Learning Structured Representations with Hyperbolic Embeddings

Most real-world datasets consist of a natural hierarchy between classes or an inherent label structure that is either already available or can be constructed cheaply. However, most existing representation learning methods ignore this hierarchy, treating labels as permutation invariant. Recent work [Zeng et al., 2022] proposes using this structured information explicitly, but the use of Euclidean distance may distort the underlying semantic context [Chen et al., 2013]. In this work, motivated by the advantage of hyperbolic spaces in modeling hierarchical relationships, we propose a novel approach HypStructure: a Hyperbolic Structured regularization approach to accurately embed the label hierarchy into the learned representations. HypStructure is a simple-yet-effective regularizer that consists of a hyperbolic tree-based representation loss along with a centering loss, and can be combined with any standard task loss to learn hierarchy-informed features. Extensive experiments on several large-scale vision benchmarks demonstrate the efficacy of HypStructure in reducing distortion and boosting generalization performance especially under low dimensional scenarios. For a better understanding of structured representation, we perform eigenvalue analysis that links the representation geometry to improved Out-of-Distribution (OOD) detection performance seen empirically. The code is available at \url{https://github.com/uiuctml/HypStructure}.

Learning Structured Representations by Embedding Class Hierarchy with Fast Optimal Transport

To embed structured knowledge within labels into feature representations, prior work (Zeng et al., 2022) proposed to use the Cophenetic Correlation Coefficient (CPCC) as a regularizer during supervised learning. This regularizer calculates pairwise Euclidean distances of class means and aligns them with the corresponding shortest path distances derived from the label hierarchy tree. However, class means may not be good representatives of the class conditional distributions, especially when they are multi-mode in nature. To address this limitation, under the CPCC framework, we propose to use the Earth Mover's Distance (EMD) to measure the pairwise distances among classes in the feature space. We show that our exact EMD method generalizes previous work, and recovers the existing algorithm when class-conditional distributions are Gaussian in the feature space. To further improve the computational efficiency of our method, we introduce the Optimal Transport-CPCC family by exploring four EMD approximation variants. Our most efficient OT-CPCC variant runs in linear time in the size of the dataset, while maintaining competitive performance across datasets and tasks.

RELand: Risk Estimation of Landmines via Interpretable Invariant Risk Minimization

Landmines remain a threat to war-affected communities for years after conflicts have ended, partly due to the laborious nature of demining tasks. Humanitarian demining operations begin by collecting relevant information from the sites to be cleared, which is then analyzed by human experts to determine the potential risk of remaining landmines. In this paper, we propose RELand system to support these tasks, which consists of three major components. We (1) provide general feature engineering and label assigning guidelines to enhance datasets for landmine risk modeling, which are widely applicable to global demining routines, (2) formulate landmine presence as a classification problem and design a novel interpretable model based on sparse feature masking and invariant risk minimization, and run extensive evaluation under proper protocols that resemble real-world demining operations to show a significant improvement over the state-of-the-art, and (3) build an interactive web interface to suggest priority areas for demining organizations. We are currently collaborating with a humanitarian demining NGO in Colombia that is using our system as part of their field operations in two areas recently prioritized for demining.