This approach is more powerful than simply taking a sum or mean of the neighbor embeddings. Instead of using a permutation-invariant reduction (e.g., a sum or mean), Janossy pooling applies a permutation-sensitive function and average the result over many possible permutations.

Let $\pi _{i} \in \Pi$ denote a permutation function that maps the set $\{ h_{v}, \forall v \in N(u) \}$ to a specific sequence $(h_{v1}, h_{v2}, ..., h_{v|N(u)|})_{\pi _{i}}$. The Janossy pooling approach then performs neighborhood aggregation by $m_{N(u)}=MLP_{\theta}(\frac{1}{|\Pi|} \sum_{\pi \in \Pi}\rho_{\phi}) (h_{v1}, h_{v2}, ..., h_{v||N(u)})_{\pi _{i}}$,

where $\Pi$ denotes a set of permutations and ρφ is a permutation-sensitive function.