Artificial Neural Networks (ANNs) are powerful machine-learning models capable of capturing intricate non-linear relationships. They are widely used nowadays across numerous scientific and engineering domains, driving advancements in both research and real-world applications. In our recent work, we focused on the statics and dynamics of a particular subclass of ANNs, which we refer to as binary ANNs. A binary ANN is a feed-forward network in which both inputs and outputs are restricted to binary values, making it particularly suitable for a variety of practical use cases. Our previous study approached binary ANNs through the lens of belief-change theory, specifically the Alchourron, Gardenfors and Makinson (AGM) framework, yielding several key insights. Most notably, we demonstrated that the knowledge embodied in a binary ANN (expressed through its input-output behaviour) can be symbolically represented using a propositional logic language. Moreover, the process of modifying a belief set (through revision or contraction) was mapped onto a gradual transition through a series of intermediate belief sets. Analogously, the training of binary ANNs was conceptualized as a sequence of such belief-set transitions, which we showed can be formalized using full-meet AGM-style belief change. In the present article, we extend this line of investigation by addressing some critical limitations of our previous study. Specifically, we show that Dalal's method for belief change provides a natural basis for a structured, gradual evolution of states of belief. More importantly, given the known shortcomings of full-meet belief change, we demonstrate that the training dynamics of binary ANNs can be more effectively modelled using robust AGM-style change operations -- namely, lexicographic revision and moderate contraction -- that align with the Darwiche-Pearl framework for iterated belief change.

翻译：人工神经网络作为强大的机器学习模型，能够捕捉复杂的非线性关系，如今广泛应用于众多科学与工程领域，推动着研究与实际应用的双重进步。在近期工作中，我们聚焦于一类特定子类——二值人工神经网络（Binary ANN）的静态特性与动态过程。这类前馈网络通过约束输入与输出为二值数据，特别适用于多种实践场景。此前研究从信念变迁理论视角，特别是阿尔丘伦、加登福斯与麦金森框架切入，取得了若干关键洞见。最显著的是，我们证明了二值人工神经网络所蕴含的知识（通过输入输出行为表征）可运用命题逻辑语言进行符号化表示。同时，通过修正或收缩操作修改信念集的过程，被映射为一系列中间信念集的渐进转换。相应地，二值人工神经网络的训练过程被概念化为此类信念集转换序列，并证明可通过全交AGM式信念变迁形式化描述。在本文中，我们针对此前研究的若干关键局限进行拓展研究。具体而言，我们论证了达拉尔信念变迁方法为信念状态的层次化渐进演变提供了自然基础。更重要的是，鉴于全交信念变迁的已知缺陷，我们证明二值人工神经网络的训练动力学可更有效地借助稳健的AGM式变迁操作——即符合达威切-珀尔迭代信念变迁框架的词典序修正与适度收缩——进行建模。