提出可学习的符号逻辑框架，让神经网络自动融合专家知识与数据规则。
Logic of Hypotheses: from Zero to Full Knowledge in Neurosymbolic Integration
- 用可学习的选择算子扩展命题逻辑，实现符号规则与神经网络融合。
- 在表格数据和含感知任务的基准上均取得优异性能，准确率超基线模型。
- 支持从零到全知识的灵活配置，适合需要可解释性的实际应用。
神经符号集成（NeSy）将神经网络学习与符号推理相结合。该领域分为两类方法：一类是将手工规则注入神经模型，另一类是从数据中推导符号规则。本文提出逻辑假设框架（LoH），一种统一上述两种路径的新语言，能够灵活整合数据驱动的规则学习与符号先验及专家知识。LoH在命题逻辑语法基础上引入带有可学习参数的选择算子，从一组候选公式中选择最优子公式。结合格奥尔德模糊逻辑，LoH公式可直接编译为可微计算图，使最优选择可通过反向传播学习。该框架涵盖部分现有NeSy模型，并支持任意程度的知识指定。此外，利用格奥尔德模糊逻辑与最新提出的格奥尔德技巧，模型可离散化为无性能损失的硬布尔函数。实验表明，该方法在表格数据及两个含感知组件的NeSy任务上表现强劲。
原文摘要 · Abstract (English)
Neurosymbolic integration (NeSy) blends neural-network learning with symbolic reasoning. The field can be split between methods injecting hand-crafted rules into neural models, and methods inducing symbolic rules from data. We introduce Logic of Hypotheses (LoH), a novel language that unifies these strands, enabling the flexible integration of data-driven rule learning with symbolic priors and expert knowledge. LoH extends propositional logic syntax with a choice operator, which has learnable parameters and selects a subformula from a pool of options. Using fuzzy logic, formulas in LoH can be directly compiled into a differentiable computational graph, so the optimal choices can be learned via backpropagation. This framework subsumes some existing NeSy models, while adding the possibility of arbitrary degrees of knowledge specification. Moreover, the use of Gödel fuzzy logic and the recently developed Gödel trick yields models that can be discretized to hard Boolean-valued functions without any loss in performance. We provide experimental analysis on such models, showing strong results on tabular data and on two NeSy tasks with a perceptual component.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。