learning

Designed phase transitions between invariant hierarchies:

Local (texture) → Global (shape) invariants.

Reduced catastrophic forgetting in 100-shot lifelong learning (Acc ↑32%).

Causal Invariance Forests

Combined invariant learning with causal discovery:

Identified intervention-invariant biomarkers in Alzheimer’s progression.

Outperformed standard causal models with 10× fewer samples.

Invariance-Boosted Synthetic Data

Generated mathematically guaranteed invariant augmentations:

5 synthetic COVID-19 X-rays preserved 99% pathognomonic invariants.

FDA-approved for radiology residency training.

Ethical and Philosophical Principles

Invariance for Justice

Proved Representation Fairness Theorem:

"Invariance to sensitive attributes emerges naturally when learning universal invariants."

Reduced racial bias in 3-shot facial recognition by 74% (NIST FRVT 2025).

Open Invariance

Launched INV-Gym: An open library of 1,200 invariance-aware few-shot tasks.

Anti-Misuse Protocols

Developed Invariance Watermarking to detect AI-generated disinformation:

Flags content violating physical invariants (e.g., impossible shadows).

Future Horizons

Topological Quantum Few-Shot Learning: Merging persistent homology with quantum ML for attosecond-scale learning.

Developmental AI: Simulating infant-like invariant acquisition in artificial agents (DARPA collaboration).

Intergalactic Invariance: Preparing frameworks for potential alien data structures (Breakthrough Listen Initiative).

Let us teach machines to grasp the eternal—so they may learn the ephemeral with wisdom.