理解TensorFlow变量的零初始化与优化器的作用

import tensorflow as tf
# 尽管原始代码中使用了tf.disable_v1_behavior()，但其API风格仍偏向TensorFlow 1.x。
# 为了确保示例的兼容性，这里明确使用tf.compat.v1来调用1.x的API。
tf.compat.v1.disable_v2_behavior() # 确保使用V1行为

def model(X, w, num_coeffs):
    terms = []
    for i in range(num_coeffs):
        term = tf.multiply(w[i], tf.pow(X, i))
        terms.append(term)
    return tf.add_n(terms)

num_coeffs = 6
# w被初始化为一个包含num_coeffs个零的向量
w = tf.Variable([0.] * num_coeffs, name="parameters")
X = tf.compat.v1.placeholder(tf.float32, name="input_X")
y_model = model(X, w, num_coeffs)

import tensorflow as tf
import numpy as np

# 确保使用TensorFlow 1.x行为
tf.compat.v1.disable_v2_behavior()

# 定义模型结构
def model(X, w, num_coeffs):
    terms = []
    for i in range(num_coeffs):
        term = tf.multiply(w[i], tf.pow(X, i))
        terms.append(term)
    return tf.add_n(terms)

num_coeffs = 6
# 初始化可训练参数w为零向量
w = tf.Variable([0.] * num_coeffs, name="parameters")

# 定义输入X和真实输出Y的占位符
X = tf.compat.v1.placeholder(tf.float32, name="input_X")
Y = tf.compat.v1.placeholder(tf.float32, name="true_Y")

# 模型预测输出
y_model = model(X, w, num_coeffs)

# 定义损失函数：均方误差
loss = tf.reduce_mean(tf.square(y_model - Y))

# 定义优化器：梯度下降优化器
learning_rate = 0.01
optimizer = tf.compat.v1.train.GradientDescentOptimizer(learning_rate).minimize(loss)

# 初始化所有变量
init = tf.compat.v1.global_variables_initializer()

# 模拟生成训练数据（例如，一个二次函数加上噪声）
# 真实系数可能是 [1, 2, 3, 0, 0, 0] (对应 x^0, x^1, x^2, ...)
true_coeffs = np.array([1., 2., 3., 0., 0., 0.])
def generate_data(x_values, true_coeffs, noise_std=0.1):
    # np.polyval 期望系数按幂次降序排列，即 [a_n, a_{n-1}, ..., a_0]
    # 我们的true_coeffs是 [a_0, a_1, ..., a_n]，所以需要反转
    y_values = np.polyval(true_coeffs[::-1], x_values)
    noise = np.random.normal(0, noise_std, x_values.shape)
    return y_values + noise

np.random.seed(0)
train_X = np.linspace(-1, 1, 100).astype(np.float32)
train_Y = generate_data(train_X, true_coeffs, noise_std=0.05).astype(np.float32)

# 启动TensorFlow会话并训练模型
with tf.compat.v1.Session() as sess:
    sess.run(init) # 初始化w为零

    print("初始权重 w:", sess.run(w)) # 此时w为[0., 0., 0., 0., 0., 0.]

    training_epochs = 1000
    for epoch in range(training_epochs):
        _, current_loss = sess.run([optimizer, loss], feed_dict={X: train_X, Y: train_Y})
        if (epoch + 1) % 100 == 0:
            print(f"Epoch {epoch + 1}, Loss: {current_loss:.4f}")

    final_w = sess.run(w)
    print("\n训练后的权重 w:", final_w)

    # 验证模型输出
    sample_X = np.array([0.5], dtype=np.float32)
    predicted_Y = sess.run(y_model, feed_dict={X: sample_X})
    print(f"对于 X={sample_X[0]}，模型预测 Y={predicted_Y[0]}")
    print(f"真实 Y (无噪声) = {np.polyval(true_coeffs[::-1], sample_X[0])}")