Geometry-aware similarity metrics for neural representations on Riemannian and statistical manifolds

1. 1Identify the limitations of existing similarity measures in capturing intrinsic geometry of neural representations
2. 2Develop a novel method called metric similarity analysis (MSA) that leverages geometry-aware similarity metrics
3. 3Apply MSA to compare neural representations on Riemannian and statistical manifolds
4. 4Evaluate the effectiveness of MSA in capturing subtle distinctions between different neural network solutions

ML researchers and engineers on a team benefit from this method as it enables them to better understand and compare the representational geometries of different neural networks, which is crucial for improving model performance and interpretability

💡 Existing similarity measures may fail to capture subtle distinctions between neural network solutions due to their focus on extrinsic geometry, whereas MSA focuses on intrinsic geometry

💡 Novel method for comparing neural representations on manifolds: Metric Similarity Analysis (MSA)