Neurosymbolic artificial intelligence is a growing field of research aiming to combine neural network learning capabilities with the reasoning abilities of symbolic systems. Informed multi-label classification is a sub-field of neurosymbolic AI which studies how to leverage prior knowledge to improve neural classification systems. A well known family of neurosymbolic techniques for informed classification use probabilistic reasoning to integrate this knowledge during learning, inference or both. Therefore, the asymptotic complexity of probabilistic reasoning is of cardinal importance to assess the scalability of such techniques. However, this topic is rarely tackled in the neurosymbolic literature, which can lead to a poor understanding of the limits of probabilistic neurosymbolic techniques. In this paper, we introduce a formalism for informed supervised classification tasks and techniques. We then build upon this formalism to define three abstract neurosymbolic techniques based on probabilistic reasoning. Finally, we show computational complexity results on several representation languages for prior knowledge commonly found in the neurosymbolic literature.

翻译：神经符号人工智能是一个快速发展的研究领域，旨在结合神经网络的学习能力与符号系统的推理能力。信息多标签分类是神经符号人工智能的一个子领域，它研究如何利用先验知识改进神经分类系统。一组成熟的用于信息分类的神经符号技术采用概率推理在学习、推理或二者过程中整合此类知识。因此，概率推理的渐近复杂度对于评估这些技术的可扩展性至关重要。然而，这一主题在神经符号文献中鲜有涉及，这可能导致对概率神经符号技术极限的理解不足。本文首先提出一种用于信息监督分类任务及技术的形式体系，继而基于该形式体系定义三种基于概率推理的抽象神经符号技术，最终证明了神经符号文献中常见的若干先验知识表示语言在计算复杂度方面的结果。