Humans can count very fast by subitizing, but slow substantially as the number of objects increases. Previous studies have shown a trained deep neural network (DNN) detector can count the number of objects in an amount of time that increases slowly with the number of objects. Such a phenomenon suggests the subitizing ability of DNNs, and unlike humans, it works equally well for large numbers. Many existing studies have successfully applied DNNs to object counting, but few studies have studied the subitizing ability of DNNs and its interpretation. In this paper, we found DNNs do not have the ability to generally count connected components. We provided experiments to support our conclusions and explanations to understand the results and phenomena of these experiments. We proposed three ML-learnable characteristics to verify learnable problems for ML models, such as DNNs, and explain why DNNs work for specific counting problems but cannot generally count connected components.

翻译：人类可以通过子化快速计数, 但随着天体数量的增加, 速度会缓慢。 先前的研究显示, 受过训练的深神经网络( DNN) 检测器可以计算出随着天体数量增长而缓慢增长的天体数量。 这种现象表明, DNN 的子化能力, 与人类不同, 它在数量上也同样有效。 许多现有研究成功地应用了 DNN 来计算天体数量, 但很少有研究 DNN 的子化能力及其解释 。 在本文中, 我们发现 DNN 不具备一般计算连接部件的能力 。 我们提供实验来支持我们的结论和解释, 以了解这些实验的结果和现象。 我们提出了三个 ML 可见的特性, 以核实ML 模型( 如 DNN) 的可学习问题, 并解释为什么 DNN 工作于具体计算问题, 但一般无法计算连接部件 。