Critical cascades are found in many self-organizing systems. Here, we examine critical cascades as a design paradigm for logic and learning under the linear threshold model (LTM), and simple biologically inspired variants of it as sources of computational power, learning efficiency, and robustness. First, we show that the LTM can compute logic, and with a small modification, universal Boolean logic, examining its stability and cascade frequency. We then frame it formally as a binary classifier and remark on implications for accuracy. Second, we examine the LTM as a statistical learning model, studying benefits of spatial constraints and criticality to efficiency. We also discuss implications for robustness in information encoding. Our experiments show that spatial constraints can greatly increase efficiency. Theoretical investigation and initial experimental results also indicate that criticality can result in a sudden increase in accuracy.

中文翻译：

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网络级联中的逻辑和学习

在许多自组织系统中都可以找到关键级联。在这里，我们将关键级联作为线性阈值模型 (LTM) 下的逻辑和学习的设计范式进行研究，并将其简单的受生物学启发的变体作为计算能力、学习效率和鲁棒性的来源。首先，我们展示了 LTM 可以计算逻辑，并通过一个小的修改，通用布尔逻辑，检查它的稳定性和级联频率。然后，我们将其正式构建为二元分类器，并评论对准确性的影响。其次，我们将 LTM 视为一种统计学习模型，研究空间约束的好处和对效率的关键性。我们还讨论了对信息编码鲁棒性的影响。我们的实验表明，空间限制可以大大提高效率。