  Federated Learning (FL) fuses collaborative models from local nodes without
centralizing users' data. The permutation invariance property of neural
networks and the non-i.i.d. data across clients make the locally updated
parameters imprecisely aligned, disabling the coordinate-based parameter
averaging. Traditional neurons do not explicitly consider position information.
Hence, we propose Position-Aware Neurons (PANs) as an alternative, fusing
position-related values (i.e., position encodings) into neuron outputs. PANs
couple themselves to their positions and minimize the possibility of
dislocation, even updating on heterogeneous data. We turn on/off PANs to
disable/enable the permutation invariance property of neural networks. PANs are
tightly coupled with positions when applied to FL, making parameters across
clients pre-aligned and facilitating coordinate-based parameter averaging. PANs
are algorithm-agnostic and could universally improve existing FL algorithms.
Furthermore, "FL with PANs" is simple to implement and computationally
friendly.
