High-Dimensional Geometric Robustness in Representation

Key Points

• The aim is to explore the geometric limits of angular metrics in high-dimensional representation learning and develop a robust retrieval architecture.
• Established fundamental geometric limits in high-dimensional representations.
• Introduced a normalization theorem for high-dimensional vectors.
• Developed CAR, a non-gradient pattern recognition architecture.
• Validated predictions through six simulations and a real-world acoustic channel experiment.
• Demonstrated noise resilience up to 10¹⁵⁰ times.
• Achieved statistical significance with a cosine similarity of 0.2519.
• Showed a Z-score of 2.22 with p < .05 in experimental results.
• Maintained geometric structure across various testing conditions.