RENEBUABENG

Greetings. I am Rene Buabeng, a mathematical machine learning researcher specializing in symmetry-driven data augmentation. With a Ph.D. in Algebraic Learning Theory (ETH Zurich, 2025) and directorship at the Max Planck Institute for Intelligent Symmetries, my work redefines data scarcity solutions through Lie group theory, geometric deep learning, and invariant representation learning. My mission: "To harness the infinite-dimensional symmetries hidden in data manifolds, transforming sparse samples into rich, physics-aware training ecosystems."

Theoretical Framework

1. Lie Group Foundations

My augmentation framework formalizes data transformations as Lie group actions:

Continuous Symmetry Exploitation: Parameterizing augmentation operators via Lie algebras (e.g., SE(3) for 3D medical imaging, SU(2) for quantum state rotations).

Orbit-Stabilizer Theorem: Generating equivalence classes of augmented samples while preserving topological invariants.

Cartan’s Moving Frames: Learning optimal symmetry alignments between data domains using Maurer-Cartan forms.

2. Symmetry-Aware Architecture

Developed LieAugment, a three-tiered system:

1. Symmetry Detector:

- Identifies latent SE(2)/SO(3) symmetries via Haar measure integration.

2. LieGAN:

- Generates symmetry-consistent augmentations with a Wasserstein discriminator.

3. Noetherian Regularizer:

- Preserves conservation laws (e.g., momentum in physics simulations) during augmentation.

Achieved 98.3% invariance preservation in augmented MNIST-360 (rotations/translations).

Key Innovations

1. Stochastic Lie Algebra Sampling

Derived LiePCA, a method to sample augmentation paths along principal symmetry axes:

Reduced ImageNet-1k training data by 60% while maintaining 95% top-5 accuracy.

Enabled 12× faster convergence in PDE-solving neural operators (NeurIPS 2025).

2. Symmetry-Aware Adversarial Training

Designed SymmAttack, generating adversarial examples confined to data manifolds’ Lie groups:

Improved robustness against 3D sensor spoofing (Waymo: +43% adversarial accuracy).

Certified invariance against arbitrary SO(3) rotations in satellite imagery.

3. Quantum Symmetry Augmentation

Collaborated with CERN on Q-LieAugment:

Generated symmetry-preserved quantum states for training error-corrected QNNs.

Achieved 99.9% fidelity in 5-qubit gate simulations using only 10 base samples.

Impactful Applications

1. Medical Imaging Revolution

Partnered with Siemens Healthineers on SymMRI:

Synthesized 15,000+ pathological brain MRIs from 100 scans using SO(3)×ℝ⁴ symmetries.

Reduced false negatives in early Alzheimer’s detection by 29% (Nature Medicine, 2026).

2. Climate Modeling

Deployed LieClimate:

Augmented paleoclimate data via SL(2,ℝ) symmetry (atmospheric pattern preservation).

Predicted Arctic ice melt rates within 2% of 2030 satellite observations.

3. Cultural Heritage Preservation

Launched SymmArt:

Reconstructed fragmented Assyrian reliefs using SE(2)-equivariant augmentations.

Enabled AI-powered restoration of 23 ISIS-damaged artifacts (UNESCO collaboration).

Methodological Contributions

Lie Group Curriculum Learning

Designed progressive symmetry exposure schedules:

Start with discrete ℤ₂ symmetries → Graduate to non-compact groups like SL(2,ℂ).

Cut catastrophic forgetting by 54% in lifelong learning benchmarks.

Symmetry Distillation

Extracted portable Lie group signatures from pretrained models:

Enabled zero-shot symmetry detection in novel domains (e.g., Martian geology).

Topological Augmentation Metrics

Introduced Persistent Homology Energy:

Quantifies augmentation-induced manifold deformations.

FDA-approved for validating synthetic clinical trial data.

Ethical and Philosophical Commitments

Symmetry for Fairness

Proved Equivariant Fairness Theorem:

"Models trained with Lie group augmentations naturally erase sensitive attributes orthogonal to task-relevant symmetries."

Reduced gender bias in 3D pose estimation by 81% (CVPR 2025).

Open Symmetry

Released LieTorch, an open-source library for symmetry-aware augmentation (GitHub stars: 23k).

Anti-Weaponization

Developed SymmScreen:

Detects symmetry-violating deepfakes in political media (AUC=0.97).

Future Directions

Infinite-Dimensional Symmetries: Extending to Virasoro/Kac-Moody algebras for NLP data augmentation.

Bio-Inspired Augmentation: Mimicking protein folding symmetries for drug discovery.

Exoplanet Symmetry Mining: Preparing frameworks for potential alien data geometries (NASA JPL collab).

Let us illuminate the dark corners of data scarcity with the torch of symmetry—where every transformation tells a truth, and every truth shapes intelligence.