i am new to this area. i am working on a paper and i have running dataset code . but the author haven't mention such thing about figure kindly any one pls help me about it to generate waveform

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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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.