发表机构
University of Central Florida（中佛罗里达大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出规范锁这一几何原语，通过高维向量相位差编码部分-整体层次，利用双向神经场热平衡与对称性破缺实现图像表示，并关联心理旋转现象。
AI 中文摘要
表征学习中的挑战之一是如何在神经网络中编码部分-整体层次结构。先前的工作依赖于将树状结构展平为字符串序列，并通过自回归训练序列到序列模型。虽然这种表示适用于自然语言处理中的解析树，但如何使其适用于图像尚不完全清楚。因此，我们提出了一种称为规范锁的几何原语。关键思想是，部分/整体可以被建模为高维向量（$d \geq 4$），并且信息可以编码在其相对相位差中。归纳地，该网络由位置绑定的自下而上和自上而下的神经场组成，它们相互驱动以达到热平衡状态。此外，我们展示了网络中存在一些对称配置。打破这些对称性所需的计算迭代取决于在高维圆盘（更准确地说，是环）上排列的部分/整体之间的角度。它似乎也与心理旋转的心理现象有关。
英文摘要
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.
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