# Connecting Sphere Manifolds Hierarchically for Regularization

Source: [Connecting Sphere Manifolds Hierarchically for Regularization](<https://www.sota2.com/research/paper/68fa6a3a1e209131cea26c7f>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T23:19:37.191Z

Authors: Damien Scieur, Youngsung Kim

Published: 2021-06-25T10:51:36.000Z

## Abstract

This paper considers classification problems with hierarchically organized classes. We force the classifier (hyperplane) of each class to belong to a sphere manifold, whose center is the classifier of its super-class. Then, individual sphere manifolds are connected based on their hierarchical relations. Our technique replaces the last layer of a neural network by combining a spherical fully-connected layer with a hierarchical layer. This regularization is shown to improve the performance of widely used deep neural network architectures (ResNet and DenseNet) on publicly available datasets (CIFAR100, CUB200, Stanford dogs, Stanford cars, and Tiny-ImageNet).

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2106.13549>)

[PDF](<https://arxiv.org/pdf/2106.13549.pdf>)