Neuro-Symbolic (NeSy) integration combines symbolic reasoning with Neural Networks (NNs) for tasks requiring perception and reasoning. Most NeSy systems rely on continuous relaxation of logical knowledge, and no discrete decisions are made within the model pipeline. Furthermore, these methods assume that the symbolic rules are given. In this paper, we propose Deep Symbolic Learning (DSL), a NeSy system that learns NeSy-functions, i.e., the composition of a (set of) perception functions which map continuous data to discrete symbols, and a symbolic function over the set of symbols. DSL learns simultaneously the perception and symbolic functions while being trained only on their composition (NeSy-function). The key novelty of DSL is that it can create internal (interpretable) symbolic representations and map them to perception inputs within a differentiable NN learning pipeline. The created symbols are automatically selected to generate symbolic functions that best explain the data. We provide experimental analysis to substantiate the efficacy of DSL in simultaneously learning perception and symbolic functions.

翻译：神经符号（Neuro-Symbolic, NeSy）整合将符号推理与神经网络（NNs）相结合，用于需要感知与推理的任务。大多数NeSy系统依赖逻辑知识的连续松弛，且在模型流程中不进行离散决策。此外，这些方法假设符号规则是已知的。本文提出深度符号学习（DSL），一种能够学习NeSy函数（即一组将连续数据映射为离散符号的感知函数与基于符号集合的符号函数的复合函数）的NeSy系统。DSL在仅对复合函数（NeSy函数）进行训练的条件下，同时学习感知函数与符号函数。DSL的关键创新在于，它能够在可微神经网络学习流程中创建内部（可解释）符号表示，并将其映射至感知输入。所生成的符号被自动选择以构造最能解释数据的符号函数。我们通过实验分析验证了DSL在同时学习感知与符号函数方面的有效性。