Tensor Networks
Tensor Networks
Tensor Networks (Penrose diagrams) are visual diagrams to represent Tensor operations. The idea behind using a visual representations is that you can study and optimize these networks. These networks are also perhaps with some minor differences, string diagrams. **String diagrams have been used in category theory to prove things (Curry Howard correspondence). Also formal proofs can be used to generalize optimizations **(Linear Algebra/Differential Equations) - Tensors - Category Theory - Formal Proofs - Optimizations
Reading
- https://www.microsoft.com/en-us/research/publication/using-tensor-diagrams-to-represent-and-solve-geometric-problems/?from=https://research.microsoft.com/apps/pubs/default.aspx?id=79791&type=exact
- https://en.wikipedia.org/wiki/Tensor_network
- https://www.math3ma.com/blog/matrices-as-tensor-network-diagrams
- https://www.tensors.net/tutorial-4
Papers
- Fong, Brendan and David I. Spivak. “Seven Sketches in Compositionality: An Invitation to Applied Category Theory.” arXiv: Category Theory (2018): n. pag.
- Bradley, Tai-Danae. “What is Applied Category Theory?” (2018).
- https://iopscience.iop.org/article/10.1088/1751-8121/aa6dc3
- https://www.mathstat.dal.ca/~selinger/papers.html#graphical
- Selinger, Peter. “A Survey of Graphical Languages for Monoidal Categories.” arXiv: Category Theory (2009): 289-355.
- https://www.cs.ox.ac.uk/people/bob.coecke/Selby.pdf