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Tensor Network Message Passing.

Yijia Wang1,2, Yuwen Ebony Zhang3, Feng Pan1

  • 1CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.

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We introduce tensor network message passing, a novel method for calculating statistical properties of interacting systems. This approach overcomes limitations of existing algorithms, offering accurate computations for complex systems in physics and machine learning.

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Area of Science:

  • Statistical physics
  • Applied mathematics
  • Machine learning

Background:

  • Computing statistical properties of interacting systems is crucial but challenging due to state space growth.
  • Existing methods like message-passing and tensor networks have limitations with loops and computational complexity.

Purpose of the Study:

  • To develop a novel method combining strengths of tensor networks and message-passing algorithms.
  • To accurately compute local observables like marginal probabilities and correlations in complex systems.

Main Methods:

  • Proposed "tensor network message passing" algorithm.
  • Combines tensor network contraction of small subgraphs with message-passing on sparse graphs.
  • Algorithm is exact for globally treelike, locally dense-connected systems with limited tree width.

Main Results:

  • Demonstrated superiority over belief propagation and loopy message-passing.
  • Successfully computed magnetizations for Ising models and spin glasses on synthetic and real-world graphs.

Conclusions:

  • Tensor network message passing effectively addresses weaknesses of prior methods.
  • Potential applications include network inference, combinatorial optimization, and quantum error correction decoding.