LogicMP: A Neuro-symbolic Approach for Encoding First-order Logic Constraints
This addresses the problem of efficiently incorporating logical constraints into neural networks for researchers and practitioners in neuro-symbolic AI, representing a novel method rather than an incremental improvement.
The paper tackles the challenge of integrating first-order logic constraints with neural networks by proposing LogicMP, a novel neural layer that performs mean-field variational inference over Markov logic networks, enabling efficient encoding of constraints. Empirical results across graph, image, and text tasks show that LogicMP outperforms advanced competitors in performance and efficiency.
Integrating first-order logic constraints (FOLCs) with neural networks is a crucial but challenging problem since it involves modeling intricate correlations to satisfy the constraints. This paper proposes a novel neural layer, LogicMP, whose layers perform mean-field variational inference over an MLN. It can be plugged into any off-the-shelf neural network to encode FOLCs while retaining modularity and efficiency. By exploiting the structure and symmetries in MLNs, we theoretically demonstrate that our well-designed, efficient mean-field iterations effectively mitigate the difficulty of MLN inference, reducing the inference from sequential calculation to a series of parallel tensor operations. Empirical results in three kinds of tasks over graphs, images, and text show that LogicMP outperforms advanced competitors in both performance and efficiency.