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Canonical locks that encode part-whole hierarchies

arXiv · AI, language, vision and robotics · article · Sep 22, 2026 · UTC

One of the challenges in representational learning is how to encode part-whole hierarchies in a neural net. Prior works rely on flattening tree-like structures into string-like sequences and training a sequence-to-sequence model via autoregression. While such a representation works for parse-trees in NLP, it is not entirely clear how to make it work for images. Thus, we propose a geometric primitive called canonical locks. The key idea is that parts/wholes can be modelled as higher-dimensional vectors ($d \geq 4$), and information can be encoded in their relative phase differences. Inductively

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