发表机构
The Ohio State University（俄亥俄州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于柏拉图式表征假说的亚里士多德流形框架，将基础模型作为通用感知滤波器，研究不同领域的几何响应特征，建立层选择与特征压缩分类体系，实现无反向传播的基础模型潜在空间利用。
AI 中文摘要
本文对亚里士多德流形进行了形式化与系统表征，该框架是基于柏拉图式表征假说构建的通用结构。我们将高容量基础模型定位为通用感知滤波器，并开展全面的逐层研究，以探究知识在这些潜在子空间内的功能合成方式。在不同架构范式与多领域数据集上，我们严格梳理了网络深度、降维及距离度量之间的相互作用。我们的表征显示，语义成熟并非遵循单一单调路径；相反，不同数据领域呈现出高度独特的几何响应特征，具体表现为：专业临床模态呈现中间丘状峰值，自然视觉任务呈现S型平台。通过分析这些流形达到表征效率峰值的精确坐标，我们建立了可预测的层选择与特征压缩分类体系。最终，该系统表征表明，映射冻结表征的内部几何结构，可提供一种鲁棒、无反向传播且可解释的框架，用于理解和利用基础模型的潜在空间。
英文摘要
This paper formalizes and systematically characterizes Aristotelian Manifolds, a generalized structural framework built upon the Platonic Representation Hypothesis. We position high-capacity foundation models as universal perceptual filters and conduct a comprehensive layer-wise investigation to map how knowledge is functionally synthesized within these latent subspaces. Across diverse architectural paradigms and multi-domain datasets, we rigorously chart the interplay between network depth, dimensionality reduction, and distance metrics. Our characterization reveals that semantic maturation does not follow a singular, monotonic path; instead, different data domains exhibit highly distinct geometric response profiles, characterized by intermediate mound-like peaks for specialized clinical modalities and sigmoidal plateaus for natural visual tasks. By profiling the exact coordinates where these manifolds achieve peak representational efficiency, we establish a predictable taxonomy for layer selection and feature compression. Ultimately, this systematic characterization demonstrates that mapping the internal geometry of frozen representations provides a robust, backpropagation-free, and interpretable framework for understanding and exploiting foundation model latent spaces.
