发表机构
Beijing Normal University（北京师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过理论刻画、结构测量与接口构造，建立神经表征中的变换定律，揭示色调结构可预测并支持零样本读取。
AI 中文摘要
神经表征如何保持输入变化的结构，这一问题将表征分析与内部干预联系起来。我们通过参考变换在神经特征上的相容作用来研究可操作的表征内容。我们刻画了变换何时能通过编码器下降，并给出一个线性设定，在该设定中，缺陷由变换对丢弃信息的需求所决定，并以表征所诱导的度量来衡量。在整流器上，变换无法实现有两个可区分的来源——源区域已经使其不可恢复的部分，以及用一个算子满足变换所访问的每个区域所需的代价——而对于一个\textit{测得的}谐波载体，同一问题有封闭答案：当且仅当保留的谐波块在该作用下不变时，线性实现存在。以颜色作为深入实例，我们发现冻结视觉特征中的色调轨道将其能量的84--88%集中在前两个谐波中，且旋转平面在不同形状间共享；这种组织在很大程度上继承自输入和架构，并由训练和深度重塑；测得的结构支持预测、从新起始状态的迁移以及组合——全局和局部实现在各自达成的目标上存在显著差异。在测量的指导下，我们构造了一个紧凑接口，其旋转作用由结构固定且从未拟合：它在未见形状上以3.4$^\circ$中位误差零样本读取色调。理论、结构测量和构造共同确立了变换定律作为一个具体对象，连接了对神经表征的理解与其设计。
英文摘要
How neural representations preserve the structure of input changes connects representation analysis with internal intervention. We study operable representational content through compatible actions of reference transformations on neural features. We characterise when a transformation descends through an encoder, and give a linear setting in which the defect is governed by the transformation's demand for discarded information, measured in the metric the representation induces. On a rectifier the failure to realise a transformation has two distinguishable sources --- what the source region has already made unrecoverable, and what it costs to satisfy every region the transformation visits with one operator --- and for a \textit{measured} harmonic carrier the same question has a closed answer: a linear realisation exists exactly when the retained harmonic blocks are invariant under the action. Using colour as the in-depth instance, we find that hue orbits in frozen visual features concentrate 84--88\% of their energy in the first two harmonics with rotation planes shared across shapes, that this organisation is substantially inherited from input and architecture and is reshaped by training and depth, and that the measured structure supports prediction, transport from new starting states, and composition --- with global and local realisations differing sharply in which they achieve. Guided by the measurements, we construct a compact interface whose rotation action is fixed by the structure and never fitted: it reads hue zero-shot at 3.4$^\circ$ median error on unseen shapes. Theory, structural measurement, and construction together establish transformation laws as a concrete object connecting the understanding of neural representations to their design.
Comments46 pages, 12 figures, 63 tables
