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About this paper
Elina Robeva, Anna Seigal
Robeva and Seigal establish a fundamental mathematical duality between undirected graphical models and tensor networks, leveraging the concept of hypergraph duality to unify their representations and operations. This work demonstrates how marginalization in graphical models is equivalent to tensor contractions, and how algorithms like the Junction Tree Algorithm correspond to tensor network contraction methods.
Key insights
- A universal duality exists between undirected discrete graphical models and tensor networks, rooted in the mathematical concept of hypergraph duality.
- Fundamental operations such as marginalization in graphical models correspond directly to tensor contractions in their dual tensor networks.
- Algorithmic similarities exist, where an exact inference algorithm for graphical models (Junction Tree Algorithm) directly maps to a tensor network contraction method (bubbling algorithm for MPS).
Summary by alphaXiv.
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