Aristotelian Manifolds: Leveraging Platonic Perceptual Features for Backpropagation Free Rapid Concept Learning

2026-08-20

AI Summary

本文通过研究基础模型内部几何结构，提出一种无需反向传播的快速概念学习方法，用于解决特征压缩和层选择问题。

Abstract

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.

Problem

• Aristotelian Manifolds
• Platonic Representation Hypothesis
• latent spaces
• semantic maturation
• foundation models

Innovation

• Aristotelian Manifolds
• Platonic Representation Hypothesis
• backpropagation-free
• semantic maturation
• latent spaces