不靠反向传播，用几何结构分析模型内部表征，实现快速概念学习。
Aristotelian Manifolds: Leveraging Platonic Perceptual Features for Backpropagation Free Rapid Concept Learning
- 基于柏拉图感知假设，构建可解释的潜在空间几何框架。
- 发现不同数据域有独特几何响应：临床模态呈山峰型，自然图像为平顶型。
- 定位最优表征层，实现无需训练的高效特征压缩与概念学习。
本文系统化地定义并刻画了阿基米德流形（Aristotelian Manifolds），该框架建立在柏拉图表征假说之上。将高容量基础模型视为通用感知滤波器，通过分层分析揭示知识在潜在子空间中的功能合成机制。在多种架构与多领域数据集上，我们严谨描绘了网络深度、维度压缩与距离度量之间的相互作用。研究发现，语义成熟并非单一单调路径；不同数据域表现出显著不同的几何响应特征：特定临床模态呈现中间山峰状峰值，自然视觉任务则表现为逻辑斯蒂型平顶。通过定位这些流形达到表征效率峰值的精确坐标，我们建立了一种可预测的层选择与特征压缩分类体系。最终表明，映射冻结表征的内部几何结构，可提供一种鲁棒、无需反向传播且可解释的框架，用于理解与利用基础模型的潜在空间。
原文摘要 · Abstract (English)
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.
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