batch_size和total batch_size、normal batch_size的区别

batch_size通常指的是在训练神经网络时，每次输入模型的样本数。而total batch_size则是指整个训练集被分成多少个batch，也就是说，total batch_size等于训练集的大小除以batch_size。normal batch_size则是指普通的batch_size，即每次输入模型的样本数。

举个例子，如果训练集大小为1000，batch_size为32，则每次输入模型的样本数为32，total batch_size为1000/32=31.25，通常向上取整为32。

相关问题

def train(notes, chords, generator, discriminator, gan, loss_fn, generator_optimizer, discriminator_optimizer): num_batches = notes.shape[0] // BATCH_SIZE for epoch in range(NUM_EPOCHS): for batch in range(num_batches): # 训练判别器 for _ in range(1): # 生成随机的噪声 noise = np.random.normal(0, 1, size=(BATCH_SIZE, LATENT_DIM)) # 随机选择一个真实的样本 idx = np.random.randint(0, notes.shape[0], size=BATCH_SIZE) real_notes, real_chords = notes[idx], chords[idx] # 生成假的样本 fake_notes = generator(noise) # 计算判别器的损失函数 real_loss = loss_fn(tf.ones((BATCH_SIZE, 1)), discriminator([real_notes, real_chords])) fake_loss = loss_fn(tf.zeros((BATCH_SIZE, 1)), discriminator([fake_notes, chords])) total_loss = real_loss + fake_loss # 计算判别器的梯度并更新参数 grads = tf.gradients(total_loss, discriminator.trainable_variables) discriminator_optimizer.apply_gradients(zip(grads, discriminator.trainable_variables))) # 训练生成器 for _ in range(1): # 生成随机的噪声 noise = np.random.normal(0, 1, size=(BATCH_SIZE, LATENT_DIM)) # 计算生成器的损失函数 fake_notes = generator(noise) fake_loss = loss_fn(tf.ones((BATCH_SIZE, 1)), discriminator([fake_notes, chords])) # 计算生成器的梯度并更新参数 grads = tf.gradients(fake_loss, generator.trainable_variables) generator_optimizer.apply_gradients(zip(grads, generator.trainable_variables))) # 打印损失函数和精度 print('Epoch {}, Batch {}/{}: Loss={:.4f}'.format(epoch+1, batch+1, num_batches, total_loss)) # 保存模型 if (epoch+1) % 10 == 0: generator.save('generator.h5') discriminator.save('discriminator.h5') gan.save('gan.h5')

这段代码实现了一个基于GAN的音乐生成模型的训练过程。主要流程如下：

1. 根据每个epoch的训练次数(NUM_EPOCHS)和每个batch的大小(BATCH_SIZE)，计算出总共需要训练的batch数(num_batches)。

2. 对于每个epoch和每个batch：

a. 从训练数据集(notes和chords)中随机选择BATCH_SIZE个样本(real_notes和real_chords)作为真实样本，同时生成BATCH_SIZE个随机噪声(noise)作为假样本。

b. 训练判别器(discriminator)：对于每个样本，计算其对应的损失函数(real_loss或fake_loss)，并将它们相加得到判别器的总损失(total_loss)。然后计算判别器的梯度(grads)，并使用判别器优化器(discriminator_optimizer)来更新判别器的参数(discriminator.trainable_variables)。

c. 训练生成器(generator)：对于每个生成的假样本，计算其对应的损失函数(fake_loss)，并计算生成器的梯度(grads)，使用生成器优化器(generator_optimizer)来更新生成器的参数(generator.trainable_variables)。

d. 打印当前训练的epoch、batch和总损失(total_loss)。

e. 如果当前epoch是10的倍数，保存生成器模型(generator.h5)、判别器模型(discriminator.h5)和GAN模型(gan.h5)。

这个模型是一个有监督的生成模型，输入是随机噪声和和弦(chords)，输出是钢琴音符(notes)。其中，判别器的作用是判断输入的钢琴音符是否是真实的，生成器的作用是将随机噪声和和弦转换为更真实的钢琴音符。GAN则是将判别器和生成器相结合，使得生成器能够生成更真实的钢琴音符，同时让判别器更好地判断真假。

Complete the code for Differentially Private Stochastic Gradient Descent. a. Fill in the code for per-example clipping and adding Gaussian noise. b. Implement the privacy budget composition. Calculate the privacy budget of the training process, which means calculating $\epsilon$ based on the variance of Gaussian noise $\sigma^2$ and the given $\delta = 10^{-5}$ in different epochs. You can use basic composition to complete the code. If you correctly apply the Moments Accountant method, you will receive bonus points. import numpy as np from scipy import optimize from scipy.stats import norm import math """ Optionally you could use moments accountant to implement the epsilon calculation. """ def get_epsilon(epoch, delta, sigma, sensitivity, batch_size, training_nums): """ Compute epsilon with basic composition from given epoch, delta, sigma, sensitivity, batch_size and the number of training set. """ return epsilon

Here is the completed code for Differentially Private Stochastic Gradient Descent, including per-example clipping and adding Gaussian noise as well as privacy budget composition:

import numpy as np
from scipy import optimize
from scipy.stats import norm
import math

def per_example_clipping(grad, clip_factor):
    """
    Clip the gradient per example with a given clip factor.
    """
    return np.clip(grad, -clip_factor, clip_factor)

def add_gaussian_noise(grad, sigma):
    """
    Add Gaussian noise to the gradient with a given standard deviation.
    """
    return grad + np.random.normal(0, sigma, grad.shape)

def get_epsilon(epoch, delta, sigma, sensitivity, batch_size, training_nums):
    """
    Compute epsilon with basic composition from given epoch, delta, sigma, sensitivity, batch_size and the number of training set.
    """
    steps = math.ceil(training_nums / batch_size) * epoch
    epsilon = sigma * math.sqrt(2 * math.log(1.25 / delta)) / sensitivity
    return epsilon * steps

def dp_sgd(X, y, epochs, batch_size, clip_factor, sigma, delta):
    n, d = X.shape
    w = np.zeros(d)
    for epoch in range(epochs):
        for i in range(0, n, batch_size):
            X_batch = X[i:i+batch_size]
            y_batch = y[i:i+batch_size]
            grad = np.mean(X_batch * (sigmoid(X_batch.dot(w)) - y_batch).reshape(-1, 1), axis=0)
            clipped_grad = per_example_clipping(grad, clip_factor)
            noise_grad = add_gaussian_noise(clipped_grad, sigma)
            w -= noise_grad
        epsilon = get_epsilon(epoch+1, delta, sigma, clip_factor/batch_size, batch_size, n)
        print("Epoch {}: Epsilon = {}".format(epoch+1, epsilon))
    return w

The `per_example_clipping` function clips the gradient per example with a given clip factor. The `add_gaussian_noise` function adds Gaussian noise to the gradient with a given standard deviation. The `get_epsilon` function computes epsilon with basic composition from given epoch, delta, sigma, sensitivity, batch_size and the number of training set.

The `dp_sgd` function performs Differentially Private Stochastic Gradient Descent. For each epoch, it loops over the training set in batches and computes the gradient of the loss function using the sigmoid function. It then clips the gradient per example, adds Gaussian noise to the clipped gradient, and updates the weight vector. Finally, it computes the privacy budget using the `get_epsilon` function and prints it out.

Note that the `get_epsilon` function uses basic composition to compute the privacy budget. It calculates the total number of steps based on the number of epochs and the batch size, and then uses the formula for epsilon with basic composition to compute the privacy budget for each epoch.

It is worth noting that basic composition may not provide the tightest bound on privacy, and using the Moments Accountant method may provide a tighter bound.