牛客题解 | 单神经元

题目

题目链接

单神经元（Single Neuron）是神经网络中的最常见的基本单元。

本题的步骤如下：

1. 初始化权重和偏置
2. 前向传播，计算预测值
   \[z = w \cdot x + b \]
   \[predictions = sigmoid(z) \]

3. 计算损失函数
   \[mse = \frac{1}{n} \sum_{i=1}^{n} (predictions_i - labels_i)^2 \]

标准代码如下

def single_neuron_model(features, labels, weights, bias):
    probabilities = []
    for feature_vector in features:
        z = sum(weight * feature for weight, feature in zip(weights, feature_vector)) + bias
        prob = 1 / (1 + math.exp(-z))
        probabilities.append(round(prob, 4))
    
    mse = sum((prob - label) ** 2 for prob, label in zip(probabilities, labels)) / len(labels)
    mse = round(mse, 4)
    
    return probabilities, mse