Deep learning has been shown to achieve impressive results in several tasks
where a large amount of training data is available. However, deep learning
solely focuses on the accuracy of the predictions, neglecting the reasoning
process leading to a decision, which is a major issue in life-critical
applications. Probabilistic logic reasoning allows to exploit both statistical
regularities and specific domain expertise to perform reasoning under
uncertainty, but its scalability and brittle integration with the layers
processing the sensory data have greatly limited its applications. For these
reasons, combining deep architectures and probabilistic logic reasoning is a
fundamental goal towards the development of intelligent agents operating in
complex environments. This paper presents Relational Neural Machines, a novel
framework allowing to jointly train the parameters of the learners and of a
First--Order Logic based reasoner. A Relational Neural Machine is able to
recover both classical learning from supervised data in case of pure
sub-symbolic learning, and Markov Logic Networks in case of pure symbolic
reasoning, while allowing to jointly train and perform inference in hybrid
learning tasks. Proper algorithmic solutions are devised to make learning and
inference tractable in large-scale problems. The experiments show promising
results in different relational tasks.

本文介绍了一种新颖的框架 Relational Neural Machines，它可以对学习器的参数和基于一阶逻辑的推理器进行联合训练，下面将介绍其在大规模关系任务中的可行性和良好效果。

关系神经机器

Relational Neural Machines

Markov Logic Networks (MLNs), which elegantly combine logic rules and
probabilistic graphical models, can be used to address many knowledge graph
problems. However, inference in MLN is computationally intensive, making the
industrial-scale application of MLN very difficult. In recent years, graph
neural networks (GNNs) have emerged as efficient and effective tools for
large-scale graph problems. Nevertheless, GNNs do not explicitly incorporate
prior logic rules into the models, and may require many labeled examples for a
target task. In this paper, we explore the combination of MLNs and GNNs, and
use graph neural networks for variational inference in MLN. We propose a GNN
variant, named ExpressGNN, which strikes a nice balance between the
representation power and the simplicity of the model. Our extensive experiments
on several benchmark datasets demonstrate that ExpressGNN leads to effective
and efficient probabilistic logic reasoning.

本研究探讨了 Markov 逻辑网络和图神经网络的组合，并使用图神经网络进行 MLN 中的变分推理。研究提出了一种名为 ExpressGNN 的 GNN 变体，并通过多个基准数据集的广泛实验表明，ExpressGNN 在有效和高效的概率逻辑推理方面具有领先优势。

基于图神经网络的高效概率逻辑推理

Efficient Probabilistic Logic Reasoning with Graph Neural Networks

Deep learning is very effective at jointly learning feature representations
and classification models, especially when dealing with high dimensional input
patterns. Probabilistic logic reasoning, on the other hand, is capable to take
consistent and robust decisions in complex environments. The integration of
deep learning and logic reasoning is still an open-research problem and it is
considered to be the key for the development of real intelligent agents. This
paper presents Deep Logic Models, which are deep graphical models integrating
deep learning and logic reasoning both for learning and inference. Deep Logic
Models create an end-to-end differentiable architecture, where deep learners
are embedded into a network implementing a continuous relaxation of the logic
knowledge. The learning process allows to jointly learn the weights of the deep
learners and the meta-parameters controlling the high-level reasoning. The
experimental results show that the proposed methodology overtakes the
limitations of the other approaches that have been proposed to bridge deep
learning and reasoning.

该研究提出了深度逻辑模型理论，并将深度学习与概率逻辑推理相结合，以实现智能代理的发展。实验结果表明，该方法优于其他深度学习和推理方法的限制。