Can not use both bias and batch normalization in convolution layers

I use slim framework for tensorflow, because of its simplicity. But I want to have convolutional layer with both biases and batch normalization. In vanilla tensorflow, I have:

def conv2d(input_, output_dim, k_h=5, k_w=5, d_h=2, d_w=2, name="conv2d"):
    with tf.variable_scope(name):
        w = tf.get_variable('w', [k_h, k_w, input_.get_shape()[-1], output_dim],

    initializer=tf.contrib.layers.xavier_initializer(uniform=False))
    conv = tf.nn.conv2d(input_, w, strides=[1, d_h, d_w, 1], padding='SAME')

    biases = tf.get_variable('biases', [output_dim], initializer=tf.constant_initializer(0.0))
    conv = tf.reshape(tf.nn.bias_add(conv, biases), conv.get_shape())

    tf.summary.histogram("weights", w)
    tf.summary.histogram("biases", biases)

    return conv

d_bn1 = BatchNorm(name='d_bn1')
h1 = lrelu(d_bn1(conv2d(h0, df_dim + y_dim, name='d_h1_conv')))

and I rewrote it to slim by this:

h1 = slim.conv2d(h0,
                 num_outputs=self.df_dim + self.y_dim,
                 scope='d_h1_conv',
                 kernel_size=[5, 5],
                 stride=[2, 2],
                 activation_fn=lrelu,
                 normalizer_fn=layers.batch_norm,
                 normalizer_params=batch_norm_params,                           
                 weights_initializer=layers.xavier_initializer(uniform=False),
                 biases_initializer=tf.constant_initializer(0.0)
                 )

But this code does not add bias to conv layer. That is because of https://github.com/tensorflow/tensorflow/blob/master/tensorflow/contrib/layers/python/layers/layers.py#L1025 where is

    layer = layer_class(filters=num_outputs,
                    kernel_size=kernel_size,
                    strides=stride,
                    padding=padding,
                    data_format=df,
                    dilation_rate=rate,
                    activation=None,
                    use_bias=not normalizer_fn and biases_initializer,
                    kernel_initializer=weights_initializer,
                    bias_initializer=biases_initializer,
                    kernel_regularizer=weights_regularizer,
                    bias_regularizer=biases_regularizer,
                    activity_regularizer=None,
                    trainable=trainable,
                    name=sc.name,
                    dtype=inputs.dtype.base_dtype,
                    _scope=sc,
                    _reuse=reuse)
    outputs = layer.apply(inputs)

in the construction of layer, which results in not having bias when using batch normalization. Does that mean that I can not have both biases and batch normalization using slim and layers library? Or is there another way to achieve having both bias and batch normalization in layer when using slim?

Answer

Batchnormalization already includes the addition of the bias term. Recap that BatchNorm is already:

gamma * normalized(x) + bias

So there is no need (and it makes no sense) to add another bias term in the convolution layer. Simply speaking BatchNorm shifts the activation by their mean values. Hence, any constant will be canceled out.

If you still want to do this, you need to remove the normalizer_fn argument and add BatchNorm as a single layer. Like I said, this makes no sense.

But the solution would be something like

net = slim.conv2d(net, normalizer_fn=None, ...)
net = tf.nn.batch_normalization(net)

Note, the BatchNorm relies on non-gradient updates. So you either need to use an optimizer which is compatible with the UPDATE_OPS collection. Or you need to manually add tf.control_dependencies.

Long story short: Even if you implement the ConvWithBias+BatchNorm, it will behave like ConvWithoutBias+BatchNorm. It is the same as multiple fully-connected layers without activation function will behave like a single one.