论文标题

分析可区分的模糊含义

Analyzing Differentiable Fuzzy Implications

论文作者

van Krieken, Emile, Acar, Erman, van Harmelen, Frank

论文摘要

结合符号和神经方法在AI社区中引起了很大的关注,因为人们经常认为这些方法的优点和缺点是互补的。文献中的一种这样的趋势是从模糊逻辑中雇用运营商的弱监督学习技术。特别是,他们使用此类逻辑中描述的先前的背景知识来帮助未标记和嘈杂数据培训神经网络。通过使用神经网络(或接地)来解释逻辑符号,可以将这些背景知识添加到常规损失功能中,从而使推理成为学习的一部分。 在本文中,我们研究了模糊逻辑文献中的含义如何在可区分的环境中行为。在这种情况下,我们分析了这些模糊含义的形式属性之间的差异。事实证明,包括一些最著名的含义,包括一些最著名的含义,非常不适合在可区分的学习环境中使用。进一步的发现表明,梯度在先决条件下驱动的梯度与含义的造成的梯度之间存在严重的失衡。此外,我们引入了一个新的模糊含义(称为sigmoidal含义)来解决这一现象。最后,我们从经验上表明,可以使用可区分的模糊逻辑进行半监督学习,并表明Sigmoidal含义的表现优于模糊含义的其他选择。

Combining symbolic and neural approaches has gained considerable attention in the AI community, as it is often argued that the strengths and weaknesses of these approaches are complementary. One such trend in the literature are weakly supervised learning techniques that employ operators from fuzzy logics. In particular, they use prior background knowledge described in such logics to help the training of a neural network from unlabeled and noisy data. By interpreting logical symbols using neural networks (or grounding them), this background knowledge can be added to regular loss functions, hence making reasoning a part of learning. In this paper, we investigate how implications from the fuzzy logic literature behave in a differentiable setting. In such a setting, we analyze the differences between the formal properties of these fuzzy implications. It turns out that various fuzzy implications, including some of the most well-known, are highly unsuitable for use in a differentiable learning setting. A further finding shows a strong imbalance between gradients driven by the antecedent and the consequent of the implication. Furthermore, we introduce a new family of fuzzy implications (called sigmoidal implications) to tackle this phenomenon. Finally, we empirically show that it is possible to use Differentiable Fuzzy Logics for semi-supervised learning, and show that sigmoidal implications outperform other choices of fuzzy implications.

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