Understanding the behavior of Artificial Neural Networks is one of the main topics in the field recently, as black-box approaches have become usual since the widespread of deep learning. Such high-dimensional models may manifest instabilities and weird properties that resemble complex systems. Therefore, we propose Complex Network (CN) techniques to analyze the structure and performance of fully connected neural networks. For that, we build a dataset with 4 thousand models and their respective CN properties. They are employed in a supervised classification setup considering four vision benchmarks. Each neural network is approached as a weighted and undirected graph of neurons and synapses, and centrality measures are computed after training. Results show that these measures are highly related to the network classification performance. We also propose the concept of Bag-Of-Neurons (BoN), a CN-based approach for finding topological signatures linking similar neurons. Results suggest that six neuronal types emerge in such networks, independently of the target domain, and are distributed differently according to classification accuracy. We also tackle specific CN properties related to performance, such as higher subgraph centrality on lower-performing models. Our findings suggest that CN properties play a critical role in the performance of fully connected neural networks, with topological patterns emerging independently on a wide range of models.

中文翻译：

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全连接神经网络的结构和性能：新兴的复杂网络特性

了解人工神经网络的行为是最近该领域的主要话题之一，因为自从深度学习广泛应用以来，黑盒方法已经变得司空见惯。这种高维模型可能表现出类似于复杂系统的不稳定性和奇怪的特性。因此，我们提出复杂网络 (CN) 技术来分析全连接神经网络的结构和性能。为此，我们构建了一个包含 4000 个模型及其各自 CN 属性的数据集。它们用于考虑四个视觉基准的监督分类设置。每个神经网络都被视为神经元和突触的加权无向图，并且在训练后计算中心性度量。结果表明，这些措施与网络分类性能高度相关。我们还提出了神经元袋 (BoN) 的概念，这是一种基于 CN 的方法，用于寻找连接相似神经元的拓扑特征。结果表明，在此类网络中出现了六种神经元类型，独立于目标域，并根据分类精度不同分布。我们还解决了与性能相关的特定 CN 属性，例如在性能较低的模型上具有更高的子图中心性。我们的研究结果表明，CN 属性在全连接神经网络的性能中起着至关重要的作用，拓扑模式在广泛的模型中独立出现。并且根据分类精度不同分布。我们还解决了与性能相关的特定 CN 属性，例如在性能较低的模型上具有更高的子图中心性。我们的研究结果表明，CN 属性在全连接神经网络的性能中起着至关重要的作用，拓扑模式在广泛的模型中独立出现。并且根据分类精度不同分布。我们还解决了与性能相关的特定 CN 属性，例如在性能较低的模型上具有更高的子图中心性。我们的研究结果表明，CN 属性在全连接神经网络的性能中起着至关重要的作用，拓扑模式在广泛的模型中独立出现。