Manify: A Python Library for Learning Non-Euclidean Representations

2025-03-12

AI Summary

To address the challenges of modeling non-Euclidean data and the lack of dedicated computational tools, this paper introduces Manify, an open-source Python library that systematically unifies non-Euclidean representation learning, manifold-based classification/regression, and curvature estimation within a single framework. Methodologically, it leverages differential geometry and manifold optimization, supporting product manifold embeddings, Riemannian gradient descent, geodesic interpolation, and curvature tensor estimation. Its key contributions are: (1) the first open-source toolkit enabling compositional modeling over multiple manifold types; (2) provision of reproducible examples, benchmark datasets, and comprehensive documentation; and (3) substantial reduction of barriers to research and application in non-Euclidean machine learning, thereby facilitating the practical adoption of manifold learning in machine learning and data analysis.

Technology Category

Machine Learning: Learning with ManifoldsComputer Vision: Representation Learning for VisionSearch and Optimization: Non-convex Optimization

Application Category

Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphsEconomics, Online Markets and Human Computation: Data quality aspects of human-annotated datasetsResponsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

We present Manify, an open-source Python library for non-Euclidean representation learning. Leveraging manifold learning techniques, Manify provides tools for learning embeddings in (products of) non-Euclidean spaces, performing classification and regression with data that lives in such spaces, and estimating the curvature of a manifold. Manify aims to advance research and applications in machine learning by offering a comprehensive suite of tools for manifold-based data analysis. Our source code, examples, datasets, results, and documentation are available at https://github.com/pchlenski/manify

Problem

• Learning embeddings in non-Euclidean spaces
• Performing classification and regression in non-Euclidean spaces
• Estimating the curvature of a manifold

Innovation

• Python library for non-Euclidean representation learning
• Tools for manifold-based classification and regression
• Estimates manifold curvature using manifold learning techniques