Visualizing Loss Functions as Topological Landscape Profiles

In machine learning, a loss function measures the difference between model predictions and ground-truth (or target) values. For neural network models, visualizing how this loss changes as model parameters are varied can provide insights into the local structure of the so-called loss landscape (e.g., smoothness) as well as global properties of the underlying model (e.g., generalization performance). While various methods for visualizing the loss landscape have been proposed, many approaches limit sampling to just one or two directions, ignoring potentially relevant information in this extremely high-dimensional space. This paper introduces a new representation based on topological data analysis that enables the visualization of higher-dimensional loss landscapes. After describing this new topological landscape profile representation, we show how the shape of loss landscapes can reveal new details about model performance and learning dynamics, highlighting several use cases, including image segmentation (e.g., UNet) and scientific machine learning (e.g., physics-informed neural networks). Through these examples, we provide new insights into how loss landscapes vary across distinct hyperparameter spaces: we find that the topology of the loss landscape is simpler for better-performing models; and we observe greater variation in the shape of loss landscapes near transitions from low to high model performance.

Evaluating Loss Landscapes from a Topology Perspective

Characterizing the loss of a neural network with respect to model parameters, i.e., the loss landscape, can provide valuable insights into properties of that model. Various methods for visualizing loss landscapes have been proposed, but less emphasis has been placed on quantifying and extracting actionable and reproducible insights from these complex representations. Inspired by powerful tools from topological data analysis (TDA) for summarizing the structure of high-dimensional data, here we characterize the underlying shape (or topology) of loss landscapes, quantifying the topology to reveal new insights about neural networks. To relate our findings to the machine learning (ML) literature, we compute simple performance metrics (e.g., accuracy, error), and we characterize the local structure of loss landscapes using Hessian-based metrics (e.g., largest eigenvalue, trace, eigenvalue spectral density). Following this approach, we study established models from image pattern recognition (e.g., ResNets) and scientific ML (e.g., physics-informed neural networks), and we show how quantifying the shape of loss landscapes can provide new insights into model performance and learning dynamics.

MultiFair: Multi-Group Fairness in Machine Learning

Algorithmic fairness is becoming increasingly important in data mining and machine learning, and one of the most fundamental notions is group fairness. The vast majority of the existing works on group fairness, with a few exceptions, primarily focus on debiasing with respect to a single sensitive attribute, despite the fact that the co-existence of multiple sensitive attributes (e.g., gender, race, marital status, etc.) in the real-world is commonplace. As such, methods that can ensure a fair learning outcome with respect to all sensitive attributes of concern simultaneously need to be developed. In this paper, we study multi-group fairness in machine learning (MultiFair), where statistical parity, a representative group fairness measure, is guaranteed among demographic groups formed by multiple sensitive attributes of interest. We formulate it as a mutual information minimization problem and propose a generic end-to-end algorithmic framework to solve it. The key idea is to leverage a variational representation of mutual information, which considers the variational distribution between learning outcomes and sensitive attributes, as well as the density ratio between the variational and the original distributions. Our proposed framework is generalizable to many different settings, including other statistical notions of fairness, and could handle any type of learning task equipped with a gradient-based optimizer. Empirical evaluations in the fair classification task on three real-world datasets demonstrate that our proposed framework can effectively debias the classification results with minimal impact to the classification accuracy.

Explaining Vulnerabilities to Adversarial Machine Learning through Visual Analytics

Machine learning models are currently being deployed in a variety of real-world applications where model predictions are used to make decisions about healthcare, bank loans, and numerous other critical tasks. As the deployment of artificial intelligence technologies becomes ubiquitous, it is unsurprising that adversaries have begun developing methods to manipulate machine learning models to their advantage. While the visual analytics community has developed methods for opening the black box of machine learning models, little work has focused on helping the user understand their model vulnerabilities in the context of adversarial attacks. In this paper, we present a visual analytics framework for explaining and exploring model vulnerabilities to adversarial attacks. Our framework employs a multi-faceted visualization scheme designed to support the analysis of data poisoning attacks from the perspective of models, data instances, features, and local structures. We demonstrate our framework through two case studies on binary classifiers and illustrate model vulnerabilities with respect to varying attack strategies.