  We present Analogical Networks, a model that encodes domain knowledge
explicitly, in a collection of structured labelled 3D scenes, in addition to
implicitly, as model parameters, and segments 3D object scenes with analogical
reasoning: instead of mapping a scene to part segments directly, our model
first retrieves related scenes from memory and their corresponding part
structures, and then predicts analogous part structures for the input scene,
via an end-to-end learnable modulation mechanism. By conditioning on more than
one retrieved memories, compositions of structures are predicted, that mix and
match parts across the retrieved memories. One-shot, few-shot or many-shot
learning are treated uniformly in Analogical Networks, by conditioning on the
appropriate set of memories, whether taken from a single, few or many memory
exemplars, and inferring analogous parses. We show Analogical Networks are
competitive with state-of-the-art 3D segmentation transformers in many-shot
settings, and outperform them, as well as existing paradigms of meta-learning
and few-shot learning, in few-shot settings. Analogical Networks successfully
segment instances of novel object categories simply by expanding their memory,
without any weight updates. Our code and models are publicly available in the
project webpage: http://analogicalnets.github.io/.
