Understanding Conventional Deep Learning Models Through the Lens of Topological Data Analysis Using the Mapper Algorithm
摘要
Topological Data Analysis (TDA) is an innovative field in applied mathematics and computer science that leverages computational topology to analyze data shapes, revealing geometric structures in complex datasets and offering unique insights beyond traditional methods. This paper employs the Mapper algorithm, a powerful TDA tool, to visualize the evolution of neural network weights in three models: Feedforward Neural Network for tabular data, Convolutional Neural Network for image data, and Recurrent Neural Network for sequential data. By transforming a single dataset into these three formats, we aim to elucidate the distinct learning styles of each model. Key contributions include evaluating model performance on an image classification task, analyzing neural network weight evolution using algebraic topology, and demonstrating TDA’s effectiveness in interpreting deep learning models.