Deep Hyperspherical Learning

TL;DR

This paper introduces SphereConv and SphereNet, a hyperspherical learning framework that improves training efficiency and classification accuracy of CNNs by encoding angular representations on hyperspheres.

Contribution

The paper proposes SphereConv and SphereNet, novel hyperspherical convolutional methods that enhance training and performance of deep neural networks.

Findings

SphereNet achieves comparable or better accuracy than traditional CNNs.

SphereNet trains faster and is easier to optimize.

Learnable SphereConv and SphereNorm further improve performance.

Abstract

Convolution as inner product has been the founding basis of convolutional neural networks (CNNs) and the key to end-to-end visual representation learning. Benefiting from deeper architectures, recent CNNs have demonstrated increasingly strong representation abilities. Despite such improvement, the increased depth and larger parameter space have also led to challenges in properly training a network. In light of such challenges, we propose hyperspherical convolution (SphereConv), a novel learning framework that gives angular representations on hyperspheres. We introduce SphereNet, deep hyperspherical convolution networks that are distinct from conventional inner product based convolutional networks. In particular, SphereNet adopts SphereConv as its basic convolution operator and is supervised by generalized angular softmax loss - a natural loss formulation under SphereConv. We show that SphereNet can effectively encode discriminative representation and alleviate training difficulty, leading to easier optimization, faster convergence and comparable (even better) classification accuracy over convolutional counterparts. We also provide some theoretical insights for the advantages of learning on hyperspheres. In addition, we introduce the learnable SphereConv, i.e., a natural improvement over prefixed SphereConv, and SphereNorm, i.e., hyperspherical learning as a normalization method. Experiments have verified our conclusions.