Nerve Theorems for Fixed Points of Neural Networks

Nerve Theorems for Fixed Points of Neural Networks

Applied Algebraic Topology Network via YouTube Direct link

Intro

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1 of 21

Intro

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Classroom Contents

Nerve Theorems for Fixed Points of Neural Networks

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  1. 1 Intro
  2. 2 How does connectivity shape activity?
  3. 3 Combinatorial Threshold-Linear Networks (CTLNs)
  4. 4 A diversity of dynamical behaviour
  5. 5 Dynamic attractors "live around fixed points"
  6. 6 Graph structure and CTLN fixed points
  7. 7 Nerves: divide and conquer
  8. 8 Directional graphs Agraph G is directional there is a partition of its nodes V
  9. 9 DAG decompositions
  10. 10 Directional graphs and feed-forward networks
  11. 11 Directional covers and their nerves
  12. 12 Basic examples
  13. 13 Theorem (DAG decomposition)
  14. 14 5-clique chain example Graph G
  15. 15 Theorem (cycle nerve)
  16. 16 Grid graph
  17. 17 Network engineering: Grid as a nerve
  18. 18 Dynamical prediction
  19. 19 Summary
  20. 20 Thank you for listening
  21. 21 Iterating the construction

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