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

A new arXiv paper (2608.20682v1) formalizes Aristotelian Manifolds, a framework built on the Platonic Representation Hypothesis that treats high-capacity foundation models as universal perceptual filters. The study's layer-wise investigation across architectures and multi-domain datasets reveals that semantic maturation follows non-monotonic paths, with clinical modalities showing mound-like peaks and natural visual tasks showing sigmoidal plateaus, enabling a predictable taxonomy for layer selection and feature compression without backpropagation. The findings provide an interpretable method for exploiting foundation model latent spaces by mapping their internal geometry.

arXiv:2608.20682v1 Announce Type: new 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.