HypLL: The Hyperbolic Learning Library (2306.06154v3)

Abstract: Deep learning in hyperbolic space is quickly gaining traction in the fields of machine learning, multimedia, and computer vision. Deep networks commonly operate in Euclidean space, implicitly assuming that data lies on regular grids. Recent advances have shown that hyperbolic geometry provides a viable alternative foundation for deep learning, especially when data is hierarchical in nature and when working with few embedding dimensions. Currently however, no accessible open-source library exists to build hyperbolic network modules akin to well-known deep learning libraries. We present HypLL, the Hyperbolic Learning Library to bring the progress on hyperbolic deep learning together. HypLL is built on top of PyTorch, with an emphasis in its design for ease-of-use, in order to attract a broad audience towards this new and open-ended research direction. The code is available at: https://github.com/maxvanspengler/hyperbolic_learning_library.

• The paper introduces HypLL, a hyperbolic deep learning library that integrates non-Euclidean geometry into standard neural network workflows.
• It details a modular architecture with tensors, manifolds, NN, and optim modules that support seamless transitions between Euclidean and hyperbolic computations.
• Its implementation leverages PyTorch and Riemannian optimization techniques to efficiently handle hierarchical data and reduce embedding distortions.

An Analysis of HypLL: The Hyperbolic Learning Library

The paper introduces HypLL, an advanced software library designed for deep learning practitioners and researchers, offering functionality within hyperbolic spaces. Developed on the PyTorch framework, HypLL addresses the increasing interest and applications of hyperbolic deep learning, particularly for hierarchical data structures common in machine learning scenarios.

Hyperbolic Learning in Context

While traditional deep learning architectures fundamentally assume Euclidean geometry, not all data naturally fit within this spatial paradigm. Hyperbolic geometry, in contrast, offers a compelling alternative, especially for hierarchical data structures where nodes grow exponentially with depth. This geometric property aligns more naturally with hyperbolic spaces, minimizing distortions that occur when embedding such structures within Euclidean space. Prior foundational work—such as Ganea et al. and Nickel et al.'s developments—has highlighted hyperbolic learning's efficacy in various domains, including graphs, text, and computer vision.

The Design and Implementation of HypLL

HypLL is meticulously crafted to be developer-friendly, mirroring PyTorch’s design to facilitate an easy transition for users accustomed to standard Euclidean deep learning practices. Its architecture is modular, composed of key segments—tensors, manifolds, neural network (nn), and optimizers—each contributing uniquely to the library's functionality.

1. Tensors Module: Central to HypLL’s structure, this module introduces manifold tensors that, unlike traditional tensors, store additional metadata regarding the manifold and dimensional attributes. This design allows precise operations across diverse manifolds, automatically instigating checks to prevent invalid computations.
2. Manifolds Module: This component embodies the mathematical operations of supported manifolds. Currently, it includes the Poincaré ball model for hyperbolic space and a Euclidean model necessary for compatibility and versatility. The module’s extensibility ensures future incorporation of additional manifolds, such as the hyperboloid model.
3. NN Module: Implemented to resemble PyTorch's nn module, it provides neural network layers that operate manifold-independently. The layers utilize operations defined within manifold objects, granting researchers the flexibility to switch seamlessly between Euclidean and hyperbolic computations.
4. Optim Module: Enhancing PyTorch's optimization strategies, this module incorporates Riemannian optimization techniques suitable for hyperbolic space, ensuring compatibility and ease of use with existing PyTorch optimization tools.

Through examples, the paper illustrates HypLL’s intuitive use case, highlighting only minor adaptations from standard Euclidean models: defining a manifold and transitioning input data onto this manifold. Such accessibility ensures that hyperbolic deep learning becomes a practical and highly adoptable tool for a wide audience.

Implications and Future Directions

HypLL fills a critical gap within the deep learning community—providing an open-source platform for hyperbolic learning. By facilitating operations in hyperbolic space, it significantly lowers the barrier for researchers eager to explore this emergent area. The library’s future promises hinge on its continuous development and adaptation to incorporate rapidly evolving hyperbolic learning methodologies. A noteworthy prospective expansion includes a geometric framework akin to PyTorch geometric for graph data structures.

Overall, the introduction of HypLL represents a methodical advancement in enabling researchers to leverage hyperbolic spaces effectively, thus broadening the horizons of applicable areas in artificial intelligence and machine learning. It positions itself not just as a tool, but as a cornerstone for future developments in hyperbolic spaces, advancing theoretical and practical applications beyond current paradigms. HypLL stands to significantly influence research geared towards data representations better suited to hyperbolic geometries, thereby refining model precision in hierarchical datasets.