CoRMF: Criticality-Ordered Recurrent Mean Field Ising Solver

• URL: http://arxiv.org/abs/2403.03391v2
• Date: Thu, 7 Mar 2024 06:03:49 GMT
• Title: CoRMF: Criticality-Ordered Recurrent Mean Field Ising Solver
• Authors: Zhenyu Pan, Ammar Gilani, En-Jui Kuo, Zhuo Liu
• Abstract summary: We propose an RNN-based efficient Ising model solver, the Criticality-ordered Recurrent Mean Field (CoRMF) By leveraging the approximated tree structure of the underlying Ising graph, the newly-obtained criticality order enables the unification between variational mean-field and RNN. CoRFM solves the Ising problems in a self-train fashion without data/evidence, and the inference tasks can be executed by directly sampling from RNN.
• Score: 4.364088891019632
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We propose an RNN-based efficient Ising model solver, the Criticality-ordered Recurrent Mean Field (CoRMF), for forward Ising problems. In its core, a criticality-ordered spin sequence of an $N$-spin Ising model is introduced by sorting mission-critical edges with greedy algorithm, such that an autoregressive mean-field factorization can be utilized and optimized with Recurrent Neural Networks (RNNs). Our method has two notable characteristics: (i) by leveraging the approximated tree structure of the underlying Ising graph, the newly-obtained criticality order enables the unification between variational mean-field and RNN, allowing the generally intractable Ising model to be efficiently probed with probabilistic inference; (ii) it is well-modulized, model-independent while at the same time expressive enough, and hence fully applicable to any forward Ising inference problems with minimal effort. Computationally, by using a variance-reduced Monte Carlo gradient estimator, CoRFM solves the Ising problems in a self-train fashion without data/evidence, and the inference tasks can be executed by directly sampling from RNN. Theoretically, we establish a provably tighter error bound than naive mean-field by using the matrix cut decomposition machineries. Numerically, we demonstrate the utility of this framework on a series of Ising datasets.

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