Deep neural networks implement a sequence of layer-by-layer operations that are each relatively easy to understand, but the resulting overall computation is generally difficult to understand. We consider a simple hypothesis for interpreting the layer-by-layer construction of useful representations: perhaps the role of each layer is to reformat information to reduce the "distance" to the desired outputs. With this framework, the layer-wise computation implemented by a deep neural network can be viewed as a path through a high-dimensional representation space. We formalize this intuitive idea of a "path" by leveraging recent advances in *metric* representational similarity. We extend existing representational distance methods by computing geodesics, angles, and projections of representations, going beyond mere layer distances. We then demonstrate these tools by visualizing and comparing the paths taken by ResNet and VGG architectures on CIFAR-10. We conclude by sketching additional ways that this kind of representational geometry can be used to understand and interpret network training, and to describe novel kinds of similarities between different models.
翻译:深神经网络实施了一系列逐层操作,这些操作相对容易理解,但由此得出的整体计算一般难以理解。我们认为,解释逐层构建有用表达的图象的简单假设:也许每一层的作用是重新整理信息,将“距离”减少到预期产出。有了这个框架,深神经网络实施的分层计算可以被视为通过高维代表空间的途径。我们通过利用最近在 * 表示相似性方面的进展,正式确定这种“路径”的直观想法。我们通过计算大地测量学、角度和对表象的预测,将现有的代表距离方法扩大到仅仅层距离以外。我们然后通过直观和比较ResNet和VGGG架构在CIFAR-10上采用的道路,来展示这些工具。我们最后通过勾画其他方法,说明这种表示式的几何方法可以用来理解和解释网络培训,并描述不同模型之间的新型相似性。