In the latest 10 or so years developments in deep neural networks Convolutional Neural Networks (CNN)s have been very popular. In these networks there is a specific procedure called pooling, which this question relates to.
Given that both Max-pooling and Average-pooling seem to be used in CNNs and the fact that the $p$-schatten norms have a max-approximating behaviour as $p$ grows without bounds:
$$\lim_{p\to \infty}\|v\|_p = \lim_{p\to \infty}\left\{\left({v_1}^p+\cdots+ {v_n}^p\right)^{1/p}\right\} \to \max(v)$$
I was wondering if any kind of $p$-schatten pooling has been tried as something of a smoother variant of max-pooling.