This is an interesting and useful overview, though it’s important not to confuse their notation with the Penrose graphical notation I use in this post, since lines in their notation seem to represent the message-passing contributions to a vector, rather than the indices of a tensor.
That said, there are connections between tensor network contractions and message passing algorithms like Belief Propagation, which I haven’t taken the time to really understand. Some references are:
Also related -
(Mathilde Papillon is really really insightful)
This is an interesting and useful overview, though it’s important not to confuse their notation with the Penrose graphical notation I use in this post, since lines in their notation seem to represent the message-passing contributions to a vector, rather than the indices of a tensor.
That said, there are connections between tensor network contractions and message passing algorithms like Belief Propagation, which I haven’t taken the time to really understand. Some references are:
Duality of graphical models and tensor networks—Elina Robeva and Anna Seigal
Tensor network contraction and the belief propagation algorithm—R. Alkabetz and I. Arad
Tensor Network Message Passing—Yijia Wang, Yuwen Ebony Zhang, Feng Pan, Pan Zhang
Gauging tensor networks with belief propagation—Joseph Tindall, Matt Fishman