NANDゲート

Pythonを使って,ANDゲートと同様に,単純な論理ゲートであるNANDゲートを考える.

def NAND_gate(input1, input2):
    if input1 == 1 and input2 == 1:
        return 0
    else:
        return 1

# テスト
print(NAND_gate(0, 0))  # 1
print(NAND_gate(0, 1))  # 1
print(NAND_gate(1, 0))  # 1
print(NAND_gate(1, 1))  # 0

実行すると,

1
1
1
0 

次に,同じくNANDゲートをパーセプトロンとして考えてみる.

import numpy as np

class Perceptron:
    def __init__(self, input_size, lr=1, epochs=10):
        self.W = np.zeros(input_size)
        self.b = 0
        self.lr = lr
        self.epochs = epochs
    
    def activation_fn(self, x):
        return 1 if x >= 0 else 0
    
    def predict(self, x):
        z = np.dot(self.W, x) + self.b
        a = self.activation_fn(z)
        return a
    
    def train(self, X, d):
        for _ in range(self.epochs):
            for i in range(d.shape[0]):
                y = self.predict(X[i])
                e = d[i] - y
                self.W += self.lr * e * X[i]
                self.b += self.lr * e
        print("Final weights:", self.W)
        print("Final bias:", self.b)

# データの準備 (NANDゲートの入力と出力)
X = np.array([[0, 0],
              [0, 1],
              [1, 0],
              [1, 1]])

d = np.array([1, 1, 1, 0])  # NANDゲートの出力

# パーセプトロンの定義と訓練
perceptron = Perceptron(input_size=2)
perceptron.train(X, d)

# テスト
print("0 AND 0 =", perceptron.predict(np.array([0, 0])))
print("0 AND 1 =", perceptron.predict(np.array([0, 1])))
print("1 AND 0 =", perceptron.predict(np.array([1, 0])))
print("1 AND 1 =", perceptron.predict(np.array([1, 1])))

出力は次のようになる.

Final weights: [-2. -1.]
Final bias: 2
0 AND 0 = 1
0 AND 1 = 1
1 AND 0 = 1
1 AND 1 = 0 

Mathematics is the language with which God has written the universe.