Analyzing Differentiable Fuzzy Implications
Analyzing Differentiable Fuzzy Implications
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DOI：
10.24963/kr.2020/92
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发表时间：
2020-06
期刊：
影响因子：
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通讯作者：
Emile van Krieken;Erman Acar;F. V. Harmelen
中科院分区：
文献类型：
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作者：
Emile van Krieken;Erman Acar;F. V. Harmelen
结合符号和神经方法在人工智能社区中获得了相当大的关注，因为有人认为它们的优势和劣势是互补的。在文献中的一个趋势是弱监督学习技术，采用模糊逻辑运算符。它们使用这种逻辑中描述的先验背景知识来帮助从未标记和噪声数据中训练神经网络。通过使用神经网络解释逻辑符号（或将其接地），可以将这些背景知识添加到常规损失函数中，从而使推理成为学习的一部分。我们研究如何影响模糊逻辑文献中的行为在可微设置。在这种情况下，我们分析了这些模糊蕴涵的形式属性之间的差异。事实证明，各种模糊含义，包括一些最著名的，是非常不适合用于可微学习设置。进一步的发现表明，由前因和后因驱动的梯度之间存在强烈的不平衡。此外，我们引入了一个新的家庭的模糊影响（称为sigmoidal影响），以解决这一现象。最后，我们的经验表明，它是可以使用可微模糊逻辑的半监督学习，并显示sigmoidal的影响优于其他选择的模糊影响。
Combining symbolic and neural approaches has gained considerable attention in the AI community, as it is argued that their strengths and weaknesses are complementary. One trend in the literature are weakly supervised learning techniques that employ operators from fuzzy logics. They use prior background knowledge described in such logics to help training neural networks 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. We investigate how implications from the fuzzy logic literature behave in a differentiable setting. In this 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.