python - 为什么第一个卷积层权重在训练过程中不改变？

Question

我从这里得到了tensorflow mnist treaining example

https://github.com/aymericdamien/TensorFlow-Examples/blob/master/examples/3_NeuralNetworks/convolutional_network.py

并添加了我从这里得到的第一个卷积层可视化代码:

https://gist.github.com/kukuruza/03731dc494603ceab0c5

(我稍微修改了代码以适应灰度图像)

我看到的是图像在训练过程中根本没有改变!但是，如果我用零而不是随机值初始化第一层，就会发生变化。我使用张量板可视化结果。完整代码如下。

我想知道，代码中是否有任何错误，或者我们真的不需要第一个卷积层来对 mnist 进行分类？

from __future__ import print_function

import tensorflow as tf

# Import MNIST data
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets("/tmp/data/", one_hot=True)

# Parameters
learning_rate = 0.001
training_iters = 200000
batch_size = 128
display_step = 10

# Network Parameters
n_input = 784 # MNIST data input (img shape: 28*28)
n_classes = 10 # MNIST total classes (0-9 digits)
dropout = 0.75 # Dropout, probability to keep units

# tf Graph input
x = tf.placeholder(tf.float32, [None, n_input])
y = tf.placeholder(tf.float32, [None, n_classes])
keep_prob = tf.placeholder(tf.float32) #dropout (keep probability)


# Create some wrappers for simplicity
def conv2d(x, W, b, strides=1):
    # Conv2D wrapper, with bias and relu activation
    x = tf.nn.conv2d(x, W, strides=[1, strides, strides, 1], padding='SAME')
    x = tf.nn.bias_add(x, b)
    return tf.nn.relu(x)


def maxpool2d(x, k=2):
    # MaxPool2D wrapper
    return tf.nn.max_pool(x, ksize=[1, k, k, 1], strides=[1, k, k, 1],
                          padding='SAME')


# Create model
def conv_net(x, weights, biases, dropout):
    # Reshape input picture
    x = tf.reshape(x, shape=[-1, 28, 28, 1])

    # Convolution Layer
    conv1 = conv2d(x, weights['wc1'], biases['bc1'])
    # Max Pooling (down-sampling)
    conv1 = maxpool2d(conv1, k=2)

    # Convolution Layer
    conv2 = conv2d(conv1, weights['wc2'], biases['bc2'])
    # Max Pooling (down-sampling)
    conv2 = maxpool2d(conv2, k=2)

    # Fully connected layer
    # Reshape conv2 output to fit fully connected layer input
    fc1 = tf.reshape(conv2, [-1, weights['wd1'].get_shape().as_list()[0]])
    fc1 = tf.add(tf.matmul(fc1, weights['wd1']), biases['bd1'])
    fc1 = tf.nn.relu(fc1)
    # Apply Dropout
    fc1 = tf.nn.dropout(fc1, dropout)

    # Output, class prediction
    out = tf.add(tf.matmul(fc1, weights['out']), biases['out'])
    return out

# Store layers weight & bias
weights = {
    # 5x5 conv, 1 input, 32 outputs
    'wc1': tf.Variable(tf.random_normal([5, 5, 1, 32])),
    # 5x5 conv, 32 inputs, 64 outputs
    'wc2': tf.Variable(tf.random_normal([5, 5, 32, 64])),
    # fully connected, 7*7*64 inputs, 1024 outputs
    'wd1': tf.Variable(tf.random_normal([7*7*64, 1024])),
    # 1024 inputs, 10 outputs (class prediction)
    'out': tf.Variable(tf.random_normal([1024, n_classes]))
}

biases = {
    'bc1': tf.Variable(tf.random_normal([32])),
    'bc2': tf.Variable(tf.random_normal([64])),
    'bd1': tf.Variable(tf.random_normal([1024])),
    'out': tf.Variable(tf.random_normal([n_classes]))
}

def put_kernels_on_grid (kernel, grid_Y, grid_X, pad = 1):

    '''Visualize conv. features as an image (mostly for the 1st layer).
    Place kernel into a grid, with some paddings between adjacent filters.

    Args:
      kernel:            tensor of shape [Y, X, NumChannels, NumKernels]
      (grid_Y, grid_X):  shape of the grid. Require: NumKernels == grid_Y * grid_X
                           User is responsible of how to break into two multiples.
      pad:               number of black pixels around each filter (between them)

    Return:
      Tensor of shape [(Y+2*pad)*grid_Y, (X+2*pad)*grid_X, NumChannels, 1].
    '''

    x_min = tf.reduce_min(kernel)
    x_max = tf.reduce_max(kernel)

    kernel1 = (kernel - x_min) / (x_max - x_min)

    # pad X and Y
    x1 = tf.pad(kernel1, tf.constant( [[pad,pad],[pad, pad],[0,0],[0,0]] ), mode = 'CONSTANT')

    # X and Y dimensions, w.r.t. padding
    Y = kernel1.get_shape()[0] + 2 * pad
    X = kernel1.get_shape()[1] + 2 * pad

    channels = kernel1.get_shape()[2]

    # put NumKernels to the 1st dimension
    x2 = tf.transpose(x1, (3, 0, 1, 2))
    # organize grid on Y axis
    x3 = tf.reshape(x2, tf.pack([grid_X, Y * grid_Y, X, channels])) #3

    # switch X and Y axes
    x4 = tf.transpose(x3, (0, 2, 1, 3))
    # organize grid on X axis
    x5 = tf.reshape(x4, tf.pack([1, X * grid_X, Y * grid_Y, channels])) #3

    # back to normal order (not combining with the next step for clarity)
    x6 = tf.transpose(x5, (2, 1, 3, 0))

    # to tf.image_summary order [batch_size, height, width, channels],
    #   where in this case batch_size == 1
    x7 = tf.transpose(x6, (3, 0, 1, 2))

    # scale to [0, 255] and convert to uint8
    return tf.image.convert_image_dtype(x7, dtype = tf.uint8)

# Construct model
pred = conv_net(x, weights, biases, keep_prob)

# Define loss and optimizer
cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(pred, y))
optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate).minimize(cost)

# Evaluate model
correct_pred = tf.equal(tf.argmax(pred, 1), tf.argmax(y, 1))
accuracy = tf.reduce_mean(tf.cast(correct_pred, tf.float32))

grid = put_kernels_on_grid (weights['wc1'], grid_Y = 4, grid_X = 8)

# Initializing the variables
init = tf.initialize_all_variables()

# Launch the graph
with tf.Session() as sess:

    train_writer = tf.train.SummaryWriter('./train',  sess.graph)

    sess.run(init)
    step = 1
    i = 0
    # Keep training until reach max iterations
    while step * batch_size < training_iters:

        wc1_summary = tf.image_summary('conv1/features'+ str(i), grid, max_images = 1)

        batch_x, batch_y = mnist.train.next_batch(batch_size)
        # Run optimization op (backprop)
        _, summary = sess.run([optimizer, wc1_summary], feed_dict={x: batch_x, y: batch_y,
                                       keep_prob: dropout})

        train_writer.add_summary(summary)

        if step % display_step == 0:

            # Calculate batch loss and accuracy
            loss, acc = sess.run([cost, accuracy], feed_dict={x: batch_x,
                                                              y: batch_y,
                                                              keep_prob: 1.})
            print("Iter " + str(step*batch_size) + ", Minibatch Loss= " + \
                  "{:.6f}".format(loss) + ", Training Accuracy= " + \
                  "{:.5f}".format(acc))
        step += 1
        i += 1

    print("Optimization Finished!")

    # Calculate accuracy for 256 mnist test images
    print("Testing Accuracy:", \
        sess.run(accuracy, feed_dict={x: mnist.test.images[:256],
                                      y: mnist.test.labels[:256],
                                      keep_prob: 1.}))

Answer 1

很可能这一层的梯度值变得太低，因此很难或不可能看到它们的更新。

梯度消失是深度网络的常见问题。

您可以检查是否是您的情况:

• 打印出卷积权重的梯度值。它们应该非常低(例如 1e-5)。
• 将学习率提高到一个较大的值(例如 20 倍)。权重应该开始变化(请注意，具有如此高 LR 的网络会迅速发散)。