Sloppy models, Information geometry, and Why science works

Module #1, Basic training in condensed matter physics, Cornell 2024

Lectures given Spring 2024 on information geometry, ill-posed multiparameter models, and emergent simplicity.

Why does science work? Complex models in physics, biology, economics, and engineering are usually successful because their microscopic details are not crucial for describing the real world. We explain their success using information geometry, combining differential geometry with approximation theory to understand the reason simplicity emerges from complex underpinnings.

• Syllabus
• References for further study
• Incomplete draft of book
• Lecture slides and notes
  • Recent seminar video
  • Emergence and sloppy models
    • Video part 1 and part 2
  • Sloppy models
  • Model manifolds and hyperribbons
  • Rigorous hyperellipsoid bounds on model manifolds: Katherine Quinn presentation
  • Visualizing model behavior: Dodging the curse of dimensionality to plot the hyperribbons
    • Video
  • Visualizing high-dimensional spaces: Replica theory and inPCA: Katherine Quinn presentation
  • InPCA as a lens: The training process of deep neural networks: Itay Griniasty presentation
  • Visualizing statistical mechanics in Minkowski space: Han Kheng Teoh presentation
  • Emergent simplicity, Occam's razor, and model reduction
    • Video
  • Challenges in multiparameter fits: an information geometry perspective (Unused)
• Exercises
  • Emergence and sloppy models
  • Hyperribbons and information geometry
  • Emergent simplicity and manifold boundaries
  • Visualizing model behavior