There is strong interest in developing mathematical methods that can be used to understand complex neural networks used in image analysis. In this paper, we introduce techniques from Linear Algebra to model neural network layers as maps between signal spaces. First, we demonstrate how signal spaces can be used to visualize weight spaces and convolutional layer kernels. We also demonstrate how residual vector spaces can be used to further visualize information lost at each layer. Second, we introduce the concept of invertible networks and an algorithm for computing input images that yield specific outputs. We demonstrate our approach on two invertible networks and ResNet18.

翻译：在图像分析领域，开发能够理解复杂神经网络的数学方法具有重要研究价值。本文引入线性代数技术，将神经网络层建模为信号空间之间的映射。首先，我们展示如何利用信号空间可视化权重空间与卷积层核函数，同时演示如何通过残差向量空间进一步呈现各层丢失的信息。其次，我们提出可逆网络概念，并给出计算特定输出对应输入图像的算法。该方法在两个可逆网络及ResNet18上得到了验证。