Tensorflow 权重初始化

Question

关于MNIST tutorial在 TensorFlow 网站上，我进行了一项实验 ( gist ) 以查看不同权重初始化对学习的影响。我注意到，与我在流行的 [Xavier, Glorot 2010] paper 中读到的内容相反。 ，无论权重初始化如何，学习都很好。



不同的曲线代表 w 的不同值用于初始化卷积层和全连接层的权重。请注意 w 的所有值工作正常，即使 0.3和 1.0最终性能较低，某些值训练得更快 - 特别是 0.03和 0.1是最快的。尽管如此，该图显示了相当大的范围 w哪个有效，表明“稳健性”w.r.t.权重初始化。

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)

问题 :为什么这个网络没有梯度消失或爆炸的问题？

我建议您阅读实现细节的要点，但这里有代码供引用。在我的 Nvidia 960m 上花费了大约一个小时，尽管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)

Answer 1

权重初始化策略可能是改进模型的一个重要且经常被忽视的步骤，由于这是现在谷歌上的最高结果，我认为它可以保证更详细的答案。

一般来说，每一层的激活函数梯度、传入/传出连接数(fan_in/fan_out)和权重方差的总乘积应该等于1。这样，当您通过网络进行反向传播时，输入和输出梯度之间的差异将保持一致，并且您不会受到梯度爆炸或消失的影响。尽管 ReLU 更能抵抗爆炸/消失梯度，但您可能仍然会遇到问题。

OP 使用的 tf.truncated_normal 进行随机初始化，鼓励权重“以不同方式”更新，但 不是 考虑上述优化策略。在较小的网络上，这可能不是问题，但如果您想要更深的网络或更快的训练时间，那么您最好尝试基于最近研究的权重初始化策略。

对于 ReLU 函数之前的权重，您可以使用以下默认设置:

tf.contrib.layers.variance_scaling_initializer

对于 tanh/sigmoid 激活层“xavier”可能更合适:

tf.contrib.layers.xavier_initializer

有关这些功能和相关论文的更多详细信息，请访问:
https://www.tensorflow.org/versions/r0.12/api_docs/python/contrib.layers/initializers

除了权重初始化策略，进一步的优化可以探索批量归一化: https://www.tensorflow.org/api_docs/python/tf/nn/batch_normalization