Tensorflow权重初始化

关于tensorflow网站上的MNIST tutorial，我进行了一项实验（gist），看看不同权重初始化对学习的影响 . 我注意到，对于我在流行的_2571824中读到的内容，无论权重初始化如何，学习都很好 .

对于初始化卷积和完全连接层的权重，不同的曲线表示 w 的不同值 . 请注意 w 的所有值都可以正常工作，即使 0.3 和 1.0 的性能较低且某些值训练更快 - 特别是 0.03 和 0.1 是最快的 . 尽管如此，该情节显示了相当大的 w 范围，这表明'robustness' w.r.t.重量初始化 .

def weight_variable(shape, w=0.1):
  initial = tf.truncated_normal(shape, stddev=w)
  return tf.Variable(initial)

def bias_variable(shape, w=0.1):
  initial = tf.constant(w, shape=shape)
  return tf.Variable(initial)

Question ：为什么这个网络不会受到消失或爆炸梯度问题的影响？

我建议你阅读有关实现细节的要点，但这里是代码供参考 . 我的nvidia 960m花了大约一个小时，虽然我想它也可以在合理的时间内在CPU上运行 .

import time
from tensorflow.examples.tutorials.mnist import input_data
import tensorflow as tf
from tensorflow.python.client import device_lib

import numpy
import matplotlib.pyplot as pyplot

mnist = input_data.read_data_sets('MNIST_data', one_hot=True)

# Weight initialization

def weight_variable(shape, w=0.1):
  initial = tf.truncated_normal(shape, stddev=w)
  return tf.Variable(initial)

def bias_variable(shape, w=0.1):
  initial = tf.constant(w, shape=shape)
  return tf.Variable(initial)


# Network architecture

def conv2d(x, W):
  return tf.nn.conv2d(x, W, strides=[1, 1, 1, 1], padding='SAME')

def max_pool_2x2(x):
  return tf.nn.max_pool(x, ksize=[1, 2, 2, 1],
                    strides=[1, 2, 2, 1], padding='SAME')

def build_network_for_weight_initialization(w):
    """ Builds a CNN for the MNIST-problem:
     - 32 5x5 kernels convolutional layer with bias and ReLU activations
     - 2x2 maxpooling
     - 64 5x5 kernels convolutional layer with bias and ReLU activations
     - 2x2 maxpooling
     - Fully connected layer with 1024 nodes + bias and ReLU activations
     - dropout
     - Fully connected softmax layer for classification (of 10 classes)

     Returns the x, and y placeholders for the train data, the output
     of the network and the dropbout placeholder as a tuple of 4 elements.
    """
    x = tf.placeholder(tf.float32, shape=[None, 784])
    y_ = tf.placeholder(tf.float32, shape=[None, 10])

    x_image = tf.reshape(x, [-1,28,28,1])
    W_conv1 = weight_variable([5, 5, 1, 32], w)
    b_conv1 = bias_variable([32], w)

    h_conv1 = tf.nn.relu(conv2d(x_image, W_conv1) + b_conv1)
    h_pool1 = max_pool_2x2(h_conv1)
    W_conv2 = weight_variable([5, 5, 32, 64], w)
    b_conv2 = bias_variable([64], w)

    h_conv2 = tf.nn.relu(conv2d(h_pool1, W_conv2) + b_conv2)
    h_pool2 = max_pool_2x2(h_conv2)

    W_fc1 = weight_variable([7 * 7 * 64, 1024], w)
    b_fc1 = bias_variable([1024], w)

    h_pool2_flat = tf.reshape(h_pool2, [-1, 7*7*64])
    h_fc1 = tf.nn.relu(tf.matmul(h_pool2_flat, W_fc1) + b_fc1)

    keep_prob = tf.placeholder(tf.float32)
    h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob)

    W_fc2 = weight_variable([1024, 10], w)
    b_fc2 = bias_variable([10], w)

    y_conv = tf.matmul(h_fc1_drop, W_fc2) + b_fc2

    return (x, y_, y_conv, keep_prob)


# Experiment

def evaluate_for_weight_init(w):
    """ Returns an accuracy learning curve for a network trained on
    10000 batches of 50 samples. The learning curve has one item
    every 100 batches."""
    with tf.Session() as sess:
    x, y_, y_conv, keep_prob = build_network_for_weight_initialization(w)
    cross_entropy = tf.reduce_mean(
        tf.nn.softmax_cross_entropy_with_logits(labels=y_, logits=y_conv))
    train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy)
    correct_prediction = tf.equal(tf.argmax(y_conv,1), tf.argmax(y_,1))
    accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
    sess.run(tf.global_variables_initializer())
    lr = []
    for _ in range(100):
        for i in range(100):
          batch = mnist.train.next_batch(50)
          train_step.run(feed_dict={x: batch[0], y_: batch[1], keep_prob: 0.5})
        assert mnist.test.images.shape[0] == 10000
        # This way the accuracy-evaluation fits in my 2GB laptop GPU.
        a = sum(
            accuracy.eval(feed_dict={
                x: mnist.test.images[2000*i:2000*(i+1)],
                y_: mnist.test.labels[2000*i:2000*(i+1)],
                keep_prob: 1.0})
            for i in range(5)) / 5
        lr.append(a)
    return lr


ws = [0.0001, 0.0003, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1.0]
accuracies = [
    [evaluate_for_weight_init(w) for w in ws]
    for _ in range(3)
]


# Plotting results

pyplot.plot(numpy.array(accuracies).mean(0).T)
pyplot.ylim(0.9, 1)
pyplot.xlim(0,140)
pyplot.xlabel('batch (x 100)')
pyplot.ylabel('test accuracy')
pyplot.legend(ws)