# What is Harmonic Convolutional Neural Networks

##### Harmonic Convolutional Neural Networks - An Overview
Introduction:

Machine learning has advanced a lot in recent times, but one of the most promising techniques which have lately found popularity is the convolutional neural network. CNNs have performed exceptionally well in image recognition and classification tasks in the past decade. Nevertheless, harmonic convolutional neural networks (HCNN) have recently gained more attention due to their helpful features in hierarchical and robust learning.

In this article, we will dive into the concept of HCNN, its architecture, how it is trained, and its performance in some specific applications in computer vision.

##### What are Harmonic Convolutional Neural Networks?

In general, a Harmonic Convolutional Neural Network is an extension of classical convolutional neural network (CNN). It is named so because it is based on the harmonic analysis of data. Indeed, the Harmonic Chain Rule for the convolutional and recurring neural networks is the fundamental idea behind the development of HCNN. As reported in the paper "Harmonic Networks for Image Classification," this architecture aims to find a unified framework under which CNNs, RNNs, and other sequential models can be described and interpreted.

Speaking of architecture, it is greatly inspired by the structure of the regular CNN architecture. However, the main bottleneck in classical CNN is padding or pooling layers. In an HCNN, the convolution and pooling layers are replaced with a single harmonic layer that performs both tasks. The Harmonic layer ensures mathematical translation invariance and is computationally efficient when compared to a standard convolution operation. It also reduces the complexity of the network and makes it easier to detect complex patterns in the data.

##### HCNN Architecture:

The HCNN model comprises the following layers: Fourier Layer, Convolution Layer, and Non-linear Layer.

• The Fourier Layer: The first layer applies a Fourier transform to the input signal. The Fourier transform is applied to represent the image in the frequency domain.
• The Convolution Layer: After the Fourier layer, the convolution layer convolves the spectral representations of the input with the learned filters.
• The Non-linear Layer: The output from the previous layer is finally passed through a non-linear layer such as the Rectifier Linear Unit (ReLU) activation function, as it helps the model to learn the complex, non-linear features of the input data.
##### Training an HCNN:

The training of an HCNN is similar to that of a regular CNN. Here are the steps involved in training an HCNN:

• Initialization: Initialize the network's parameters randomly
• Forward Pass: Input the data through the model to compute the output.
• Calculate the loss: Calculate the difference between the predicted and the actual output, which is called the loss.
• Backward Pass: Use the loss value to update the weights of the network through backward propagation.
• Repeat: Iterate the above steps with different data samples until convergence or in other words, until the network learns the optimal weights.
##### Performance of HCNN in few applications:

Here are some applications in which HCNN has shown promising results:

• Texture Classification: HCNN has shown improved texture classification results when compared to classical CNN.
• Image Recognition: HCNN has shown a similar performance in image recognition as CNN, but with reduced computational time and fewer parameters.
• MRI Reconstruction: Reconstruction of MRI using HCNN has shown better accuracy than traditional methods like Fourier reconstruction, particularly for low SNR images.
##### Conclusion:

Harmonic Convolutional Neural Networks have shown their potential in various computer vision applications. Their frequency-domain analysis and ability to handle complex patterns have shown improved classification results. Moreover, HCNN's computational efficiency makes it a favorable choice for low-power embedded systems. As we see more challenging real-world applications in the field of computer vision, the future of HCNN looks promising.