Neurosymbolic AI is a growing field of research aiming to combine neural networks learning capabilities with the reasoning abilities of symbolic systems. This hybridization can take many shapes. In this paper, we propose a new formalism for supervised multi-label classification with propositional background knowledge. We introduce a new neurosymbolic technique called semantic conditioning at inference, which only constrains the system during inference while leaving the training unaffected. We discuss its theoritical and practical advantages over two other popular neurosymbolic techniques: semantic conditioning and semantic regularization. We develop a new multi-scale methodology to evaluate how the benefits of a neurosymbolic technique evolve with the scale of the network. We then evaluate experimentally and compare the benefits of all three techniques across model scales on several datasets. Our results demonstrate that semantic conditioning at inference can be used to build more accurate neural-based systems with fewer resources while guaranteeing the semantic consistency of outputs.

翻译：神经符号人工智能是一个新兴的研究领域，旨在将神经网络的学习能力与符号系统的推理能力相结合。这种融合可以呈现多种形式。本文针对具有命题背景知识的监督式多标签分类提出了一种新的形式化方法。我们引入了一种名为"推理时语义约束"的新型神经符号技术，该技术仅在推理阶段对系统施加约束，而训练过程不受影响。我们讨论了该技术相较于另外两种主流神经符号技术（语义约束与语义正则化）在理论与实用层面的优势。我们开发了一种新的多尺度评估方法，用以分析神经符号技术带来的收益如何随网络规模变化。随后，我们在多个数据集上对三种技术在不同模型尺度下的收益进行了实验对比。结果表明，推理时语义约束能够在保证输出语义一致性的前提下，用更少的资源构建更精准的神经网络系统。