Word vector embeddings have been shown to contain and amplify biases in the data they are extracted from. Consequently, many techniques have been proposed to identify, mitigate, and attenuate these biases in word representations. In this article, we utilize interactive visualization to increase the interpretability and accessibility of a collection of state-of-the-art debiasing techniques. To aid this, we present the Visualization of Embedding Representations for deBiasing (VERB) system, an open-source web-based visualization tool that helps users gain a technical understanding and visual intuition of the inner workings of debiasing techniques, with a focus on their geometric properties. In particular, VERB offers easy-to-follow examples that explore the effects of these debiasing techniques on the geometry of high-dimensional word vectors. To help understand how various debiasing techniques change the underlying geometry, VERB decomposes each technique into interpretable sequences of primitive transformations and highlights their effect on the word vectors using dimensionality reduction and interactive visual exploration. VERB is designed to target natural language processing (NLP) practitioners who are designing decision-making systems on top of word embeddings and researchers working with the fairness and ethics of machine learning systems in NLP. It can also serve as a visual medium for education, which helps an NLP novice understand and mitigate biases in word embeddings.

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 towards 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.

We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph into its graph representations, known as the line graph and clique expansion. A topological simplification of such a graph representation induces a simplification of the hypergraph. In simplifying a hypergraph, we allow vertices to be combined if they belong to almost the same set of hyperedges, and hyperedges to be merged if they share almost the same set of vertices. Our proposed approaches are general and mathematically justifiable, and put vertex simplification and hyperedge simplification in a unifying framework.

The mapper algorithm is a popular tool from topological data analysis for extracting topological summaries of high-dimensional datasets. In this paper, we present Mapper Interactive, a web-based framework for the interactive analysis and visualization of high-dimensional point cloud data. It implements the mapper algorithm in an interactive, scalable, and easily extendable way, thus supporting practical data analysis. In particular, its command-line API can compute mapper graphs for 1 million points of 256 dimensions in about 3 minutes (4 times faster than the vanilla implementation). Its visual interface allows on-the-fly computation and manipulation of the mapper graph based on user-specified parameters and supports the addition of new analysis modules with a few lines of code. Mapper Interactive makes the mapper algorithm accessible to nonspecialists and accelerates topological analytics workflows.

Word vector embeddings have been shown to contain and amplify biases in data they are extracted from. Consequently, many techniques have been proposed to identify, mitigate, and attenuate these biases in word representations. In this tutorial, we will review a collection of state-of-the-art debiasing techniques. To aid this, we provide an open source web-based visualization tool and offer hands-on experience in exploring the effects of these debiasing techniques on the geometry of high-dimensional word vectors. To help understand how various debiasing techniques change the underlying geometry, we decompose each technique into interpretable sequences of primitive operations, and study their effect on the word vectors using dimensionality reduction and interactive visual exploration.

Abstract Deep neural networks such as GoogLeNet, ResNet, and BERT have achieved impressive performance in tasks such as image and text classification. To understand how such performance is achieved, we probe a trained deep neural network by studying neuron activations, i.e.combinations of neuron firings, at various layers of the network in response to a particular input. With a large number of inputs, we aim to obtain a global view of what neurons detect by studying their activations. In particular, we develop visualizations that show the shape of the activation space, the organizational principle behind neuron activations, and the relationships of these activations within a layer. Applying tools from topological data analysis, we presentTopoAct, a visual exploration system to study topological summaries of activation vectors. We present exploration scenarios usingTopoActthat provide valuable insights into learned representations of neural networks. We expectTopoActto give a topological perspective that enriches the current toolbox of neural network analysis, and to provide a basis for network architecture diagnosis and data anomaly detection.