The Information Geometry of Representation Formation

TL;DR

This paper introduces information geometry to study how neural representations evolve during training, revealing that the trajectory—rather than just the endpoint—encodes critical information about computational complexity and stability. It shows that higher-order interactions lead to more tortuous paths, and that path geometry predicts future drift and robustness better than endpoint measures. Representation-aware optimization can actively shape these trajectories, making formation history both measurable and actionable.

Why It Matters

Understanding representation formation enables better control over model stability and generalization, offering new avenues for optimizing neural networks beyond final performance. This insight could lead to more robust and interpretable models, especially in safety-critical applications where representational stability matters. It also opens doors to novel training strategies that target the learning process itself.

Key Findings

• Representation trajectories reveal computational complexity through path tortuosity, which increases with higher-order input interactions.
• Path geometry predicts subsequent representational drift and sensitivity to perturbations better than endpoint displacement.
• Representation-aware optimization can actively shape formation trajectories, demonstrating that geometry is both measurable and actionable.