בינה מלאכותית RB108-6 : בינה מלאכותית – איך נוירון לומד

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פורסם:נובמבר 23, 2025
קטגוריה:רובוטרוניקס כללי

בינה מלאכותית RB108-6 : בינה מלאכותית – איך נוירון לומד

חלק א :

x = [-3, -2, -1, 0, 1, 2, 3]

y = [-5, -3, -1, 1, 3, 5, 7]

those are the true values :y = [-5, -3, -1, 1, 3, 5, 7]

1) The Neuron Model

The neuron predicts:

Starting values:

2) Forward Pass (Prediction)

For each x:

x	y_true	y_predict
-3	-5	-3
-2	-3	-2
-1	-1	-1
0	1	0
1	3	1
2	5	2
3	7	3

3).Error , lost Function

we start w=1,b=0

`y_true = w * x + b`

`y_predict = w * x + b`

x	y_true	y_predict = 1·x + 0	error = y_predict – y_true	loss = (y_true – y_predict)²
-3	-5	-3	+2	4
-2	-3	-2	+1	1
-1	-1	-1	0	0
0	1	0	-1	1
1	3	1	-2	4
2	5	2	-3	9
3	7	3	-4	16

Totals for Step 3

Sum of errors:

$2 + 1 + 0 - 1 - 2 - 3 - 4 = - 7$

Sum of loss values:

$4 + 1 + 0 + 1 + 4 + 9 + 16 = 35$

Mean Loss (The Value Used for Learning)

The Mean Loss is:

$samples\text{mean loss} = \frac{\text{sum of all losses}}{\text{number of samples}}$

In our case:

Total loss = 35
Number of samples = 7

So:

MSE (mean squared error) = cost function = Error loss

3.1 Why we use the Loss and not the Error

Example:

Loss converts both to:

So the neuron learns how big the mistake is, not just the sign.

Raw error cancels out:

Loss does NOT cancel out → always correct for learning.

4) Gradients are computed from the loss

Why We Don’t Solve With Derivative = 0 (Except for One Neuron)

1) For a single neuron (like your example):

$y = w x + b$

This is a simple line.

We can take the derivative of the loss, set it to 0, and solve for the exact best:

$2,\quad b = 1$

This works because the loss surface is a perfect parabola (a simple bowl shape).

2) But for many neurons (real neural networks):

When you add:

more neurons
more layers
activation functions (ReLU, sigmoid)
millions of parameters

The loss surface becomes:

twisted
curved
full of valleys and hills
impossible to solve with algebra