发表机构
University of Tübingen; International Max Planck Research School for Intelligent Systems; Allen Institute for Neural Dynamics; Gatsby Computational Neuroscience Unit, University College London; Sainsbury Wellcome Centre, University College London; University of Alberta; Amii（图宾根大学; 国际马克斯·普朗克智能系统研究学院; 艾伦神经动力学研究所; 伦敦大学学院盖茨比计算神经科学中心; 伦敦大学学院塞恩斯伯里惠康中心; 阿尔伯塔大学; 艾伯塔机器智能研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明参数对称性通过加法、复制和缩放三种变换影响表征几何，并给出闭式分解及选择规则，以解决过参数化导致的退化问题。
AI 中文摘要
表征在机器学习、心理学和神经科学中常被用来推断生物和人工系统的计算过程。此类推断假定表征几何与所执行的计算之间存在有意义的联系。然而，对于人工神经网络而言，函数在多大程度上约束表征仍不清楚。一个关键障碍是这些网络存在参数对称性：参数化的变化在精确保持函数的同时重塑表征几何。在此，我们证明了一大类参数对称性通过仅三种原始特征变换作用于表征：加法、复制和缩放。这种特征层面的刻画产生了表征几何的闭式分解，将其分为本质部分和辅助部分，从而精确说明了即使函数保持不变，表征几何的退化如何随过参数化而增长。最后，我们表明实现层面的选择规则可以解决这种退化，产生可识别的几何，其中特征根据其对网络函数的贡献被加权。总之，我们的结果界定了表征何时能支持对计算的推断，何时不能。
英文摘要
Representations are routinely used across machine learning, psychology, and neuroscience to draw inferences about the computations of biological and artificial systems. Such inferences presume a meaningful link between representational geometry and the computation being performed. For artificial neural networks, however, the extent to which function constrains representation remains unclear. One key obstacle is that these networks admit parameter symmetries: changes in parameterization that preserve function exactly while reshaping representational geometry. Here, we show that a broad class of parameter symmetries acts on representations through just three primitive feature transformations: addition, duplication, and scaling. This feature-level characterization yields a closed-form decomposition of representational geometry into essential and auxiliary components, which makes precise how degeneracy in representational geometry can grow with overparameterization even when function is held fixed. Finally, we show that implementation-level selection rules can resolve this degeneracy, yielding identifiable geometries in which features are weighted according to their contributions to the network's function. Together, our results delineate when representations can support inferences about computation, and when they cannot.
CommentsTo appear in NeurIPS 2026. 89 pages, 9 figures. Code: https://github.com/mrvnthss/symmetries-representational-geometry
