Canonical locks that encode part-whole hierarchies

2026-09-22

AI Summary

该研究提出了一种称为canonical locks的几何原语，用于在神经网络中编码部分-整体层次结构，通过高维向量间的相对相位差来表示信息。

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 ($d \geq 4$), 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.

Problem

• part-whole hierarchies
• representational learning
• neural network
• geometric primitive
• canonical locks

Innovation

• canonical locks
• part-whole hierarchies
• high-dimensional vectors
• relative phase differences
• mental rotation