Source: Deep Learning on Medium

*by Abien Fred Agarap, **Senti AI*

Google announced a major upgrade on the world’s most popular open-source machine learning library, TensorFlow, with a promise of focusing on simplicity and ease of use, eager execution, intuitive high-level APIs, and flexible model building on any platform.

This post is a humble attempt to contribute to the body of working TensorFlow 2.0 examples. Specifically, we shall discuss the subclassing API implementation of an **autoencoder**.

To install TensorFlow 2.0, it is recommended to create a virtual environment for it,

`pip install tensorflow==2.0.0-alpha`

or if you have a GPU in your system,

`pip install tensorflow-gpu==2.0.0-alpha`

More details on its installation through this guide from tensorflow.org.

Before diving into the code, let’s discuss first what an **autoencoder** is.

### Autoencoder

We deal with huge amount of data in machine learning which naturally leads to more computations. However, we can also just pick the parts of the data that contribute the most to a model’s learning, thus leading to less computations. The process of choosing the *important parts* of the data is known as *feature selection, *which is among the number of use cases for an ** autoencoder**.

But what exactly is an **autoencoder**? Well, let’s first recall that a neural network is a computational model that is used for *finding* a *function* *describing* *the* *relationship* between data *features* ** x** and its

*values*(a

*regression*task) or

*labels*(a

*classification*task)

**, i.e.**

*y***.**

*y = f(x)*Now, an **autoencoder** is also a neural network. But instead of finding the function *mapping* the *features* ** x **to

*their corresponding values*or

*labels*

**, it aims to find the function mapping the**

*y**features*

*x**to their corresponding features*

**. Wait, what? Why would we do that?**

*x*Well, what’s interesting is what happens inside the **autoencoder**. Let’s bring up a graphical illustration of an **autoencoder** for an even better understanding.

From the illustration above, an **autoencoder** consists of two components: (1) an **encoder** which learns the data representation, i.e. the *important* *features *** z** of the data, and (2) a

**decoder**which reconstructs the data based on its idea

**of how it is structured.**

*z*Going back, we established that an **autoencoder** wants to find the function that maps ** x **to

**. It does so through its components. Mathematically,**

*x*The **encoder** *h-sub-e *learns the data representation ** z **from the input features

**, then the said representation serves as the input to the**

*x***decoder**

*h-sub-d*in order to reconstruct the original data

**.**

*x*We shall further dissect this model below.

### Encoder

The first component, the **encoder**, is similar to a conventional feed-forward network. However, it is not tasked on predicting values or labels. Instead, it is tasked to learn how the data is structured, i.e. data representation ** z**.

The *encoding* is done by passing data input ** x **to the

**encoder**’s hidden layer

**in order to learn the data representation**

*h***. We can implement the**

*z = f(h(x))*`Encoder`

layer as follows,We first define an `Encoder`

** **class that inherits the `tf.keras.layers.Layer`

to define it as a layer instead of a model. Why a layer instead of a model? Recall that the encoder is a *component* of the **autoencoder** model.

Going through the code, the `Encoder`

layer is defined to have a single hidden layer of neurons (`self.hidden_layer`

) to learn the activation of the input features. Then, we connect the hidden layer to a layer (`self.output_layer`

) that encodes the data representation to a lower dimension, which consists of what it thinks as important features. Hence, the “output” of the `Encoder`

layer is the *learned data representation *** z **for the input data

**.**

*x*### Decoder

The second component, the **decoder**, is also similar to a feed-forward network. However, instead of reducing data to a lower dimension, it reconstructs the data from its lower dimension representation ** z **to its original dimension

**.**

*x*The *decoding* is done by passing the lower dimension representation ** z **to the

**decoder**’s hidden layer

**in order to reconstruct the data to its original dimension**

*h***. We can implement the**

*x = f(h(z))***decoder**layer as follows,

We define a `Decoder`

** **class that also inherits the `tf.keras.layers.Layer`

.

The `Decoder`

layer is also defined to have a single hidden layer of neurons to reconstruct the input features from the learned representation by the encoder. Then, we connect its hidden layer to a layer that decodes the data representation from a lower dimension to its original dimension. Hence, the “output” of the decoder layer is the reconstructed data ** x **from the data representation

**. Ultimately, the output of the decoder is the**

*z***autoencoder**’s output.

Now that we have defined the components of our **autoencoder**, we can finally build the model.

### Building the Autoencoder model

We can now build the **autoencoder** model by instantiating the `Encoder`

and the `Decoder`

layers.

As we discussed above, we use the output of the **encoder** layer as the input to the **decoder** layer. So, that’s it? No, not exactly.

To this point, we have only discussed the components of an **autoencoder** and how to build it, but we have not yet talked about how it actually learns. All we know to this point is the *flow of data*; from the input layer to the **encoder** layer which learns the data representation, and use that representation as input to the **decoder** layer that reconstructs the original data.

Like other neural networks, an **autoencoder** learns through backpropagation. However, instead of comparing the values or labels of the model, we compare the *reconstructed data* ** x-hat **and the

*original data*

**. Let’s call this comparison the**

*x**reconstruction error*function, and it is given by the following equation,

In TensorFlow, the above equation could be expressed as follows,

Are we there yet? Close enough. Just a few more things to add. Now that we have our error function defined, we can finally write the training function for our model.

This way of implementing backpropagation affords us with more freedom by enabling us to keep track of the gradients, and the application of an optimization algorithm to them.

Are we done now? Let’s see.

- Define an
**encoder**layer.*Checked*. - Define a
**decoder**layer.*Checked*. - Build the
**autoencoder**using the**encoder**and**decoder**layers.*Checked*. - Define the reconstruction error function.
*Checked*. - Define the training function.
*Checked*.

Yes! We’re done here! We can finally train our model!

But before doing so, let’s instantiate an `Autoencoder`

class that we defined before, and an optimization algorithm to use. Then, let’s load the data we want to reconstruct. For this post, let’s use the *unforgettable* MNIST handwritten digit dataset.

We can visualize our training results by using TensorBoard, and to do so, we need to define a summary file writer for the results by using `tf.summary.create_file_writer`

.

Next, we use the defined summary file writer, and record the training summaries using `tf.summary.record_if`

.

We can finally (for real now) train our model by feeding it with mini-batches of data, and compute its loss and gradients per iteration through our previously-defined `train`

function, which accepts the defined *error function*, the *autoencoder** model*, the *optimization algorithm*, and the *mini-batch* of data.

After each iteration of training the model, the computed reconstruction error should be decreasing to see if it the model is actually learning (just like in other neural networks). Lastly, to record the training summaries in TensorBoard, we use the `tf.summary.scalar`

for recording the reconstruction error values, and the `tf.summary.image`

for recording the mini-batch of the original data and reconstructed data.

After some epochs, we can start to see a relatively good reconstruction of the MNIST images.

The reconstructed images might be good enough but they are quite blurry. A number of things could be done to improve this result, e.g. adding more layers and/or neurons, or using a convolutional neural network architecture as the basis of the **autoencoder** model, or use a different kind of **autoencoder**.

### Closing remarks

**Autoencoders** are quite useful for dimensionality reduction. But it could also be used for data denoising, and for learning the distribution of a dataset. I hope we have covered enough in this article to make you excited to learn more about **autoencoders**!

The full code is available here. In case you have any feedback, you may reach me through Twitter. We can also connect through Facebook, Instagram, and/or LinkedIn!

### References

- Martín Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geoffrey Irving, Michael Isard, Rafal Jozefowicz, Yangqing Jia, Lukasz Kaiser, Manjunath Kudlur, Josh Levenberg, Dan Mané, Mike Schuster, Rajat Monga, Sherry Moore, Derek Murray, Chris Olah, Jonathon Shlens, Benoit Steiner, Ilya Sutskever, Kunal Talwar, Paul Tucker, Vincent Vanhoucke, Vijay Vasudevan, Fernanda Viégas, Oriol Vinyals, Pete Warden, Martin Wattenberg, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng.
*TensorFlow: Large-scale machine learning on heterogeneous systems,*

2015. Software available from tensorflow.org. - Chollet, F. (2016, May 14). Building Autoencoders in Keras. Retrieved March 19, 2019, from https://blog.keras.io/building-autoencoders-in-keras.html
- Goodfellow, I., Bengio, Y., & Courville, A. (2016).
*Deep learning*. MIT press.

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