  Recently, Neural Fields have emerged as a powerful modelling paradigm to
represent continuous signals. In a conditional neural field, a field is
represented by a latent variable that conditions the NeF, whose parametrisation
is otherwise shared over an entire dataset. We propose Equivariant Neural
Fields based on cross attention transformers, in which NeFs are conditioned on
a geometric conditioning variable, a latent point cloud, that enables an
equivariant decoding from latent to field. Our equivariant approach induces a
steerability property by which both field and latent are grounded in geometry
and amenable to transformation laws if the field transforms, the latent
represents transforms accordingly and vice versa. Crucially, the equivariance
relation ensures that the latent is capable of (1) representing geometric
patterns faitfhully, allowing for geometric reasoning in latent space, (2)
weightsharing over spatially similar patterns, allowing for efficient learning
of datasets of fields. These main properties are validated using classification
experiments and a verification of the capability of fitting entire datasets, in
comparison to other non-equivariant NeF approaches. We further validate the
potential of ENFs by demonstrate unique local field editing properties.
