DeepAI AI Chat
Log In Sign Up

Connecting Sphere Manifolds Hierarchically for Regularization

by   Damien Scieur, et al.

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).


page 1

page 2

page 3

page 4


Properties of Digital n-Dimensional Spheres and Manifolds. Separation of Digital Manifolds

In the present paper, we study basic properties of digital n-dimensional...

Connection between continuous and digital n-manifolds and the Poincare conjecture

We introduce LCL covers of closed n-dimensional manifolds by n-dimension...

A Reeb sphere theorem in graph theory

We prove a Reeb sphere theorem for finite simple graphs. The result brid...

Deep Networks and the Multiple Manifold Problem

We study the multiple manifold problem, a binary classification task mod...

Spatially-Coupled Neural Network Architectures

In this work, we leverage advances in sparse coding techniques to reduce...

Visual Confusion Label Tree For Image Classification

Convolution neural network models are widely used in image classificatio...