A Demonstration of Artificial Intelligence for Beginners

Introduction

predicted_measurement_a = prediction_coefficient x measurement_b

Once you understand this equation as it applies to artificial intelligence, you will have a solid foundation for understanding the basic functions of artificial intelligence systems like ChatGPT. 

The basic functions are:

1. prediction

2. preparation of the system for prediction

To aid understanding of the equation and functions is the purpose of the following demonstration of a very simple artificial intelligence system. Systems like ChatGPT -- although far more complex -- were developed from this type of system. 

The Demonstration Part 1

Consider the following data:

length  height

23.2    11.52      

26.8    13.6    

27.6    14.0    

28.4    14.26   

28.5    14.23   

28.7    14.37   

29.4    14.95   

30.9    15.63   

31.4    15.99   

31.5    15.52   

31.9    16.24

32      16.36     

32.7    16.52

37.4    18.64     

It's length and height data in centimeters for a group of fish (Bream). In addition to giving information about the fish, the data can also be used to create an equation to predict the height of other Bream using the length of the fish, i.e., the prediction function of the system. The equation is the one given above:

predicted_measurement_a = prediction_coefficient x measurement_b

To deal with the fish data, it is better expressed as:

predicted_height = prediction_coefficient x length

The following are the calculations done by this very simple AI system to produce a value for prediction_coefficient of .5037 and the following equation:

predicted_height = .5037 x length

The calculations are the second of the basic functions in every AI system, i.e.,  the preparation of the system for prediction.

The Calculations

Take the first record in the data:

length  height

23.2    11.52

Get a prediction for the height using this equation:

predicted_height = prediction_coefficient x length

with these values: 

prediction_coefficient = 0

length = 23.2

Here is the arithmetic:

predicted_height = 0 x 23.2

    = 0.0

Next get the amount of error in the prediction using this equation:

error = actual_height - predicted_height

with these values:

actual_height = 11.52

predicted_height = 0.0

Here is the arithmetic: 

error = 11.52 - 0.0

    = 11.52

Next try to improve the value for prediction_coefficient using this equation:

prediction_coefficient = prediction_coefficient + adjustment_factor x error

with these values: 

prediction_coefficient = 0

adjustment_factor = 0.001 (The adjustment_factor regulates the amount by which the prediction_coefficient is changed in the effort to improve it. It is established by experiment.)

error = 11.52

Here is the arithmetic:

prediction_coefficient = 0 + 0.001 x 11.52

    = 0.0115

These are the only calculations for getting the prediction coefficient! If you do them for every record in the set of records and then keep doing it until the value for error no longer decreases, the prediction_coefficient will become .5037, giving the equation for predicting fish height from fish length:

predicted_height = .5037 x length

Here is a summary of the process:

begin loop

    load records

    begin loop

        get next record

        predicted_height = prediction_coefficient x length

        error = actual_height - predicted_height

        prediction_coefficient = prediction_coefficient + 

                learning_rate x error

    end loop

    quit if error has not decreased 

end loop

The Demonstration Part 2

If you're curious about what the next few sets of calculations look like, here are the next 5 of them. If not, skip to Part 3, which gives the last set of calculations and concludes the article.

Take the next record in the data:

length  height

26.8    13.6

Get a prediction for the height using this equation:

predicted_height = prediction_coefficient x length

with these values: 

prediction_coefficient = 0.0115

length = 26.8

Here is the arithmetic:

predicted_height = 0.0115 x 26.8

    = 0.3082

Next get the amount of error in the prediction:

error = actual_height - predicted_height

with these values:

actual_height = 13.6

predicted_height = 0.3082

Here is the arithmetic: 

error = 13.6 - 0.3082

    = 13.2918

Next try to improve the value for prediction_coefficient with this equation:

prediction_coefficient = prediction_coefficient + adjustment_factor x error

with these values: 

prediction_coefficient = 0.0115

adjustment_factor = 0.001

error = 13.2918

Here is the arithmetic:

prediction_coefficient = 0.0115 + 0.001 x 13.2918

    = 0.0248

------------------

Take the next record in the data:

length  height

27.6    14.0

Get a prediction for the height using this equation:

predicted_height = prediction_coefficient x length

with these values: 

prediction_coefficient = 0.0248

length = 27.6

Here is the arithmetic:

predicted_height = 0.0248 x 27.6

    = 0.6845

Next get the amount of error in the prediction:

error = actual_height - predicted_height

with these values:

actual_height = 14.0

predicted_height = 0.6845

Here is the arithmetic: 

error = 14.0 - 0.6845

    = 13.3155

Next try to improve the value for prediction_coefficient with this equation:

prediction_coefficient = prediction_coefficient + adjustment_factor x error

with these values: 

prediction_coefficient = 0.0248

adjustment_factor = 0.001

error = 13.3155

Here is the arithmetic:

prediction_coefficient = 0.0248 + 0.001 x 13.3155

    = 0.0381

------------------

Take the next record in the data:

length  height

28.4    14.26

Get a prediction for the height using this equation:

predicted_height = prediction_coefficient x length

with these values: 

prediction_coefficient = 0.0381

length = 28.4

Here is the arithmetic:

predicted_height = 0.0381 x 28.4

    = 1.082

Next get the amount of error in the prediction:

error = actual_height - predicted_height

with these values:

actual_height = 14.26

predicted_height = 1.082

Here is the arithmetic: 

error = 14.26 - 1.082

    = 13.178

Next try to improve the value for prediction_coefficient with this equation:

prediction_coefficient = prediction_coefficient + adjustment_factor x error

with these values: 

prediction_coefficient = 0.0381

adjustment_factor = 0.001

error = 13.178

Here is the arithmetic:

prediction_coefficient = 0.0381 + 0.001 x 13.178

    = 0.0513

------------------

Take the next record in the data:

length  height

28.5    14.23

Get a prediction for the height using this equation:

predicted_height = prediction_coefficient x length

with these values: 

prediction_coefficient = 0.0513

length = 28.5

Here is the arithmetic:

predicted_height = 0.0513 x 28.5

    = 1.462

Next get the amount of error in the prediction:

error = actual_height - predicted_height

with these values:

actual_height = 14.23

predicted_height = 1.462

Here is the arithmetic: 

error = 14.23 - 1.462

    = 12.768

Next try to improve the value for prediction_coefficient with this equation:

prediction_coefficient = prediction_coefficient + adjustment_factor x error

with these values: 

prediction_coefficient = 0.0513

adjustment_factor = 0.001

error = 12.768

Here is the arithmetic:

prediction_coefficient = 0.0513 + 0.001 x 12.768

    = 0.0641

------------------

Take the next record in the data:

length  height

28.7    14.37

Get a prediction for the height using this equation:

predicted_height = prediction_coefficient x length

with these values: 

prediction_coefficient = 0.0641

length = 28.7

Here is the arithmetic:

predicted_height = 0.0641 x 28.7

    = 1.8397

Next get the amount of error in the prediction:

error = actual_height - predicted_height

with these values:

actual_height = 14.37

predicted_height = 1.8397

Here is the arithmetic: 

error = 14.37 - 1.8397

    = 12.5303

Next try to improve the value for prediction_coefficient with this equation:

prediction_coefficient = prediction_coefficient + adjustment_factor x error

with these values: 

prediction_coefficient = 0.0641

adjustment_factor = 0.001

error = 12.5303

Here is the arithmetic:

prediction_coefficient = 0.0641 + 0.001 x 12.5303

    = 0.0766

The Demonstration Part 3

Here's what the last of the calculations looks like:

Take the next record in the data:

length  height

37.4    18.64

Get a prediction for the height using this equation:

predicted_height = prediction_coefficient x length

with these values: 

prediction_coefficient = 0.5039

length = 37.4

Here is the arithmetic:

predicted_height = 0.5039 x 37.4

    = 18.8459

Next get the amount of error in the prediction:

error = actual_height - predicted_height

with these values:

actual_height = 18.64

predicted_height = 18.8459

Here is the arithmetic: 

error = 18.64 - 18.8459

    = -0.2059

Next try to improve the value for prediction_coefficient with this equation:

prediction_coefficient = prediction_coefficient + adjustment_factor x error

with these values: 

prediction_coefficient = 0.5039

adjustment_factor = 0.001

error = -0.2059

Here is the arithmetic:

prediction_coefficient = 0.5039 + 0.001 x -0.2059

    = 0.5037

The total number of calculations needed to produce the prediction coefficient of .5037 is 757. Doing the calculations by hand would take most of us a day or so. Using a fast desktop it would take a few seconds. Using the ChatGPT computer, the time shrinks to less than a nanosecond.

Tom Arnall

Eureka, CA

kloro2006@gmail.com

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