2層のニューラルネット

2層のニューラルネットをPythonで定義する.

import numpy as np

class NeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        # 重みとバイアスの初期化
        self.weights_input_hidden = np.random.rand(input_size, hidden_size)
        self.bias_input_hidden = np.random.rand(1, hidden_size)
        self.weights_hidden_output = np.random.rand(hidden_size, output_size)
        self.bias_hidden_output = np.random.rand(1, output_size)
        
    def sigmoid(self, x):
        # シグモイド活性化関数
        return 1 / (1 + np.exp(-x))
    
    def sigmoid_derivative(self, x):
        # シグモイド関数の導関数
        return x * (1 - x)
    
    def forward(self, inputs):
        # 入力層から隠れ層への伝播
        hidden_inputs = np.dot(inputs, self.weights_input_hidden) + self.bias_input_hidden
        hidden_outputs = self.sigmoid(hidden_inputs)
        
        # 隠れ層から出力層への伝播
        final_inputs = np.dot(hidden_outputs, self.weights_hidden_output) + self.bias_hidden_output
        final_outputs = self.sigmoid(final_inputs)
        
        return final_outputs
    
    def train(self, inputs, targets, learning_rate):
        # 順伝播
        hidden_inputs = np.dot(inputs, self.weights_input_hidden) + self.bias_input_hidden
        hidden_outputs = self.sigmoid(hidden_inputs)
        
        final_inputs = np.dot(hidden_outputs, self.weights_hidden_output) + self.bias_hidden_output
        final_outputs = self.sigmoid(final_inputs)
        
        # 出力層の誤差
        output_errors = targets - final_outputs
        
        # 出力層から隠れ層への逆伝播
        hidden_errors = np.dot(output_errors, self.weights_hidden_output.T)
        
        # 誤差に対する重みの勾配
        output_gradient = output_errors * self.sigmoid_derivative(final_outputs)
        hidden_gradient = hidden_errors * self.sigmoid_derivative(hidden_outputs)
        
        # 重みとバイアスの更新
        self.weights_hidden_output += np.dot(hidden_outputs.T, output_gradient) * learning_rate
        self.bias_hidden_output += np.sum(output_gradient, axis=0, keepdims=True) * learning_rate
        self.weights_input_hidden += np.dot(inputs.T, hidden_gradient) * learning_rate
        self.bias_input_hidden += np.sum(hidden_gradient, axis=0, keepdims=True) * learning_rate

        
# ニューラルネットワークのインスタンス化
input_size = 3
hidden_size = 4
output_size = 2
learning_rate = 0.1

nn = NeuralNetwork(input_size, hidden_size, output_size)

# ダミーの入力データとターゲットデータの生成
inputs = np.array([[0, 0, 1],
                   [1, 1, 1],
                   [1, 0, 1],
                   [0, 1, 1]])

targets = np.array([[0, 1],
                    [1, 0],
                    [1, 0],
                    [0, 1]])

# 訓練
for epoch in range(10000):
    nn.train(inputs, targets, learning_rate)

# 新しいデータでの予測
new_data = np.array([[1, 0, 0]])

predicted_output = nn.forward(new_data)

print("Predicted Output:", predicted_output)

出力は次のようになる.

Predicted Output: [[0.99036751 0.00946958]]

ここで用いられた行列の値は次のようになる.

Weights (Input to Hidden):
[[0.86559079 0.35543461 0.98290313 0.63647904]
 [0.24819431 0.26436123 0.84597465 0.94019566]
 [0.67297261 0.43592189 0.127277   0.37049044]]

Bias (Input to Hidden):
[[0.10011356 0.7652955  0.20811188 0.8234742 ]]

Weights (Hidden to Output):
[[0.06777084 0.38948834]
 [0.24392602 0.34049731]
 [0.53378961 0.09676239]
 [0.6962991  0.53805222]]

Bias (Hidden to Output):
[[0.85133557 0.34678493]]

訓練後の行列の値は以下の通り.

Trained Weights (Input to Hidden):
[[ 9.55904228 -8.06777488 -6.38659746  9.20550939]
 [-0.16364794  0.19104817  0.25018966 -0.14233093]
 [-2.02104794  1.68517317  1.51901674 -1.82576135]]

Trained Bias (Input to Hidden):
[[-2.58297613  2.15517165  1.44218629 -2.61282293]]

Trained Weights (Hidden to Output):
[[ 3.43550539 -3.05135711]
 [-1.63683914  2.43330975]
 [-1.27509865  1.14375031]
 [ 2.9603573  -2.71384294]]

Trained Bias (Hidden to Output):
[[-1.74223759  1.09382922]]

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