Equivariant Neural Network for Factor Graphs

• URL: http://arxiv.org/abs/2109.14218v1
• Date: Wed, 29 Sep 2021 06:54:04 GMT
• Title: Equivariant Neural Network for Factor Graphs
• Authors: Fan-Yun Sun, Jonathan Kuck, Hao Tang, Stefano Ermon
• Abstract summary: We propose two inference models: Factor-Equivariant Neural Belief Propagation (FE-NBP) and Factor-Equivariant Graph Neural Networks (FE-GNN) FE-NBP achieves state-of-the-art performance on small datasets while FE-GNN achieves state-of-the-art performance on large datasets.
• Score: 83.26543234955855
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Several indices used in a factor graph data structure can be permuted without changing the underlying probability distribution. An algorithm that performs inference on a factor graph should ideally be equivariant or invariant to permutations of global indices of nodes, variable orderings within a factor, and variable assignment orderings. However, existing neural network-based inference procedures fail to take advantage of this inductive bias. In this paper, we precisely characterize these isomorphic properties of factor graphs and propose two inference models: Factor-Equivariant Neural Belief Propagation (FE-NBP) and Factor-Equivariant Graph Neural Networks (FE-GNN). FE-NBP is a neural network that generalizes BP and respects each of the above properties of factor graphs while FE-GNN is an expressive GNN model that relaxes an isomorphic property in favor of greater expressivity. Empirically, we demonstrate on both real-world and synthetic datasets, for both marginal inference and MAP inference, that FE-NBP and FE-GNN together cover a range of sample complexity regimes: FE-NBP achieves state-of-the-art performance on small datasets while FE-GNN achieves state-of-the-art performance on large datasets.

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