Neural networks are remarkably efficient tools to solve a number of really difficult problems. The first application of neural networks usually solves classification problems. How do we encode and decode the image for both operations? We can simply use a feed forward neural network or when we deal with images, we often use a convolutional neural network which usually performs better.

Autoencoders are becoming increasingly popular in AI and machine learning due to their ability to learn complex representations of data. They are a type of neural network that can learn to compress and decompress data. The autoencoder first encodes the data into a lower dimensional representation, then reconstructs it back to its original form. They can be used for a variety of tasks, such as denoising, anomaly detection, feature extraction & are able to learn features from unlabeled data, becoming popular for unsupervised learning tasks.

They have also been used for generative models, such as image generation, and for transfer learning. They are an effective way to compress data for storage or for data processing tasks such as feature extraction and dimensionality reduction. Their ability to learn complex nonlinear data distributions makes them particularly useful for tasks such as denoising, anomaly detection, and generative modeling. Additionally, they are relatively easy to implement and can be trained using standard backpropagation techniques.

**What are Autoencoders?**

Autoencoders are a type of neural network which generates an “n-layer” coding of the given input and attempts to reconstruct the input using the code generated. This Neural Network architecture is divided into the encoder structure, the decoder structure, and the latent space, also known as “bottleneck”.To learn the data representations of the input, the network is trained using Unsupervised data. These compressed, data representations go through a decoding process wherein the input is reconstructed. An autoencoder is a regression task that models an identity function.

**Convolutional Variational Autoencoder**

A convolutional variational autoencoder (CVAE) is a type of deep generative model that combines the capabilities of a variational autoencoder (VAE) and a convolutional neural network (CNN). The CVAE is a generative model that learns the latent space representation of data by encoding it into a lower-dimensional state space and decoding it back into the original data space. The CVAE can be used for image generation, image reconstruction, and anomaly detection. The main advantage of the CVAE is that it is able to capture the spatial relationships between pixels in an image, which is not possible with a standard VAE. This allows for accurate image reconstruction and image generation.

When we regularize an autoencoder so that its latent representation is not overfitted to a single data point but the entire data distribution, we can perform random sampling from the latent space and hence generate unseen images from the distribution, making our autoencoder ‘variational’. For generating this, we incorporate the idea of KL divergence for our loss function design.

**Sample Example**

The first application of neural networks usually revolved around classification problems. Classification means that we have an image as an input and the output is let’s say: a simple decision, whether it depicts a cat or a dog. The input will have as many nodes as there are pixels in the input image, and the output will have 2 units and we look at one of these two that fires the most to decide whether it thinks it is a cat or dog.

Between these two, there are hidden layers where the neural network is asked to build an inner representation of the problem that is efficient at recognizing animals. An autoencoder here is an interesting variant with two important changes;

- First, the number of neurons is the same in the input and the output therefore we can expect the output is an image that is not only the same size as the input, but actually is the same image. Now, this normally wouldn’t make any sense, why would we want to invent a neural network to do the job of a copying machine?

- Second, we have a bottleneck in one of these layers, this means that the number of neurons in that layer is much less than we would normally see, therefore it has to find a way to represent this kind of data with a much smaller number of neurons. If you have a smaller budget, you have to let go of all the fluff and concentrate on the bare essentials, therefore we can’t expect the image to be the same but they are hopefully quite close. These autoencoders are capable of creating sparse representations of the input data and can therefore be used for image compression. Autoencoders offer no tangible advantage over classical image compression algorithms like JPEG. However, as a crumb of comfort, many different variants exist that are useful for different tasks other than compression.

**What is a convolutional encoder?**

A convolutional encoder is a type of encoder used for encoding data for transmission or storage. It combines the input data with a set of predetermined values, called the convolutional code, to produce a series of output symbols. Convolutional encoders are widely used in digital communication systems and data storage systems, as they offer good performance with low complexity.

*References: **https://github.com/arthurmeyer/Saliency_Detection_Convolutional_Autoencoder*

**A sample problem: **

**Suppose from a large collection of landscapes, can a network learn to generate new landscape pictures?**: You have a collection of pictures maybe landscapes of this kind and you want to train a neural network model that can learn from all of these landscape pictures and then not classify not make predictions about them but to actually paint a new landscape of it’s own so you want the neural network to generate new samples of the kind of data that you have actually trained it from so again we have seen neural networks can classify they can perform regression but now what we really want to see is where the neural networks can be trained as generative models where they can generate newer data of the kind that they have seen where the data can be arbitrarily complex like paintings of landscapes but before we even get there the important question is what is a generative model? What are the various things we need to know about generative models?

Let’s derive generative models:

- A model for the probability distribution of a data x

Ex: Multinomial, Gaussian etc.

- Computational equivalent: a model that can be used to “generate” data with a distribution similar to the given data “x”

- Typical setting: a box that takes in random seeds and outputs random samples like “x”
- How do we generate random seeds?

Topic: Neural Network Generator’s Model

AIM: Generate samples from the distribution of “landscape” images

Learning a generative model for data:

- Let’s say you are given a given set of some observed data X= (
*x*) - You choose a model
*P*(*x,θ*) for the distribution of*x* *Θ are the parameters of the model*

- Estimate the
*θ*such that*P*(*x;θ*) best fits the observations*X=(x)* - Hoping it will also represent data outside the training set

Ex: **Multinomials**

Our full Multinomial VAE model is given as follows:

*p(x|η) = Mult(φ(Ψη)) *

*p(η|z; θdec) = N (W z + µ, σ2 Id−1) *

*q(z|x; θenc) = N (FL ΨT (log( f x) − µ) , D)******

where θdec = {W, σ2} denotes the decoder parameters, θenc = {FL, D} denotes the encoder parameters and µ ∈ R d−1 is a bias parameter.

Here, *q(z|x; θenc)* denotes the variational posterior distribution of *z *given by the encoder represented as an L-layer dense neural network with appropriate activations. This encoder is directly used to evaluate *p(η|z; θdec)*. Furthermore, flat priors are assumed for all variables except z. It is important to note potentially challenging modeling issues when designing the encoder. The ILR transform is not directly applicable to count data, since log*(0)* is undefined. A common approach to this problem is to introduce a pseudocount before applying a logarithm, which we will denote as log*( f x) = log(x + 1)*. The choice of pseudocount is arbitrary and can introduce biases. To alleviate this issue, we introduce the deep encoder neural network highlighted in above equation*****; we expect that the universal approximation theorem would apply here and that the accuracy of estimating the latent representation *z* will improve with more complex neural networks. This is supported in our simulation benchmarks; more complex encoder architectures can better remove biases induced from the pseudocounts.

**Implementing Autoencoders **

1. Prepare the data: Before implementing an autoencoder, it is important to prepare the data for the model. This includes normalizing the data and splitting the data into a training and test set.

2. Choose an architecture: Autoencoders come in many different architectures, such as convolutional autoencoders, variational autoencoders, and denoising autoencoders. Choose the architecture that best suits your data and problem.

3. Choose a loss function: Loss functions are used to measure the difference between the predictions of the autoencoder and the true labels. The most commonly used loss functions are mean squared error and binary cross-entropy.

4. Choose an optimization algorithm: The optimization algorithm is used to update the weights of the model during training. Popular optimization algorithms include stochastic gradient descent and Adam.

5. Train the model: Train the model using the training data. Monitor the loss to ensure the model is learning properly.

6. Evaluate the model: Once the model is trained, evaluate it on the test data to see how well it performs.

In Autoencoder's case, we deal with an input image and we want to encode it to get a low dimensional embedding of the image and after that we want to decode it again and reconstruct the original image as good as possible which is the whole mechanism behind it. So, we deal with an original image, get an encoded image and reconstruct the original image again.

One of the most used applications is video compression where we want to send the images over the network from one end to another so instead of sending the whole image we could simply send the encoded data only and on the other side we then have a decoder stored & can decode the image again. This would save a lot of cost and could be much faster.

**Types of Autoencoders:**

- Standard Autoencoders: They produce data/images from the latent vector. But they try to replicate or copy the image data while doing so.

- Variational Autoencoders: They are good at generating new images from the latent vector. Although they generate new data/images, still, those are very similar to the data they are trained on.

**How to Implement Autoencoders in PyTorch? **

1. Begin by importing the necessary libraries and modules such as PyTorch, NumPy, Matplotlib, and Scikit-Learn.

2. Next, define a class for the Autoencoder model. This class should contain the necessary layers and functions for building the model.

3. Define the forward pass of the model, which should include the encoder, decoder, and loss functions.

4. After defining the model, create an object of the class and initialize the parameters of the model such as the learning rate and the optimizer.

5. Next, define the training loop which should include iterating through the dataset, calculating the loss, updating the parameters, and saving the model.

6. Finally, evaluate the model on the test set and visualize the results.

Follow the steps here: https://github.com/patrickloeber/pytorch-examples/blob/master/Autoencoder.ipynb

**How to Implement Convolutional Autoencoder in PyTorch with CUDA? **

1. Install all necessary packages for the implementation of Convolutional Autoencoder in PyTorch with CUDA. This includes PyTorch, NumPy, and CUDA Toolkit.

2. Create a new project directory and change the current working directory to the new project directory.

3. Create the necessary Python files for our Convolutional Autoencoder. This will include a model file, a data loader file, a training script and a main file.

4. Write the necessary code for the Convolutional Autoencoder model. This should include the definition of the encoder, decoder and autoencoder architectures, as well as the forward pass of the model.

5. Create the data loader class that will be responsible for loading and preprocessing the data.

6. Write the training script that will be responsible for training the autoencoder. This should include instantiating the model, data loader, optimizer, and loss function, as well as the training loop.

7. Create the main file to initialize the training process.

8. Initialize the CUDA device to utilize the GPU.

9. Run the main file to start.

**Conclusion:**

In this article, we discussed autoencoders in the context of using it on PyTorch. We went on to take a look at what exactly a convolutional autoencoder does, and how it does it with a view at developing an intuition of its working principle. Thereafter, we touched on its different sections to share a glimpse to define a custom autoencoder of your own, training it and discussing the results of the model training.