What is global max pooling layer and what is its advantage over maxpooling layer? Can somebody explain what is a global max pooling layer and why and when do we use it for training a neural network. Do they have any advantage over ordinary max pooling layer?
 A: Global max pooling  =  ordinary max pooling layer with pool size equals to the size of the input (minus filter size + 1, to be precise). You can see that MaxPooling1D takes a pool_length argument, whereas GlobalMaxPooling1D does not.
For example, if the input of the max pooling layer  is $0,1,2,2,5,1,2$, global max pooling outputs $5$, whereas  ordinary max pooling layer with pool size equals to 3 outputs $2,2,5,5,5$ (assuming stride=1).
This can be seen in the code:
class GlobalMaxPooling1D(_GlobalPooling1D):
    """Global max pooling operation for temporal data.
    # Input shape
        3D tensor with shape: `(samples, steps, features)`.
    # Output shape
        2D tensor with shape: `(samples, features)`.
    """

    def call(self, x, mask=None):
        return K.max(x, axis=1)

In some domains, such as natural language processing, it is common to use global max pooling. In some other domains, such as computer vision, it is common to use a max pooling that isn't global.
A: As described in this paper that proposed global average pooling (GAP):
Conventional convolutional neural networks perform convolution in the lower layers of the network. For classification, the feature maps of the last convolutional layer are vectorized and fed into fully connected layers followed by a softmax logistic regression layer. This structure bridges the convolutional structure with traditional neural network classifiers. It treats the convolutional layers as feature extractors, and the resulting feature is classified in a traditional way.
However, the fully connected layers are prone to overfitting, thus hampering the generalization ability of the overall network. Dropout is proposed by Hinton et al as a regularizer which randomly sets half of the activations to the fully connected layers to zero during training. It has improved the
generalization ability and largely prevents overfitting.
In this paper, we propose another strategy called global average pooling to replace the traditional fully connected layers in CNN. The idea is to generate one feature map for each corresponding category of the classification task in the last mlpconv layer. Instead of adding fully connected layers on top of the feature maps, we take the average of each feature map, and the resulting vector is fed directly into the softmax layer. One advantage of global average pooling over the fully connected layers is that it is more native to the convolution structure by enforcing correspondences between feature maps and categories. Thus the feature maps can be easily interpreted as categories confidence maps. Another advantage is that there is no parameter to optimize in the global average pooling thus overfitting is avoided at this layer. Futhermore, global average pooling sums out the spatial information, thus it is more robust to spatial translations of the input. We can see global average pooling as a structural regularizer that explicitly enforces feature maps to be confidence maps of concepts (categories). This is made possible by the mlpconv layers, as they makes better approximation to the confidence maps than GLMs.
Edit:
As suggested by  @MaxLawnboy, here is another paper on the same topic .
