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.

我们提出了基于交叉注意力变换器的等变神经场，其中神经场被条件变量以及几何条件变量所控制，从而实现了从潜变量到场的等变解码。我们的等变方法具有可调整性，当神经场发生变换时，潜变量也相应地表示变换，反之亦然。这种等变关系确保了潜变量能够 (1) 忠实地表示几何模式，从而实现潜空间中的几何推理，(2) 在空间上相似的模式之间共享权重，从而实现对数据集的高效学习。通过分类实验验证了这些主要特性，并与其他非等变的神经场方法进行了对比。我们进一步通过展示独特的局部场编辑属性验证了等变神经场的潜在能力。