Fangfei Lan presents Uncertainty Visualization for Graph Coarsening
Abstract:The complexity of large real-world graphs makes their analyses prohibitively costly and their visualizations uninformative. The idea behind graph reduction is to reduce the size of a graph while preserving its properties of interest. To improve computational efficiency and to provide provable guarantees, many graph reduction techniques employ randomization. However, the uncertainty associated with randomized graph reduction and its subsequent interpretation has remained largely unexplored. In this paper, we present a framework to quantify and visualize the uncertainty associated with randomized graph reduction techniques. We focus on spectral clustering introduced by Ng, Jordan, and Weiss, a popular graph reduction technique that reduces the number of nodes by clustering the nodes of a graph into super-nodes. We introduce two uncertainty measures -- local adjusted Rand indices and co-occurrences -- to quantify and visualize uncertainty associated with an ensemble of reduced graphs. We demonstrate via experiments, that these measures complement each other in visualizing uncertainty and guiding the selection of optimal numbers of clusters.


Youjia Zhou presents Experimental Observations of the Topology of Convolutional Neural Network Activations
Abstract:Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of parameters associated with a series of transformations defined by the model architecture resulting in high-dimensional, difficult-to-interpret internal representations of input data. As DNNs become more ubiquitous across multiple sectors of our society, there is increasing recognition that mathematical methods are needed to aid analysts, researchers, and practitioners in understanding and interpreting how these models' internal representations relate to the final classification. In this paper, we apply cutting-edge techniques from TDA with the goal of gaining insight into the interpretability of convolutional neural networks used for image classification. We use two common TDA approaches to explore several methods for modeling hidden layer activations as high-dimensional point clouds, and provide experimental evidence that these point clouds capture valuable structural information about the model's process. First, we demonstrate that a distance metric based on persistent homology can be used to quantify meaningful differences between layers and discuss these distances in the broader context of existing representational similarity metrics for neural network interpretability. Second, we show that a mapper graph can provide semantic insight as to how these models organize hierarchical class knowledge at each layer. These observations demonstrate that TDA is a useful tool to help deep learning practitioners unlock the hidden structures of their models.