论文标题
神经网络层表示的拓扑数据分析
Topological Data Analysis of Neural Network Layer Representations
论文作者
论文摘要
本文是一项关于如何保留在神经网络层的内部表示中的拓扑特征的粗略研究。使用拓扑数据分析中的技术，即持续的同源性，计算了一个简单的馈电神经网络层的拓扑特征，它的修饰圆环的带有klein瓶状扭曲的修饰圆环的层表示。该网络似乎在早期的同层中近似同态，然后在更深层的层中显着更改数据的拓扑。由此产生的噪声阻碍了持续的同源性计算这些特征的能力，但是在具有生物激活函数的网络中，相似的拓扑特征似乎持续更长。
This paper is a cursory study on how topological features are preserved within the internal representations of neural network layers. Using techniques from topological data analysis, namely persistent homology, the topological features of a simple feedforward neural network's layer representations of a modified torus with a Klein bottle-like twist were computed. The network appeared to approximate homeomorphisms in early layers, before significantly changing the topology of the data in deeper layers. The resulting noise hampered the ability of persistent homology to compute these features, however similar topological features seemed to persist longer in a network with a bijective activation function.
