Why no weight decay on the convolutional layers in the cifar10 example of tensorflow?

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There seems to be no weight decay on convolutional layers in the cifar10 example on tensorflow. Actually there is no weight decay on any layers except for the two fully connected layers. Is this a common practice? I thought weight decay was applied to all weights (except biases).

For reference, here's the relevant code (wd is the weight decay factor):

  # conv1
  with tf.variable_scope('conv1') as scope:
    kernel = _variable_with_weight_decay('weights', shape=[5, 5, 3, 64],
                                         stddev=1e-4, wd=0.0)
    conv = tf.nn.conv2d(images, kernel, [1, 1, 1, 1], padding='SAME')
    biases = _variable_on_cpu('biases', [64], tf.constant_initializer(0.0))
    bias = tf.nn.bias_add(conv, biases)
    conv1 = tf.nn.relu(bias, name=scope.name)
    _activation_summary(conv1)

  # pool1
  pool1 = tf.nn.max_pool(conv1, ksize=[1, 3, 3, 1], strides=[1, 2, 2, 1],
                         padding='SAME', name='pool1')
  # norm1
  norm1 = tf.nn.lrn(pool1, 4, bias=1.0, alpha=0.001 / 9.0, beta=0.75,
                    name='norm1')

  # conv2
  with tf.variable_scope('conv2') as scope:
    kernel = _variable_with_weight_decay('weights', shape=[5, 5, 64, 64],
                                         stddev=1e-4, wd=0.0)
    conv = tf.nn.conv2d(norm1, kernel, [1, 1, 1, 1], padding='SAME')
    biases = _variable_on_cpu('biases', [64], tf.constant_initializer(0.1))
    bias = tf.nn.bias_add(conv, biases)
    conv2 = tf.nn.relu(bias, name=scope.name)
    _activation_summary(conv2)

  # norm2
  norm2 = tf.nn.lrn(conv2, 4, bias=1.0, alpha=0.001 / 9.0, beta=0.75,
                    name='norm2')
  # pool2
  pool2 = tf.nn.max_pool(norm2, ksize=[1, 3, 3, 1],
                         strides=[1, 2, 2, 1], padding='SAME', name='pool2')

  # local3
  with tf.variable_scope('local3') as scope:
    # Move everything into depth so we can perform a single matrix multiply.
    dim = 1
    for d in pool2.get_shape()[1:].as_list():
      dim *= d
    reshape = tf.reshape(pool2, [FLAGS.batch_size, dim])

    weights = _variable_with_weight_decay('weights', shape=[dim, 384],
                                          stddev=0.04, wd=0.004)
    biases = _variable_on_cpu('biases', [384], tf.constant_initializer(0.1))
    local3 = tf.nn.relu(tf.matmul(reshape, weights) + biases, name=scope.name)
    _activation_summary(local3)

  # local4
  with tf.variable_scope('local4') as scope:
    weights = _variable_with_weight_decay('weights', shape=[384, 192],
                                          stddev=0.04, wd=0.004)
    biases = _variable_on_cpu('biases', [192], tf.constant_initializer(0.1))
    local4 = tf.nn.relu(tf.matmul(local3, weights) + biases, name=scope.name)
    _activation_summary(local4)

  # softmax, i.e. softmax(WX + b)
  with tf.variable_scope('softmax_linear') as scope:
    weights = _variable_with_weight_decay('weights', [192, NUM_CLASSES],
                                          stddev=1/192.0, wd=0.0)
    biases = _variable_on_cpu('biases', [NUM_CLASSES],
                              tf.constant_initializer(0.0))
    softmax_linear = tf.add(tf.matmul(local4, weights), biases, name=scope.name)
    _activation_summary(softmax_linear)

  return softmax_linear
conv-neural-network tensorflow
1 Answers

Weight decay doesn't necessarily improve performance. In my own experience, I've found reasonably often that my models perform worse (as measured by some metric on a held-out set) with any significant amount of weight decay. It is a useful form of regularization to be aware of, but you don't need to add it to every model without considering if it seems needed or comparing the performance with and without.

As for whether weight decay on only part of a model can be good compared with weight decay on the entire model, it does seem less common to only regularize some of the weights this way. I don't know that there's a theoretical reason for this, however. In general, neural networks already have too many hyperparameters to configure. Whether to use weight decay or not is already a question, and how strongly to regularize the weights if you do. If you also wonder, which layers should I regularize this way, you'll quickly run out of time to test the performance of all of the different ways you could turn it on and off for each layer.

I imagine that there are models that would benefit from weight decay on only part of the model; I don't think it's done often because it's difficult to test all of the possibilities and find out which one works best.

user_48800030
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