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
   $$mse=\frac{1}{n}\sum _{i=1}^n(prediction{s}_i-label{s}_i{)}^2$$

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