Neuron: Building block of Deep learning
Summary
TLDRThis 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
- đ§ The script introduces the concept of a neuron in deep learning, explaining its ability to transform data and make predictions through repeated processes.
- đ 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.
- đ 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.
- đ 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.
- đ 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.
- đ The script explains the summation operation in the context of linear algebra, equating it to the dot product of the input and weight matrices.
- đ 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.
- đ 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.
- đ€ 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.
- đ» 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.
- đŹ 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
đ§ 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.
đ 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.
Mindmap
Keywords
đĄNeuron
đĄWeights
đĄActivation Function
đĄSummation Operation
đĄWeighted Sum
đĄDot Product
đĄBias
đĄPerceptron Algorithm
đĄTensorFlow
đĄInput Matrix
đĄy_pred
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.
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