  The x-vector architecture has recently achieved state-of-the-art results on
the speaker verification task. This architecture incorporates a central layer,
referred to as temporal pooling, which stacks statistical parameters of the
acoustic frame distribution. This work proposes to highlight the significant
effect of the temporal pooling content on the training dynamics and task
performance. An evaluation with different pooling layers is conducted, that is,
including different statistical measures of central tendency. Notably, 3rd and
4th moment-based statistics (skewness and kurtosis) are also tested to complete
the usual mean and standard-deviation parameters. Our experiments show the
influence of the pooling layer content in terms of speaker verification
performance, but also for several classification tasks (speaker, channel or
text related), and allow to better reveal the presence of external information
to the speaker identity depending on the layer content.
