The notion of equality (identity) is simple and ubiquitous, making it a key case study for broader questions about the representations supporting abstract relational reasoning. Previous work suggested that neural networks were not suitable models of human relational reasoning because they could not represent mathematically identity, the most basic form of equality. We revisit this question. In our experiments, we assess out-of-sample generalization of equality using both arbitrary representations and representations that have been pretrained on separate tasks to imbue them with structure. We find neural networks are able to learn (a) basic equality (mathematical identity), (b) sequential equality problems (learning ABA-patterned sequences) with only positive training instances, and (c) a complex, hierarchical equality problem with only basic equality training instances (“zero-shot” generalization). In the two latter cases, our models perform tasks proposed in previous work to demarcate human-unique symbolic abilities. These results suggest that essential aspects of symbolic reasoning can emerge from data-driven, nonsymbolic learning processes.

中文翻译：

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使用非符号神经网络的关系推理和泛化。

平等（身份）的概念简单而普遍，使其成为关于支持抽象关系推理的表示的更广泛问题的关键案例研究。之前的工作表明，神经网络不适合人类关系推理的模型，因为它们无法在数学上表示身份，即平等的最基本形式。我们重新审视这个问题。在我们的实验中，我们使用任意表示和在单独任务上预先训练的表示来评估平等的样本外泛化，以赋予它们结构。我们发现神经网络能够学习 (a) 基本等式（数学恒等式），(b) 序列等式问题（学习 ABA 模式序列）只有正训练实例，以及 (c) 一个复杂的，只有基本平等训练实例的层次平等问题（“零样本”泛化）。在后两种情况下，我们的模型执行先前工作中提出的任务来划分人类独特的符号能力。这些结果表明，符号推理的基本方面可以从数据驱动的非符号学习过程中出现。