Deep Learning Using TensorFlow. In this TensorFlow tutorial for professionals and enthusiasts who are interested in applying Deep Learning Algorithm using TensorFlow to solve various problems.

In this TensorFlow tutorial for professionals and enthusiasts who are interested in applying Deep Learning Algorithm using TensorFlow to solve various problems.

TensorFlow is an open source deep learning library that is based on the concept of data flow graphs for building models. It allows you to create large-scale neural networks with many layers. Learning the use of this library is also a fundamental part of the AI & Deep Learning course curriculum. Following are the topics that will be discussed in this TensorFlow tutorial:

**What is TensorFlow****TensorFlow Code Basics****TensorFlow UseCase**

In this **TensorFlow tutorial**, before talking about TensorFlow, let us first understand *what are tensors*. **Tensors **are nothing but a de facto for representing the data in deep learning.

As shown in the image above, tensors are just multidimensional arrays, that allows you to represent data having higher dimensions. In general, Deep Learning you deal with high dimensional data sets where dimensions refer to different features present in the data set. In fact, the name “**TensorFlow**” has been derived from the operations which neural networks perform on tensors. It’s literally a flow of tensors. Since, you have understood what are tensors, let us move ahead in this **TensorFlow **tutorial and understand – *what is TensorFlow?*

**TensorFlow **is a library based on Python that provides different types of functionality for implementing **Deep Learning Models**. As discussed earlier, the term **TensorFlow** is made up of two terms – Tensor & Flow:

In **TensorFlow**, the term tensor refers to the representation of data as multi-dimensional array whereas the term flow refers to the series of operations that one performs on tensors as shown in the above image.

Now we have covered enough background about **TensorFlow**.

Next up, in this TensorFlow tutorial we will be discussing about TensorFlow code-basics.

TensorFlow Tutorial: Code BasicsBasically, the overall process of writing a **TensorFlow program** involves two steps:

- Building a Computational Graph
- Running a Computational Graph

Let me explain you the above two steps one by one:

So, *what is a computational graph?* Well, a computational graph is a series of TensorFlow operations arranged as nodes in the graph. Each nodes take 0 or more tensors as input and produces a tensor as output. Let me give you an example of a simple computational graph which consists of three nodes – * a*,

**What is TensorFlow** TensorFlow Code Basics**TensorFlow UseCase **

Basically, one can think of a computational graph as an alternative way of conceptualizing mathematical calculations that takes place in a TensorFlow program. The operations assigned to different nodes of a Computational Graph can be performed in parallel, thus, providing a better performance in terms of computations.

Here we just describe the computation, it doesn’t compute anything, it does not hold any values, it just defines the operations specified in your code.

Let us take the previous example of computational graph and understand how to execute it. Following is the code from previous example:

```
import tensorflow as tf
# Build a graph
a = tf.constant(5.0)
b = tf.constant(6.0)
c = a * b
```

Now, in order to get the output of node c, we need to run the computational graph within a **session**. Session places the graph operations onto Devices, such as CPUs or GPUs, and provides methods to execute them.

A session encapsulates the control and state of the *TensorFlow *runtime i.e. it stores the information about the order in which all the operations will be performed and passes the result of already computed operation to the next operation in the pipeline. Let me show you how to run the above computational graph within a session (Explanation of each line of code has been added as a comment):

```
# Create the session object
sess = tf.Session()
#Run the graph within a session and store the output to a variable
output_c = sess.run(c)
#Print the output of node c
print(output_c)
#Close the session to free up some resources
sess.close()
Output:
30
```

So, this was all about session and running a computational graph within it. Now, let us talk about variables and placeholders that we will be using extensively while building deep learning model using *TensorFlow*.

In *TensorFlow*, constants, placeholders and variables are used to represent different parameters of a deep learning model. Since, I have already discussed constants earlier, I will start with placeholders.

A *TensorFlow* constant allows you to store a value but, what if, you want your nodes to take inputs on the run? For this kind of functionality, placeholders are used which allows your graph to take external inputs as parameters. Basically, a placeholder is a promise to provide a value later or during runtime. Let me give you an example to make things simpler:

```
import tensorflow as tf
# Creating placeholders
a = tf. placeholder(tf.float32)
b = tf. placeholder(tf.float32)
# Assigning multiplication operation w.r.t. a & b to node mul
mul = a*b
# Create session object
sess = tf.Session()
# Executing mul by passing the values [1, 3] [2, 4] for a and b respectively
output = sess.run(mul, {a: [1,3], b: [2, 4]})
print('Multiplying a b:', output)
Output:
[2. 12.]
```

**What is TensorFlow** TensorFlow Code Basics**TensorFlow UseCase **

Now, let us move ahead and understand –

In deep learning, placeholders are used to take arbitrary inputs in your model or graph. Apart from taking input, you also need to modify the graph such that it can produce new outputs w.r.t. same inputs. For this you will be using variables. In a nutshell, a variable allows you to add such parameters or node to the graph that are trainable i.e. the value can be modified over the period of a time. Variables are defined by providing their initial value and type as shown below:

```
var = tf.Variable( [0.4], dtype = tf.float32 )
```

**Note: **

**What is TensorFlow** TensorFlow Code Basics**TensorFlow UseCase **

Constants are initialized when you call

```
init = tf.global_variables_initializer()
sess.run(init)
```

Always remember that a variable must be initialized before a graph is used for the first time.

**Note:** *TensorFlow variables are in-memory buffers that contain tensors, but unlike normal tensors that are only instantiated when a graph is run and are immediately deleted afterwards, variables survive across multiple executions of a graph.*

Now that we have covered enough basics of *TensorFlow*, let us go ahead and understand how to implement a linear regression model using *TensorFlow*.

Linear Regression Model is used for predicting the unknown value of a variable (Dependent Variable) from the known value of another variables (Independent Variable) using linear regression equation as shown below:

Therefore, for creating a linear model, you need:

- Building a Computational Graph
- Running a Computational Graph

So, let us begin building linear model using TensorFlow:

Copy the code by clicking the button given below:

```
# Creating variable for parameter slope (W) with initial value as 0.4
W = tf.Variable([.4], tf.float32)
#Creating variable for parameter bias (b) with initial value as -0.4
b = tf.Variable([-0.4], tf.float32)
# Creating placeholders for providing input or independent variable, denoted by x
x = tf.placeholder(tf.float32)
# Equation of Linear Regression
linear_model = W * x + b
# Initializing all the variables
sess = tf.Session()
init = tf.global_variables_initializer()
sess.run(init)
# Running regression model to calculate the output w.r.t. to provided x values
print(sess.run(linear_model {x: [1, 2, 3, 4]}))
```

**Output:**

```
[ 0. 0.40000001 0.80000007 1.20000005]
```

The above stated code just represents the basic idea behind the implementation of regression model i.e. how you follow the equation of regression line so as to get output w.r.t. a set of input values. But, there are two more things left to be added in this model to make it a complete regression model:

**What is TensorFlow** TensorFlow Code Basics**TensorFlow UseCase **

Now let us understand how can I incorporate the above stated functionalities into my code for regression model.

A loss function measures how far apart the current output of the model is from that of the desired or target output. I’ll use a most commonly used loss function for my linear regression model called as Sum of Squared Error or SSE. SSE calculated w.r.t. model output (represent by linear_model) and desired or target output (y) as:

```
y = tf.placeholder(tf.float32)
error = linear_model - y
squared_errors = tf.square(error)
loss = tf.reduce_sum(squared_errors)
print(sess.run(loss, {x:[1,2,3,4], y:[2, 4, 6, 8]})
```

```
Output:
90.24
```

As you can see, we are getting a high loss value. Therefore, we need to adjust our weights (W) and bias (b) so as to reduce the error that we are receiving.

TensorFlow provides **optimizers** that slowly change each variable in order to minimize the loss function or error. The simplest optimizer is **gradient descent**. It modifies each variable according to the magnitude of the derivative of loss with respect to that variable.

```
#Creating an instance of gradient descent optimizer
optimizer = tf.train.GradientDescentOptimizer(0.01)
train = optimizer.minimize(loss)
for i in range(1000):
sess.run(train, {x:[1, 2, 3, 4], y:[2, 4, 6, 8]})
print(sess.run([W, b]))
```

```
Output:
[array([ 1.99999964], dtype=float32), array([ 9.86305167e-07], dtype=float32)]
```

So, this is how you create a linear model using TensorFlow and train it to get the desired output.

Complete hands-on Machine Learning tutorial with Data Science, Tensorflow, Artificial Intelligence, and Neural Networks. Introducing Tensorflow, Using Tensorflow, Introducing Keras, Using Keras, Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), Learning Deep Learning, Machine Learning with Neural Networks, Deep Learning Tutorial with Python

Machine Learning, Data Science and Deep Learning with PythonExplore the full course on Udemy (special discount included in the link): http://learnstartup.net/p/BkS5nEmZg

In less than 3 hours, you can understand the theory behind modern artificial intelligence, and apply it with several hands-on examples. This is machine learning on steroids! Find out why everyone’s so excited about it and how it really works – and what modern AI can and cannot really do.

In this course, we will cover:

• Deep Learning Pre-requistes (gradient descent, autodiff, softmax)

• The History of Artificial Neural Networks

• Deep Learning in the Tensorflow Playground

• Deep Learning Details

• Introducing Tensorflow

• Using Tensorflow

• Introducing Keras

• Using Keras to Predict Political Parties

• Convolutional Neural Networks (CNNs)

• Using CNNs for Handwriting Recognition

• Recurrent Neural Networks (RNNs)

• Using a RNN for Sentiment Analysis

• The Ethics of Deep Learning

• Learning More about Deep Learning

At the end, you will have a final challenge to create your own deep learning / machine learning system to predict whether real mammogram results are benign or malignant, using your own artificial neural network you have learned to code from scratch with Python.

Separate the reality of modern AI from the hype – by learning about deep learning, well, deeply. You will need some familiarity with Python and linear algebra to follow along, but if you have that experience, you will find that neural networks are not as complicated as they sound. And how they actually work is quite elegant!

This is hands-on tutorial with real code you can download, study, and run yourself.

A step-by-step guide to setting up Python for Deep Learning and Data Science for a complete beginner

A step-by-step guide to setting up Python for Deep Learning and Data Science for a complete beginner

You can code your own Data Science or Deep Learning project in just a couple of lines of code these days. This is not an exaggeration; many programmers out there have done the hard work of writing tons of code for us to use, so that all we need to do is plug-and-play rather than write code from scratch.

You may have seen some of this code on Data Science / Deep Learning blog posts. Perhaps you might have thought: “Well, if it’s really that easy, then why don’t I try it out myself?”

If you’re a beginner to Python and you want to embark on this journey, then this post will guide you through your first steps. A common complaint I hear from complete beginners is that it’s pretty difficult to set up Python. How do we get everything started in the first place so that we can plug-and-play Data Science or Deep Learning code?

This post will guide you through in a step-by-step manner how to set up Python for your Data Science and Deep Learning projects. We will:

- Set up Anaconda and Jupyter Notebook
- Create Anaconda environments and install packages (code that others have written to make our lives tremendously easy) like tensorflow, keras, pandas, scikit-learn and matplotlib.

Once you’ve set up the above, you can build your first neural network to predict house prices in this tutorial here:

Build your first Neural Network to predict house prices with Keras

The main programming language we are going to use is called Python, which is the most common programming language used by Deep Learning practitioners.

The first step is to download Anaconda, which you can think of as a platform for you to use Python “out of the box”.

Visit this page: https://www.anaconda.com/distribution/ and scroll down to see this:

This tutorial is written specifically for Windows users, but the instructions for users of other Operating Systems are not all that different. Be sure to click on “Windows” as your Operating System (or whatever OS that you are on) to make sure that you are downloading the correct version.

This tutorial will be using Python 3, so click the green Download button under “Python 3.7 version”. A pop up should appear for you to click “Save” into whatever directory you wish.

Once it has finished downloading, just go through the setup step by step as follows:

Click Next

Click “I Agree”

Click Next

Choose a destination folder and click Next

Click Install with the default options, and wait for a few moments as Anaconda installs

Click Skip as we will not be using Microsoft VSCode in our tutorials

Click Finish, and the installation is done!

Once the installation is done, go to your Start Menu and you should see some newly installed software:

You should see this on your start menu

Click on Anaconda Navigator, which is a one-stop hub to navigate the apps we need. You should see a front page like this:

Anaconda Navigator Home Screen

Click on ‘Launch’ under Jupyter Notebook, which is the second panel on my screen above. Jupyter Notebook allows us to run Python code interactively on the web browser, and it’s where we will be writing most of our code.

A browser window should open up with your directory listing. I’m going to create a folder on my Desktop called “Intuitive Deep Learning Tutorial”. If you navigate to the folder, your browser should look something like this:

Navigating to a folder called Intuitive Deep Learning Tutorial on my Desktop

On the top right, click on New and select “Python 3”:

Click on New and select Python 3

A new browser window should pop up like this.

Browser window pop-up

Congratulations — you’ve created your first Jupyter notebook! Now it’s time to write some code. Jupyter notebooks allow us to write snippets of code and then run those snippets without running the full program. This helps us perhaps look at any intermediate output from our program.

To begin, let’s write code that will display some words when we run it. This function is called *print*. Copy and paste the code below into the grey box on your Jupyter notebook:

```
print("Hello World!")
```

Your notebook should look like this:

Entering in code into our Jupyter Notebook

Now, press Alt-Enter on your keyboard to run that snippet of code:

Press Alt-Enter to run that snippet of code

You can see that Jupyter notebook has displayed the words “Hello World!” on the display panel below the code snippet! The number 1 has also filled in the square brackets, meaning that this is the first code snippet that we’ve run thus far. This will help us to track the order in which we have run our code snippets.

Instead of Alt-Enter, note that you can also click Run when the code snippet is highlighted:

Click Run on the panel

If you wish to create new grey blocks to write more snippets of code, you can do so under Insert.

Jupyter Notebook also allows you to write normal text instead of code. Click on the drop-down menu that currently says “Code” and select “Markdown”:

Now, our grey box that is tagged as markdown will not have square brackets beside it. If you write some text in this grey box now and press Alt-Enter, the text will render it as plain text like this:

If we write text in our grey box tagged as markdown, pressing Alt-Enter will render it as plain text.

There are some other features that you can explore. But now we’ve got Jupyter notebook set up for us to start writing some code!

Now we’ve got our coding platform set up. But are we going to write Deep Learning code from scratch? That seems like an extremely difficult thing to do!

The good news is that many others have written code and made it available to us! With the contribution of others’ code, we can play around with Deep Learning models at a very high level without having to worry about implementing all of it from scratch. This makes it extremely easy for us to get started with coding Deep Learning models.

For this tutorial, we will be downloading five packages that Deep Learning practitioners commonly use:

- Set up Anaconda and Jupyter Notebook
- Create Anaconda environments and install packages (code that others have written to make our lives tremendously easy) like tensorflow, keras, pandas, scikit-learn and matplotlib.

The first thing we will do is to create a Python environment. An environment is like an isolated working copy of Python, so that whatever you do in your environment (such as installing new packages) will not affect other environments. It’s good practice to create an environment for your projects.

Click on Environments on the left panel and you should see a screen like this:

Anaconda environments

Click on the button “Create” at the bottom of the list. A pop-up like this should appear:

A pop-up like this should appear.

Name your environment and select Python 3.7 and then click Create. This might take a few moments.

Once that is done, your screen should look something like this:

Notice that we have created an environment ‘intuitive-deep-learning’. We can see what packages we have installed in this environment and their respective versions.

Now let’s install some packages we need into our environment!

The first two packages we will install are called Tensorflow and Keras, which help us plug-and-play code for Deep Learning.

On Anaconda Navigator, click on the drop down menu where it currently says “Installed” and select “Not Installed”:

A whole list of packages that you have not installed will appear like this:

Search for “tensorflow”, and click the checkbox for both “keras” and “tensorflow”. Then, click “Apply” on the bottom right of your screen:

A pop up should appear like this:

Click Apply and wait for a few moments. Once that’s done, we will have Keras and Tensorflow installed in our environment!

Using the same method, let’s install the packages ‘pandas’, ‘scikit-learn’ and ‘matplotlib’. These are common packages that data scientists use to process the data as well as to visualize nice graphs in Jupyter notebook.

This is what you should see on your Anaconda Navigator for each of the packages.

**Pandas:**

Installing pandas into your environment

**Scikit-learn:**

Installing scikit-learn into your environment

**Matplotlib:**

Installing matplotlib into your environment

Once it’s done, go back to “Home” on the left panel of Anaconda Navigator. You should see a screen like this, where it says “Applications on intuitive-deep-learning” at the top:

Now, we have to install Jupyter notebook in this environment. So click the green button “Install” under the Jupyter notebook logo. It will take a few moments (again). Once it’s done installing, the Jupyter notebook panel should look like this:

Click on Launch, and the Jupyter notebook app should open.

Create a notebook and type in these five snippets of code and click Alt-Enter. This code tells the notebook that we will be using the five packages that you installed with Anaconda Navigator earlier in the tutorial.

```
import tensorflow as tf
import keras
import pandas
import sklearn
import matplotlib
```

If there are no errors, then congratulations — you’ve got everything installed correctly:

A sign that everything works!

If you have had any trouble with any of the steps above, please feel free to comment below and I’ll help you out!

*Originally published by ** Joseph Lee Wei En** at *

===================================================================

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In this article, we will learn how deep learning works and get familiar with its terminology — such as backpropagation and batch size

Originally published by Milad Toutounchian at https://towardsdatascience.com

Deep learning is one of the most popular models currently being used in real-world, Data Science applications. It’s been an effective model in areas that range from image to text to voice/music. With the increase in its use, the ability to quickly and scalably implement deep learning becomes paramount. The rise of deep learning platforms such as Tensorflow, help developers implement what they need to in easier ways.

In this article, we will learn how deep learning works and get familiar with its terminology — such as backpropagation and batch size. We will implement a simple deep learning model — from theory to scratch implementation — for a predefined input and output in Python, and then do the same using deep learning platforms such as Keras and Tensorflow. We have written this simple deep learning model using Keras and Tensorflow version 1.x and version 2.0 with three different levels of complexity and ease of coding.

Deep Learning Implementation from ScratchConsider a simple multi-layer-perceptron with four input neurons, one hidden layer with three neurons and an output layer with one neuron. We have three data-samples for the input denoted as X, and three data-samples for the desired output denoted as yt. So, each input data-sample has four features.

```
# Inputs and outputs of the neural net:
import numpy as np
X=np.array([[1.0, 0.0, 1.0, 0.0],[1.0, 0.0, 1.0, 1.0],[0.0, 1.0, 0.0, 1.0]])
yt=np.array([[1.0],[1.0],[0.0]])
```

The * x**(m)

The goal of a neural net (NN) is to obtain weights and biases such that for a given input, the NN provides the desired output. But, we do not know the appropriate weights and biases in advance, so we update the weights and biases such that the error between the output of NN, *yp(m)*, and desired ones, *yt(m)*, is minimized. This iterative minimization process is called the NN training.

Assume the activation functions for both hidden and output layers are sigmoid functions. Therefore,

The size of weights, biases and the relationships between input and outputs of the neural net

Where activation function is the sigmoid, *m* is the *m*th data-sample and *yp(m)* is the NN output.

The error function, which measures the difference between the output of NN with the desired one, can be expressed mathematically as:

The Error defined for the neural net which is squared error

The pseudocode for the above NN has been summarized below:

pseudocode for the neural net training

From our pseudocode, we realize that the partial derivative of Error (E) with respect to parameters (weights and biases) should be computed. Using the chain rule from calculus we can write:

We have two options here for updating the weights and biases in backward path (backward path means updating weights and biases such that error is minimized):

- Use all *N * samples of the training data
- Use one sample (or a couple of samples)

For the first one, we say the batch size is *N*. For the second one, we say batch size is 1, if use one sample to updates the parameters. So batch size means how many data samples are being used for updating the weights and biases.

You can find the implementation of the above neural net, in which the gradient of the error with respect to parameters is calculated Symbolically, with different batch sizes here.

As you can see with the above example, creating a simple deep learning model from scratch involves methods that are very complex. In the next section, we will see how deep learning frameworks can assist in introducing scalability and greater ease of implementation to our model.

Deep Learning implementation using Keras, Tensorflow 1.x and 2.0In the previous section, we computed the gradient of Error w.r.t. parameters from using the chain rule. We saw first-hand that it is not an easy or scalable approach. Also, keep in mind that we evaluate the partial derivatives at each iteration, and as a result, the Symbolic Gradient is not needed although its value is important. This is where deep-learning frameworks such as Keras and Tensorflow can play their role. The deep-learning frameworks use an AutoDiff method for numerical calculations of partial gradients. If you’re not familiar with AutoDiff, StackExchange has a great example to walk through.

The AutoDiff decomposes the complex expression into a set of primitive ones, i.e. expressions consisting of at most a single function call. As the differentiation rules for each separate expression are already known, the final results can be computed in an efficient way.

We have implemented the NN model with three different levels in Keras, Tensorflow 1.x and Tensorflow 2.0:

**1- High-Level (Keras and Tensorflow 2.0): **High-Level Tensorflow 2.0 with Batch Size 1

**2- Medium-Level (Tensorflow 1.x and 2.0): **Medium-Level Tensorflow 1.x with Batch Size 1 , Medium-Level Tensorflow 1.x with Batch Size N, Medium-Level Tensorflow 2.0 with Batch Size 1, Medium-Level Tensorflow v 2.0 with Batch Size N

**3- Low-Level (Tensorflow 1.x): **Low-Level Tensorflow 1.x with Batch Size N

**Code Snippets:**

For the High-Level, we have accomplished the implementation using Keras and Tensorflow v 2.0 with *model.train_on_batch*:

```
# High-Level implementation of the neural net in Tensorflow:
model.compile(loss=mse, optimizer=optimizer)
for _ in range(2000):
for step, (x, y) in enumerate(zip(X_data, y_data)):
model.train_on_batch(np.array([x]), np.array([y]))
```

In the Medium-Level using Tensorflow 1.x, we have defined:

```
E = tf.reduce_sum(tf.pow(ypred - Y, 2))
optimizer = tf.train.GradientDescentOptimizer(0.1)
grads = optimizer.compute_gradients(E, [W_h, b_h, W_o, b_o])
updates = optimizer.apply_gradients(grads)
```

This ensures that in the *for loop*, the updates variable will be updated. For Medium-Level, the gradients and their updates are defined outside the for_loop and inside the for_loop updates is iteratively updated. In the Medium-Level using Tensorflow v 2.x, we have used:

```
# Medium-Level implementation of the neural net in Tensorflow
# In for_loop
with tf.GradientTape() as tape:
x = tf.convert_to_tensor(np.array([x]), dtype=tf.float64)
y = tf.convert_to_tensor(np.array([y]), dtype=tf.float64)
ypred = model(x)
loss = mse(y, ypred)
gradients = tape.gradient(loss, model.trainable_weights)
optimizer.apply_gradients(zip(gradients, model.trainable_weights))
```

In Low-Level implementation, each weight and bias is updated separately. In the Low-Level using Tensorflow v 1.x, we have defined:

```
# Low-Level implementation of the neural net in Tensorflow:
E = tf.reduce_sum(tf.pow(ypred - Y, 2))
dE_dW_h = tf.gradients(E, [W_h])[0]
dE_db_h = tf.gradients(E, [b_h])[0]
dE_dW_o = tf.gradients(E, [W_o])[0]
dE_db_o = tf.gradients(E, [b_o])[0]
# In for_loop:
evaluated_dE_dW_h = sess.run(dE_dW_h,
feed_dict={W_h: W_h_i, b_h: b_h_i, W_o: W_o_i, b_o: b_o_i, X: X_data.T, Y: y_data.T})
W_h_i = W_h_i - 0.1 * evaluated_dE_dW_h
evaluated_dE_db_h = sess.run(dE_db_h,
feed_dict={W_h: W_h_i, b_h: b_h_i, W_o: W_o_i, b_o: b_o_i, X: X_data.T, Y: y_data.T})
b_h_i = b_h_i - 0.1 * evaluated_dE_db_h
evaluated_dE_dW_o = sess.run(dE_dW_o,
feed_dict={W_h: W_h_i, b_h: b_h_i, W_o: W_o_i, b_o: b_o_i, X: X_data.T, Y: y_data.T})
W_o_i = W_o_i - 0.1 * evaluated_dE_dW_o
evaluated_dE_db_o = sess.run(dE_db_o,
feed_dict={W_h: W_h_i, b_h: b_h_i, W_o: W_o_i, b_o: b_o_i, X: X_data.T, Y: y_data.T})
b_o_i = b_o_i - 0.1 * evaluated_dE_db_o
```

As you can see with the above low level implementation, the developer has more control over every single step of numerical operations and calculations.

ConclusionWe have now shown that implementing from scratch even a simple deep learning model by using Symbolic gradient computation for weight and bias updates is not an easy or scalable approach. Using deep learning frameworks accelerates this process as a result of using AutoDiff, which is basically a stable numerical gradient computation for updating weights and biases.

**Thanks for reading** ❤

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