Enhance Hyperbolic Representation Learning via Second-order Pooling

TL;DR

This paper introduces second-order pooling with kernel approximation regularization to enhance hyperbolic representation learning, effectively increasing sample distances without harming generalization, demonstrated through experiments on graph datasets.

Contribution

It proposes a novel integration of second-order pooling and kernel approximation regularization into hyperbolic learning to improve hierarchical representation capabilities.

Findings

Improved sample distance expansion in hyperbolic space.

Enhanced performance on graph-structured datasets.

Maintained generalization ability with the new method.

Abstract

Hyperbolic representation learning is well known for its ability to capture hierarchical information. However, the distance between samples from different levels of hierarchical classes can be required large. We reveal that the hyperbolic discriminant objective forces the backbone to capture this hierarchical information, which may inevitably increase the Lipschitz constant of the backbone. This can hinder the full utilization of the backbone's generalization ability. To address this issue, we introduce second-order pooling into hyperbolic representation learning, as it naturally increases the distance between samples without compromising the generalization ability of the input features. In this way, the Lipschitz constant of the backbone does not necessarily need to be large. However, current off-the-shelf low-dimensional bilinear pooling methods cannot be directly employed in hyperbolic representation learning because they inevitably reduce the distance expansion capability. To solve this problem, we propose a kernel approximation regularization, which enables the low-dimensional bilinear features to approximate the kernel function well in low-dimensional space. Finally, we conduct extensive experiments on graph-structured datasets to demonstrate the effectiveness of the proposed method.