Designing Rotationally Invariant Neural Networks from PDEs and Variational Methods

08/31/2021
by   Tobias Alt, et al.
17

Partial differential equation (PDE) models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which is desirable in applications such as image analysis. Convolutional neural networks (CNNs) do not share this property, and existing remedies are often complex. The goal of our paper is to investigate how diffusion and variational models achieve rotation invariance and transfer these ideas to neural networks. As a core novelty we propose activation functions which couple network channels by combining information from several oriented filters. This guarantees rotation invariance within the basic building blocks of the networks while still allowing for directional filtering. The resulting neural architectures are inherently rotationally invariant. With only a few small filters, they can achieve the same invariance as existing techniques which require a fine-grained sampling of orientations. Our findings help to translate diffusion and variational models into mathematically well-founded network architectures, and provide novel concepts for model-based CNN design.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

07/30/2021

Connections between Numerical Algorithms for PDEs and Neural Networks

We investigate numerous structural connections between numerical algorit...
03/19/2020

Local Rotation Invariance in 3D CNNs

Locally Rotation Invariant (LRI) image analysis was shown to be fundamen...
04/22/2016

Learning rotation invariant convolutional filters for texture classification

We present a method for learning discriminative filters using a shallow ...
02/20/2020

Roto-Translation Equivariant Convolutional Networks: Application to Histopathology Image Analysis

Rotation-invariance is a desired property of machine-learning models for...
02/07/2020

Translating Diffusion, Wavelets, and Regularisation into Residual Networks

Convolutional neural networks (CNNs) often perform well, but their stabi...
04/22/2021

Equivariant Wavelets: Fast Rotation and Translation Invariant Wavelet Scattering Transforms

Wavelet scattering networks, which are convolutional neural networks (CN...
03/29/2021

Translating Numerical Concepts for PDEs into Neural Architectures

We investigate what can be learned from translating numerical algorithms...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.