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/.

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