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Mean Field Initialization of the Annealed Importance Sampling Algorithm for an Efficient Evaluation of the Partition

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Annealed Importance Sampling (AIS) estimates partition functions for complex physical models. Using a mean-field distribution significantly improves AIS accuracy and computational efficiency for magnetic systems in Restricted Boltzmann Machines (RBMs).

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Area of Science:

  • Statistical physics
  • Machine learning
  • Computational physics

Background:

  • Probabilistic models in physics necessitate calculating partition functions (Z), which is computationally intensive for large systems.
  • Annealed Importance Sampling (AIS) offers a stochastic method for estimating Z, particularly suitable for parallel implementation in Restricted Boltzmann Machines (RBMs).

Purpose of the Study:

  • To evaluate the partition function (Z) of magnetic spin systems using AIS within RBMs.
  • To enhance the efficiency and accuracy of AIS by optimizing the starting probability distribution.

Main Methods:

  • Applied AIS to estimate the partition function (Z) for magnetic spin and spin-like systems mapped to RBMs.
  • Investigated the impact of using a mean-field starting probability distribution compared to the standard uniform distribution.
  • Conducted systematic analyses on small and large systems, comparing results with known exact values.

Main Results:

  • A properly selected mean-field starting distribution significantly improves the quality of Z estimation and reduces computational cost.
  • Two successful strategies for using mean-field distributions with AIS were identified and validated across various problem sizes.
  • The proposed methods provide reliable Z estimations with reduced computational expense, independent of any learning process or training data.

Conclusions:

  • Optimized starting distributions, specifically mean-field ones, enhance AIS performance for partition function estimation in RBMs.
  • The presented strategies offer efficient and accurate methods for estimating partition functions, applicable to magnetic systems without requiring prior training data.
  • This work provides practical improvements for applying AIS in computational physics and machine learning contexts.