Reproduce “Probabilistic Graphical Models and Tensor Networks: A Hybrid Framework” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Jacob Miller, Geoffrey Roeder, Tai-Danae Bradley
Researchers from Mila, Princeton, and X (formerly Google X) introduce Decohered Born Machines (DBMs), a hybrid framework that bridges Probabilistic Graphical Models (PGMs) and Tensor Networks (TNs). The framework allows for the principled integration of quantum-like correlations into PGM models while maintaining PGM-style conditional independence. DBMs achieve lower negative log-likelihood on sequential data and exhibit improved training efficiency compared to classical Undirected Graphical Models (UGMs).
Key insights
- A fully-decohered Born Machine is mathematically equivalent to a discrete Undirected Graphical Model (UGM), demonstrating a principled way to recover classical PGM behavior from quantum-inspired models.
- Decohered Born Machines (DBMs) are shown to be equivalent in expressive power to Locally Purified States (LPS), indicating they retain the ability to capture complex correlations beyond classical UGMs.
- DBMs satisfy a conditional independence property: if a set of decohered edges forms a cut set, the associated random variables exhibit PGM-like conditional independence, overcoming a limitation of general Born Machines.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.