Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space

TL;DR

Hypformer is a new hyperbolic Transformer model that fully adapts all core modules to hyperbolic space, enabling scalable processing of large-scale graph and sequence data with improved efficiency.

Contribution

The paper introduces Hypformer, the first complete hyperbolic Transformer with all modules defined in hyperbolic space and a linear self-attention mechanism for scalability.

Findings

Effective on various datasets

Handles billion-scale graph data

Scalable to long sequences

Abstract

Hyperbolic geometry have shown significant potential in modeling complex structured data, particularly those with underlying tree-like and hierarchical structures. Despite the impressive performance of various hyperbolic neural networks across numerous domains, research on adapting the Transformer to hyperbolic space remains limited. Previous attempts have mainly focused on modifying self-attention modules in the Transformer. However, these efforts have fallen short of developing a complete hyperbolic Transformer. This stems primarily from: (i) the absence of well-defined modules in hyperbolic space, including linear transformation layers, LayerNorm layers, activation functions, dropout operations, etc. (ii) the quadratic time complexity of the existing hyperbolic self-attention module w.r.t the number of input tokens, which hinders its scalability. To address these challenges, we propose, Hypformer, a novel hyperbolic Transformer based on the Lorentz model of hyperbolic geometry. In Hypformer, we introduce two foundational blocks that define the essential modules of the Transformer in hyperbolic space. Furthermore, we develop a linear self-attention mechanism in hyperbolic space, enabling hyperbolic Transformer to process billion-scale graph data and long-sequence inputs for the first time. Our experimental results confirm the effectiveness and efficiency of Hypformer across various datasets, demonstrating its potential as an effective and scalable solution for large-scale data representation and large models.