  The effectiveness of neural processes (NPs) in modelling posterior prediction
maps -- the mapping from data to posterior predictive distributions -- has
significantly improved since their inception. This improvement can be
attributed to two principal factors: (1) advancements in the architecture of
permutation invariant set functions, which are intrinsic to all NPs; and (2)
leveraging symmetries present in the true posterior predictive map, which are
problem dependent. Transformers are a notable development in permutation
invariant set functions, and their utility within NPs has been demonstrated
through the family of models we refer to as TNPs. Despite significant interest
in TNPs, little attention has been given to incorporating symmetries. Notably,
the posterior prediction maps for data that are stationary -- a common
assumption in spatio-temporal modelling -- exhibit translation equivariance. In
this paper, we introduce of a new family of translation equivariant TNPs that
incorporate translation equivariance. Through an extensive range of experiments
on synthetic and real-world spatio-temporal data, we demonstrate the
effectiveness of TE-TNPs relative to their non-translation-equivariant
counterparts and other NP baselines.
