Neuron: Building block of Deep learning

Summary

This deep learning video explores the inner workings of a neuron, focusing on its two primary components: the summation operation and the activation function. It explains the role of weights in determining the importance of inputs and introduces the concept of bias for adjusting the neuron's output. The video uses a simple car pricing example to illustrate these concepts and provides a mathematical explanation of the weighted sum calculation. It also briefly touches on the Perceptron algorithm and concludes with a TensorFlow demonstration of creating a neuron and calculating its output.

Takeaways

• 🧠 The script introduces the concept of a neuron in deep learning, explaining its ability to transform data and make predictions through repeated processes.
• 🔍 It delves into the internal workings of a neuron, highlighting the division into two parts: one for summation and the other for activation, with a focus on the former in this video.
• 📊 The importance of weights in a neuron is emphasized, illustrating how they represent the strength of the connection between inputs and the neuron, and how they can vary based on the relevance of different inputs.
• 🚗 An example is provided using car pricing to explain how weights can be adjusted based on the influence of different factors such as engine type, buyer's name, and fuel price on the car's price.
• 📈 The concept of the 'weighted sum' is introduced, which is the result of multiplying each input by its corresponding weight and summing them up, often represented in matrix form.
• 📚 The script explains the summation operation in the context of linear algebra, equating it to the dot product of the input and weight matrices.
• 🔄 The role of bias is introduced, describing it as a single value added to the weighted sum that can shift the decision boundary in classification problems, allowing for better data fitting.
• 📉 The script uses a visual example to demonstrate how altering the slope (weights) and introducing bias can help in separating data points in a classification scenario.
• 🤖 The Perceptron algorithm is mentioned, which is foundational to understanding neurons, and Frank Rosenblatt is recognized as a pioneer in the field of deep learning.
• 💻 Practical implementation is discussed, with TensorFlow being used to create a simple neuron and numpy for data manipulation, showing how weights and biases are initialized and used in calculations.
• 🔬 The script concludes with an anticipation of the next video, which will focus on activation functions, a critical component of neurons that was only briefly mentioned in this script.

Q & A

What is the basic function of a neuron in deep learning?

A neuron in deep learning applies a transformation to input data and repeatedly adjusts this transformation to eventually predict the output of new data.

How is a neuron divided to perform its function?

A neuron is divided into two parts: the left side performs the summation operation, while the right side carries out the activation operation.

What are the weights in a neuron and why are they important?

Weights in a neuron represent the strength of the connection between inputs and the neuron. They are important because they determine the influence each input feature has on the prediction.

Can you give an example of how weights are determined in a neuron?

In the example of predicting a car's price, weights would be higher for the type of engine due to its significant influence on price, lower for the buyer's name as it has little influence, and intermediate for the price of fuel due to its indirect effect.

What is the summation operation in the context of a neuron?

The summation operation multiplies each input value by its corresponding weight, sums these products, and the result is known as the 'weighted sum'.

How are inputs and weights typically represented in deep learning?

Inputs and weights are usually represented in the form of matrices, where the input matrix contains the training data and the weights matrix defines the strength between each input feature and the neuron.

What is the algebraic definition of the dot product and how does it relate to the weighted sum?

The dot product is an algebraic operation that multiplies corresponding elements of two matrices and sums the results. It is equivalent to the calculation of the weighted sum in a neuron.

What is the role of bias in a neuron?

Bias is a single value added to the weighted sum that allows the neuron to shift its decision boundary, enabling it to fit the data better by adjusting the position of the line or hyperplane in the feature space.

How does the bias help in visualizing and separating data points in a classification problem?

Bias helps by allowing the decision boundary (e.g., a line separating blue and orange points) to be shifted up and down, which can be crucial when the data points are not easily separable by altering the slope alone.

What is the significance of the Perceptron algorithm in the history of deep learning?

The Perceptron algorithm, invented by Frank Rosenblatt in 1958, is foundational in deep learning as it represents the basic structure of a neuron, including the summation of weighted inputs and the application of an activation function.

How does TensorFlow's Dense layer relate to the concept of a neuron as described in the script?

The TensorFlow's Dense layer is a class that creates a neuron or a layer of neurons. It uses the concepts of weights and biases to calculate the weighted sum, which is then passed through an activation function to produce the final output.

What is the purpose of training a model in the context of adjusting weights and biases?

Training a model involves adjusting the weights and biases through multiple epochs so that the model learns to minimize the error in its predictions, thus improving accuracy.

Why is the activation function an important topic in the study of neurons?

The activation function is crucial as it introduces non-linearity into the neuron's output, allowing the network to learn and model complex patterns in the data.

Outlines

00:00

🧠 Understanding Neurons in Deep Learning

This paragraph introduces the concept of a neuron in deep learning, explaining how it processes data through repeated transformations to make predictions. It delves into the neuron's internal workings, highlighting the role of weights in determining the strength of input connections. The paragraph uses the example of predicting car prices to illustrate how weights can vary based on the relevance of different features. It then explains the summation operation, which involves multiplying inputs by their corresponding weights and adding them up to form a 'weighted sum'. The concept of a matrix is introduced for handling inputs and weights, and the paragraph concludes with a discussion on the importance of the dot product in calculating the weighted sum and the introduction of the bias term, which allows for adjustments in the neuron's output to better fit the data.

05:04

📚 Practical Implementation of Neurons with TensorFlow

The second paragraph focuses on the practical application of neuron concepts using TensorFlow and numpy. It begins by creating a simple neuron model with TensorFlow's tf.keras.layers.Dense, specifying a single neuron. The paragraph then explores the initial state of the weight matrix and bias, which are randomly initialized but will be adjusted during training to improve accuracy. A demonstration is provided on how to calculate the output of the neuron manually using numpy, by performing a dot product of the input matrix and weights, and then adding the bias. The results are compared with TensorFlow's output to validate the manual calculation. The paragraph ends with a teaser for the next video, which will discuss activation functions, a critical topic in understanding how neurons operate.

Keywords

💡Neuron

A neuron, in the context of the video, refers to the fundamental unit of a neural network that processes information. It is defined by its ability to receive input, perform calculations, and produce an output, which can be thought of as a prediction or decision. The video script discusses how a neuron takes inputs, applies transformations through weights and biases, and outputs a prediction, which is central to understanding the theme of deep learning.

💡Weights

Weights are numerical values that represent the strength of the connection between inputs and the neuron. They are crucial in determining the importance of each input feature in influencing the output. In the script, weights are denoted as w1, w2, w3, etc., and they are used to calculate the 'weighted sum', which is a key step in the neuron's operation. The example of predicting car prices illustrates how weights can vary based on the relevance of different inputs.

💡Activation Function

Although not deeply discussed in the script, the activation function is mentioned as a component of the neuron that follows the summation operation. It is a mathematical function applied to the weighted sum to introduce non-linear properties to the model, enabling it to learn more complex patterns. The activation operation is essential for the neuron's ability to make predictions, but the specifics are reserved for a future video.

💡Summation Operation

The summation operation is the process where each input value is multiplied by its corresponding weight and then all these products are added together to form the 'weighted sum'. This operation is fundamental to the neuron's function, as it combines the influence of all inputs to produce an intermediate result. The script explains this process using a matrix representation, where the input matrix is multiplied by the weights matrix to obtain the weighted sum.

💡Weighted Sum

The weighted sum is the result of the summation operation, where each input is weighted by its corresponding weight and then all are summed up. It is a critical intermediate value in the neuron's computation process. The script describes how this value is obtained by multiplying the input matrix with the weights matrix and adding the bias, which is then used to calculate the final output or prediction.

💡Dot Product

The dot product is an algebraic operation that is used to calculate the weighted sum in the context of the video. It is the multiplication of corresponding elements of two matrices and then summing those products. The script mentions that the formula for the weighted sum is equivalent to the dot product, which is a fundamental concept in linear algebra and is used to generalize the calculation of the weighted sum.

💡Bias

Bias is a single value added to the weighted sum in the neuron's computation. It serves to adjust the output by shifting the decision boundary, allowing for better fitting of the model to the data. The script provides an example of a classification problem where altering the bias helps in separating classes of data points, illustrating its importance in the model's predictive capabilities.

💡Perceptron Algorithm

The perceptron algorithm is the foundational concept of neural networks, introduced by Frank Rosenblatt in 1958. The script mentions it as the entire process of calculating the weighted sum and output within a neuron, which is considered the simplest form of a neural network. The perceptron is the basis for more complex deep learning models and is essential to understanding the evolution of neural networks.

💡TensorFlow

TensorFlow is an open-source software library for machine learning, which is used in the script to demonstrate the creation and operation of a neuron. The script shows how to use TensorFlow to initialize a neuron with the `tf.keras.layers.Dense` class and how to calculate the output by passing an input matrix. TensorFlow is a key tool in implementing and training neural networks.

💡Input Matrix

The input matrix is a matrix representation of the data provided for training the neuron. Each column in the matrix represents a feature, and each row represents an instance of data. The script uses an example of an input matrix with three features (type of engine, buyer's name, and fuel price) to illustrate how the neuron processes the inputs to make predictions.

💡y_pred

y_pred, or predicted y, is the output of the neuron after the weighted sum has been calculated and potentially passed through an activation function. It represents the neuron's prediction or decision based on the input data. The script explains that this value is the result of the dot product between the input matrix and the weight matrix, plus the bias, which is central to the neuron's predictive capabilities.

Highlights

A neuron in deep learning applies transformations to data repeatedly to make predictions.

Neurons are divided into two parts: the summation operation on the left and the activation operation on the right.

Weights are crucial as they represent the strength of the connection between inputs and the neuron.

The importance of different inputs is determined by the weights, which can adjust based on their influence on the output.

The summation operation involves multiplying input values by their corresponding weights and adding them up to form a 'weighted sum'.

Inputs and weights are typically represented in matrix form, facilitating the summation operation.

The formula for the weighted sum can be expressed as a dot product between the input and weight matrices.

Bias is introduced as a single value added to the weighted sum, allowing for shifts in the model's predictions.

Bias helps in adjusting the position of the decision boundary in classification problems.

The Perceptron algorithm, invented by Frank Rosenblatt, is the foundation of modern neural networks.

TensorFlow can be used to create a neuron, with its weights and biases being adjustable during training.

Weights and biases are initially random but are optimized through training to improve model accuracy.

The output of a neuron, or y_pred, can be calculated using the dot product of the input matrix and weights, plus the bias.

Activation functions, to be discussed in the next video, play a critical role in the neuron's operation.

The video provides a comprehensive introduction to the inner workings of a neuron in deep learning.

The speaker emphasizes the importance of understanding both the theoretical and practical aspects of neurons for effective deep learning.

The video concludes with an invitation to explore further resources and future videos in the series.

Transcripts

In the first video of this deep learning series we saw how a neuron applies some transformation

to our data and by doing it again and again he was magically able to guess the output

of the new data!

Now, we will logically see how he does it and go into some amount of depth.

[INTRO] As far as you know, neurons take something

as input and output the prediction but something is going inside this neuron by which he can

calculate this prediction.

So, to calculate it the neuron is partitioned into two.

The left side of it does the summation operation and the right side does the activation operation

we won't talk much about activation functions in this video as it is the topic of our next

video.

First of all, what is this string-like structure here?

It is not just for fashion they are the weights of our neuron.

The weights are the amount of strength by which inputs are connected with the neuron.

And they are denoted as w1, w2, w3 as follows!

But what do I mean by strength?

Let's discuss that with a simple example.

Suppose, you want to predict the price of a car given three inputs.

The first is a type of engine, then the name of buyer, and last is the price of fuel so

as the training proceeds our neuron will come to know that the type of engine in the car

influences the price too much so strength between this feature and neuron will be high

but in the case of buyer's name the weight is very less because its obvious that buyer's

name does not affect the price of a car at all.

The last is the price of fuel which our model has kept value intermediate between the above

two because it indirectly affects the price of car but not that much.

After all, more the price of fuel, lesser the demand for cars and less will be the price

of cars... something like that!

That's why weights are essential to tell the importance of input.

Now we will talk about this summation operation.

The summation operation takes every input value and multiplies them with their consecutive

weights and adds all of them and the output we get after doing this is knows as the 'weighted

sum'.

Usually, we deal with inputs and weights in the form of a matrix.

The input matrix is the matrix we give for training and every column in this matrix is

a feature... in the previous example type of engine, buyer's name, and fuel price are

features.

Now, if there are three columns in the input matrix the weights matrix will contain three

rows, and each of the values is the strength between that input column and neuron.

Like, for the first column the strength between that and the neuron is 1.4 which is the first

row of the weights matrix and the same goes for all.

Now, we can do the summation operation...

For that, we will multiply every column of the input matrix with every row of weight

matrix and sum all of them and the answer we get will be our weighted sum as discussed

previously.

That's why to generalize the formula of weighted sum it can also be written like this.

But if you even know a little linear algebra you can guess that this formula is of "Dot

product".

In the algebraic definition of the dot product in Wikipedia, you can see that it is exactly

equal to our previous equation.

So, we can modify it and write it in dot product form.

This dot here is the dot product between the input matrix and weight matrix.

One thing which I have not introduced till now is the term "bias"...

Bias is a single value that is added to the summation operation or the weighted sum.

With bias, we can shift our weighted sum equation to either left or right.

The best way to understand this is via Visualization.

Let's take an example of a simple classification problem that you have to separate the Blue

points and the Orange points you have to bring this line a little down.

We can do that by altering the slope of this line.

Slope is nothing but the steepness of the line.

Which is a synonym for weights in mathematics.

Currently, the slope is two but to separate these points we have to bring this line a

little to the down so let's change that 2 with 1.2.

Yes, now we have separated the points.

But what if these points are like this now we cannot separate these points easily.

This is where bias comes to the rescue...

By bias, you can shift this line either upwards or downwards.

Bias is the point where our line intersects the y-axis.

Now, our line is intersecting the y-axis is at 2 that's why the value of bias is also

two and now we can alter the slope of this line and we have separated the data.

The real-world data are even complex than this so without bias our neuron can never

fit the data well.

In short, this is the final thing that is happening inside the neuron to calculate the

weighted sum and this weighted sum is nothing but the y_pred.

You can also see the same formula in the TensorFlow documentation of the Dense layer.

The entire diagram you are seeing now is known as the Perceptron algorithm it was invented

by Frank Rosenblatt in 1958 and he is also considered as the "Father of Deep learning".

Now, enough of theory stuff and let's dig into some code part of what we have learned

till now.

First, we will import TensorFlow to create a neuron and numpy to create 'fake data'.

I have just arranged numbers from 0 to 23 in 3 columns and 8 rows and the matrix we

have now is our 'Input Matrix'.

Now, let's create a neuron that is quite simple with TensorFlow.

We will write tf.keras.layers.Dense which is a class and the first parameter it accepts

is the number of neurons we want in our case we only want 1 neuron so I have just written

'1' here...

Now, we can calculate the output by passing our input matrix but before viewing the output

let us see how are weight matrix and bias looks like.

We can easily get weights by typing neuron.kernel and bias by neuron.bias...

I am writing this .numpy() to convert our matrix from tensor format to numpy format.

Now, let's see the weights...

It has one row and three columns as we discussed previously!

And bias contains only one row with a value of 0...

As of now, these weights and biases are completely useless because they are randomly initialized

but when we actually train our model these two variables change with every epoch to make

the accuracy higher.

Just let it go if this thing is not making sense now it will completely become clear

in some more future videos!

Now, let's see the output and this is our weighted sum matrix or the y_pred.

But we have deduced the equation of y_pred earlier which is the dot product between input

matrix and weights plus the bias so by this knowledge we can even calculate output on

our own... let's do that, I have used numpy to do dot product between input matrix and

weights and simply added the bias to it and if we see our output now, it is completely

equal to Tensorflow's.

If you have understood everything up to this point then yes you almost know everything

that is happening in this neuron to calculate the y_pred but we haven't discussed the right

side of this neuron which is the activation operation though we have come along the word

activation two times in this video only!

So, in the next video, we will discuss about activation functions which is an extremely

important topic.

Until then see my other videos and if you are from very future I may have already uploaded

many videos in this series so you can get this playlist link in the description and

many other useful resources.

See you in the next video.