The goal of artificial neural network machine learning algorithms is to mimic the way the human brain organizes and understands information in order to arrive at various predictions.
Neural networks, with their remarkable ability to derive meaning from complicated or imprecise data, can be used to extract patterns and detect trends that are too complex to be noticed by either humans or other computer techniques.
Artificial neural networks, like real brains, are formed from connected "neurons", all capable of carrying out a data-related task, such as recognizing something, matching a piece of information to another piece, and answering a question about the relationship between them.
Each neuron is capable of passing on the results of its work to a neighboring neuron, which can then process it further.
Typically, neurons are organized in layers. Different layers may perform different kinds of transformations on their inputs. Signals travel from the first (input), to the last (output) layer, possibly after traversing the layers multiple times.
This is what a typical simple neural network looks like:
Each neuron is capable of passing on the results of its work to a neighboring neuron, which can then process it further.
Typically, neurons are organized in layers. Different layers may perform different kinds of transformations on their inputs. Signals travel from the first (input), to the last (output) layer, possibly after traversing the layers multiple times.
This is what a typical simple neural network looks like:
Because the network is capable of changing and adapting based on the data that passes through it, the connections between these neurons are fine-tuned until the network yields highly accurate predictions. It can be thought of as "learning", in much the same way as our brains do.
Neural networks have been used on a variety of tasks, including computer vision, speech recognition, machine translation, playing board and video games, medical diagnosis, and in many other domains.
A Simple Neural Network to Recognize Patterns
Lets create a program that will teach the computer to recognize simple patterns using neural networks.
An artificial neural networks, like real brains, are formed from connected "neurons", all capable of carrying out a data-related task, such as answering a question about the relationship between them.
An artificial neural networks, like real brains, are formed from connected "neurons", all capable of carrying out a data-related task, such as answering a question about the relationship between them.
Let's take the following pattern:
1 1 1 = 1
1 0 1 = 1
0 1 1 = 0
Each input, and the output can be only a 1 or a 0. If we look closer, we will realize that the output is 1, if the first input is 1. However, we will not tell that to the computer. We will only provide the sample inputs and outputs and ask it to "guess" the output of the input 1 0 0 (which should be 1).
To make it really simple, we will just model a single neuron, with three inputs and one output.
The three examples above are called a training set.
We're going to train the neuron to work out the pattern and solve the task for input 1 0 0, by just having the training set and without knowing what operation it performs.
1 1 1 = 1
1 0 1 = 1
0 1 1 = 0
Each input, and the output can be only a 1 or a 0. If we look closer, we will realize that the output is 1, if the first input is 1. However, we will not tell that to the computer. We will only provide the sample inputs and outputs and ask it to "guess" the output of the input 1 0 0 (which should be 1).
To make it really simple, we will just model a single neuron, with three inputs and one output.
The three examples above are called a training set.
We're going to train the neuron to work out the pattern and solve the task for input 1 0 0, by just having the training set and without knowing what operation it performs.
Training
We will give each input a weight, which can be a positive or negative number. An input with a large positive weight or a large negative weight, will have a strong effect on the neuron's output. Before we start, we set each weight to a random number. Then we begin the training process:
1. Take the inputs from the training set, adjust them by the weights, and pass them through a special formula to calculate the neuron's output.
2. Calculate the error, which is the difference between the neuron's output and the desired output in the training set example.
3. Depending on the direction of the error, adjust the weights.
4. Repeat this process 10,000 times.
Eventually the weights of the neuron will reach an optimum for the training set. This process is called back propagation.
We will give each input a weight, which can be a positive or negative number. An input with a large positive weight or a large negative weight, will have a strong effect on the neuron's output. Before we start, we set each weight to a random number. Then we begin the training process:
1. Take the inputs from the training set, adjust them by the weights, and pass them through a special formula to calculate the neuron's output.
2. Calculate the error, which is the difference between the neuron's output and the desired output in the training set example.
3. Depending on the direction of the error, adjust the weights.
4. Repeat this process 10,000 times.
Eventually the weights of the neuron will reach an optimum for the training set. This process is called back propagation.
For the formula, we will take the weighted sum of the inputs and normalize it between 0 and 1:
After each iteration, we need to adjust the weight based on the error (the difference of the calculated output and the real output). We will use this formula:
adjustment = error*input*output*(1-output)
This will make the adjustment proportional to the size of the error. After each adjustment the error size should get smaller and smaller.
adjustment = error*input*output*(1-output)
This will make the adjustment proportional to the size of the error. After each adjustment the error size should get smaller and smaller.
After the 10.000 iterations, we will have optimum weights and then we can give the program our desired inputs. The program will use the weights and calculate the output using the same weighted sum formula as above.
Teaching Math using Neural Networks
Lets build a program, that will teach the computer to predict the output of a mathematical expression without "knowing" the exact formula.
Consider the following expression: (a+b)*2
For two inputs a and b the operation will have one distinct output.
The goal is to create a program, that will predict the output for given inputs, without knowing the formula of the expression.
For this, we will use neural networks. Artificial neural networks, like real brains, are formed from connected "neurons", all capable of carrying out a data-related task, such as answering a question about the relationship between them.
To make it really simple, we will just model a single neuron, with two inputs and one output.
These first four examples are called a training set:
Inputs Output
2 3 10
1 1 4
5 2 14
12 3 30
We're going to train the neuron to work out the pattern and solve the task for custom inputs, by just having the training set and without knowing what operation it performs.
Consider the following expression: (a+b)*2
For two inputs a and b the operation will have one distinct output.
The goal is to create a program, that will predict the output for given inputs, without knowing the formula of the expression.
For this, we will use neural networks. Artificial neural networks, like real brains, are formed from connected "neurons", all capable of carrying out a data-related task, such as answering a question about the relationship between them.
To make it really simple, we will just model a single neuron, with two inputs and one output.
These first four examples are called a training set:
Inputs Output
2 3 10
1 1 4
5 2 14
12 3 30
We're going to train the neuron to work out the pattern and solve the task for custom inputs, by just having the training set and without knowing what operation it performs.
Training
We give each input a weight, which can be a positive or negative number. An input with a large positive weight or a large negative weight has a strong effect on the neuron's output. Before we start, we set each weight to a random number. Then we begin the training process:
1. Take the inputs from the training set, adjust them by the weights, and pass them through a special formula to calculate the neuron's output.
2. Calculate the error, which is the difference between the neuron's output and the desired output in the training set example.
3. Depending on the direction of the error, adjust the weights.
4. Repeat this process 10,000 times.
Eventually the weights of the neuron will reach an optimum for the training set. This process is called back propagation.
We give each input a weight, which can be a positive or negative number. An input with a large positive weight or a large negative weight has a strong effect on the neuron's output. Before we start, we set each weight to a random number. Then we begin the training process:
1. Take the inputs from the training set, adjust them by the weights, and pass them through a special formula to calculate the neuron's output.
2. Calculate the error, which is the difference between the neuron's output and the desired output in the training set example.
3. Depending on the direction of the error, adjust the weights.
4. Repeat this process 10,000 times.
Eventually the weights of the neuron will reach an optimum for the training set. This process is called back propagation.
For the formula, we take the weighted sum of the inputs:
output = weight1*input1+weight2*input2
output = weight1*input1+weight2*input2
After each iteration, we need to adjust the weight based on the error (the difference of the calculated output and the real output). We use this formula for each weight:
adjustment = 0.01*error*input
This makes the adjustment proportional to the size of the error. After each adjustment the error size should get smaller and smaller.
adjustment = 0.01*error*input
This makes the adjustment proportional to the size of the error. After each adjustment the error size should get smaller and smaller.
After the 10.000 iterations, we will have optimum weights and then we can give the program our desired inputs. The program will use the weights and calculate the output using the same weighted sum as above.
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