????? ??? ???,

????? ?????? ?? ???? ???? ?? ? ?????. ???? ??? ???? ?? ?? ??????. ? ?????? Python?? Perceptron? ???? ???? ???? ??? ???????.

????!

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?????? ??????

????? ?? ???? ?? ??? ?? ?? ???????. ?? ??? ???? ????? ??? ??? ??? ???? ???? ???? ? ??? ?? ???? ?????. ??? ??? ?? ??? ??? ????.

1. ??: ??? ??(?: [x1, x2]).
2. ???: ? ?? ???? ???? ???, ??? ??? ?? ??? ?? ?????.
3. ??? ??: ?? ??? ?? ??? ???? ???? ???? ??? ? ???? ???? ?? ???? ???? ?????.

?????? ??? ????.

f(x) = w1*x1 w2*x2 ... wn*xn b

??:

• f(x)? ????,
• w? ???? ????,
• x? ?? ??? ????
• b? ?? ?????.

f(x)? ????? ??? ??? ??? ??? 1???. ??? ??? ??? 0???.

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1??: ????? ????

????? ???? ?? ?? ??? NumPy? ???????.

import numpy as np

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2??: ???? ??? ??

?? ?? ???? ?? ????? ???? ???????. ???? ?? ? ?? ??? ?????.

class Perceptron:
    def __init__(self, learning_rate=0.01, epochs=1000):
        self.learning_rate = learning_rate
        self.epochs = epochs
        self.weights = None
        self.bias = None

    def fit(self, X, y):
        # Number of samples and features
        n_samples, n_features = X.shape

        # Initialize weights and bias
        self.weights = np.zeros(n_features)
        self.bias = 0

        # Training
        for _ in range(self.epochs):
            for idx, x_i in enumerate(X):
                # Calculate linear output
                linear_output = np.dot(x_i, self.weights) + self.bias
                # Apply step function
                y_predicted = self._step_function(linear_output)

                # Update weights and bias if there is a misclassification
                if y[idx] != y_predicted:
                    update = self.learning_rate * (y[idx] - y_predicted)
                    self.weights += update * x_i
                    self.bias += update

    def predict(self, X):
        # Calculate linear output and apply step function
        linear_output = np.dot(X, self.weights) + self.bias
        y_predicted = self._step_function(linear_output)
        return y_predicted

    def _step_function(self, x):
        return np.where(x >= 0, 1, 0)

? ????:

• fit: ? ??? ?? ?? ??? ??? ???? ??? ???? ??? ?????.
• ??: ? ??? ? ???? ?? ??? ?????.
• _step_function: ? ??? ???? ???? ?? ???? ?????.

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3??: ??? ??? ?? ??

??? ?? ???? ? ??? ?? ??? ??? ???????. ??? ??? AND ??? ????????.

# AND gate dataset
X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
y = np.array([0, 0, 0, 1])  # Labels for AND gate

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4??: ???? ?? ? ???

?? ????? ???? ??? ???? ?????.

# Initialize Perceptron
p = Perceptron(learning_rate=0.1, epochs=10)

# Train the model
p.fit(X, y)

# Test the model
print("Predictions:", p.predict(X))

AND ???? ?? ??:

import numpy as np

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???? ?? ??? ?? ??

1. ??? ? ?? ???: ???? ???? 0?? ???? ??? ???? ??? ??? ? ????.
2. ?? ?? ??: ? ??? ???? ?? ????? ??? ?? ??? ??? ?????.
3. ???(?? ??): ?? ??? 0?? ??? ??? ??? 1? ?????. ??? ??? ??? 0? ?????.
4. ???? ??: ??? ??? ?? ??? ??? ??? ???? ???? ??? ?????. ???? ??? ??? ?? ?????. ??? = ??? * (y_true - y_pred) * x

??? ?? ?? ??? ??? ???? ????? ?????? ??? ?? ??? ?? ??? ??????.

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?? ?? ???

?? ? ?? ??? ??????. ?? ? ??? ??? ??? ???? ?? ?? ?????. ??? AND ???? ???? ???? ???????.

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MLP(?? ????)? ??

????? ?? ?? ??? ??? ????? MLP(?? ????)? ?? ? ??? ???? ?????. MLP? ???? ??? ???? ??? ??(ReLU ?? Sigmoid ?)? ???? ??? ??? ??? ? ????.

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??

????? ????? ???? ?? ?? ???????. ?? ??? ???? ???? ?????? ?? ?? ? ???? ?? ??? ?? ???? ????. ????? ????? ???? ??? AI? ??? ?? ?? ???? ??? ???? ???.

? ??? Python?? ???? ???? ??? ?? ?????. ??? ??? PHP ??? ????? ?? ?? ??? ?????!