Yang Wen

Yao Lu, Wen Yang, Yunzhe Zhang et al.

There are good arguments to support the claim that deep neural networks (DNNs) capture better feature representations than the previous hand-crafted feature engineering, which leads to a significant performance improvement. In this paper, we move a tiny step towards understanding the dynamics of feature representations over layers. Specifically, we model the process of class separation of intermediate representations in pre-trained DNNs as the evolution of communities in dynamic graphs. Then, we introduce modularity, a generic metric in graph theory, to quantify the evolution of communities. In the preliminary experiment, we find that modularity roughly tends to increase as the layer goes deeper and the degradation and plateau arise when the model complexity is great relative to the dataset. Through an asymptotic analysis, we prove that modularity can be broadly used for different applications. For example, modularity provides new insights to quantify the difference between feature representations. More crucially, we demonstrate that the degradation and plateau in modularity curves represent redundant layers in DNNs and can be pruned with minimal impact on performance, which provides theoretical guidance for layer pruning. Our code is available at https://github.com/yaolu-zjut/Dynamic-Graphs-Construction.

Zuohui Chen, Yao Lu, Jinxuan Hu et al.

Understanding the black-box representations in Deep Neural Networks (DNN) is an essential problem in deep learning. In this work, we propose Graph-Based Similarity (GBS) to measure the similarity of layer features. Contrary to previous works that compute the similarity directly on the feature maps, GBS measures the correlation based on the graph constructed with hidden layer outputs. By treating each input sample as a node and the corresponding layer output similarity as edges, we construct the graph of DNN representations for each layer. The similarity between graphs of layers identifies the correspondences between representations of models trained in different datasets and initializations. We demonstrate and prove the invariance property of GBS, including invariance to orthogonal transformation and invariance to isotropic scaling, and compare GBS with CKA. GBS shows state-of-the-art performance in reflecting the similarity and provides insights on explaining the adversarial sample behavior on the hidden layer space.