Difference between dynamic pooling and static pooling in convolutional neural networks

Question

Since yesterday I was thinking that pooling layer in CNN has fixed size(e.g. 2 by 2). Then I saw in this paper: http://phd.nal.co/papers/Kalchbrenner_DCNN_ACL14

We define a convolutional neural network architecture and apply it to the semantic modelling of sentences. The network handles input sequences of varying length. The layers in the network interleave one-dimensional convolutional layers and dynamic k-max pooling layers. Dynamic k-max pooling is a generalisation of the max pooling operator. The max pooling operator is a non-linear subsampling function that returns the maximum of a set of values (LeCun et al., 1998). The operator is generalised in two respects. First, k-max pooling over a linear sequence of values returns the subsequence of k maximum values in the sequence, instead of the single maximum value. Secondly, the pooling parameter k can be dynamically chosen by making k a function of other aspects of the network or the input

Am I correct thinking, that this dynamic pooling is for trim sentences(of variable lengths of words), to have vector(vector for supervised learning - see picture on page 4) of constant size?

Answer 1

Actually k-max pooling is used to sample down different length vectors into the same length before fully connected layer. Hence, it is applied after top convolution layer. Dynamic k-max pooling is used to sample features proportional to its input size. That make sense, if you want to keep more features from longer sentences. So dynamic k-max pooling doesn't necessarily equalize number of samples from different sized vectors. It is the work of k-max pooling which is independent from the input size. Section 3.2 and 3.3 explains it better.

The pooling layers used in (LeCun et al., 1998) are local, so output size of a pooling layer is a function of the input size.