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

• URL: http://arxiv.org/abs/2608.20682v1
• Date: Fri, 21 Aug 2026 02:38:12 GMT
• Title: Aristotelian Manifolds: Leveraging Platonic Perceptual Features for Backpropagation Free Rapid Concept Learning
• Abstract summary: This paper formalizes and systematically characterizes Aristotelian Manifolds.<n>Our characterization reveals that semantic maturation does not follow a singular, monotonic path.<n>Ultimately, this systematic characterization demonstrates that mapping the internal geometry of frozen representations provides a robust, backpropagation-free, and interpretable framework.
• Score: 4.941630596191806
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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