We present a novel neurosymbolic system called NeSyFOLD that classifies
images while providing a logic-based explanation of the classification.
NeSyFOLD's training process is as follows: (i) We first pre-train a CNN on the
input image dataset and extract activations of the last layer filters as binary
values; (ii) Next, we use the FOLD-SE-M rule-based machine learning algorithm
to generate a logic program that can classify an image -- represented as a
vector of binary activations corresponding to each filter -- while producing a
logical explanation. The rules generated by the FOLD-SE-M algorithm have filter
numbers as predicates. We use a novel algorithm that we have devised for
automatically mapping the CNN filters to semantic concepts in the images. This
mapping is used to replace predicate names (filter numbers) in the rule-set
with corresponding semantic concept labels. The resulting rule-set is highly
interpretable, and can be intuitively understood by humans. We compare our
NeSyFOLD system with the ERIC system that uses a decision-tree like algorithm
to obtain the rules. Our system has the following advantages over ERIC: (i)
NeSyFOLD generates smaller rule-sets without compromising on the accuracy and
fidelity; (ii) NeSyFOLD generates the mapping of filter numbers to semantic
labels automatically.

本研究提出了一种名为 NeSyFOLD 的新型神经符号系统，通过以下步骤进行训练：（一）我们首先对输入图像数据集进行 CNN 预训练，并提取最后一层过滤器的激活作为二进制值；（二）接下来，我们使用基于规则的机器学习算法 FOLD-SE-M 生成一个逻辑程序，可以对表示为每个过滤器对应的二进制激活向量的图像进行分类，并生成逻辑解释。