Canonical locks that encode part-whole hierarchies

arXiv:2609.26046 · cs.AI · Submitted 2026-09-22 · Read on arXiv

cs.AI

Submitted: 2026-09-22

Updated: 2026-09-28

Comments: Work in Progress

License: http://creativecommons.org/licenses/by/4.0/

The gist: One of the challenges in representational learning is how to encode part-whole hierarchies in a neural net.

Terminology

Abstract

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 at least 4), and information can be encoded in their relative phase differences. Inductively, the net consists of positionally-bound bottom-up and top-down neural fields, which drive each other to achieve a state of thermal equilibrium. Additionally, we show the existence of a few symmetrical configurations in the net. The computational iterations taken to break these symmetries depend on the angle between parts/wholes arranged on a disk (or more precisely a ring) in higher dimensions. It also appears to have connections to the psychological phenomenon of mental rotation.

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