From Plato to Aristotle: Toward a General Theory of Representation Hypotheses
Abstract
The Platonic Representation Hypothesis (PRH) holds that increasingly capable models converge toward a common representation. However, recent studies have shown different views on aligning representations via their neighborhoods, spanning trees, and distances. We show that these views can differ because the alignment criteria behind them sit at different points of one lattice, and we formalize this explanation as the Lattice Representation Hypothesis (LRH). Under the LRH, the convergence claimed by the PRH is agreement at the top of the lattice, whereas its evidence comes from neighbor overlap, a criterion near the bottom. The Aristotelian Representation Hypothesis (ARH) restricts convergence to local neighborhoods because calibration keeps the growth of neighbor overlap with model size but largely removes that of centered kernel alignment. We show that this removal can come from calibrating a maximum over layers, so global convergence remains open. Back into Plato's Cave (BPC) infers coarse shared structure from the collapse of neighbor overlap on larger evaluation sets, whereas we trace it at least partly to a fixed number of neighbors covering shorter distances. We show that the spanning-tree overlap used by Structure over Geometry (SOG) mostly repeats one-nearest-neighbor overlap. The LRH also extends to independently trained models, whose training procedure and objective decide the criteria met reliably across runs. We prove this claim for the training procedure in a linear autoencoder and for the objective in a finite contrastive Gibbs model. Experiments on dozens of pretrained vision and language models and thousands of runs of both theoretical models support these conclusions. We hope this work paves the way toward a general theory of representation hypotheses, with a framework to analyze them and compare their evidence. Project page: https://eethanshi.github.io/LRH
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BibTeX
@misc{shi2026from,
title = {{From Plato to Aristotle: Toward a General Theory of Representation Hypotheses}},
author = {Dai Shi and Andi Han and Xiaoyu Li and Luke Thompson and José Miguel Hernández-Lobato},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20286},
eprint = {2610.20286},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20286},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From Plato to Aristotle: Toward a General Theory of Representation Hypotheses
AU - Dai Shi
AU - Andi Han
AU - Xiaoyu Li
AU - Luke Thompson
AU - José Miguel Hernández-Lobato
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20286
UR - https://arxiv.org/abs/2610.20286
AB - The Platonic Representation Hypothesis (PRH) holds that increasingly capable models converge toward a common representation. However, recent studies have shown different views on aligning representations via their neighborhoods, spanning trees, and distances. We show that these views can differ because the alignment criteria behind them sit at different points of one lattice, and we formalize this explanation as the Lattice Representation Hypothesis (LRH). Under the LRH, the convergence claimed by the PRH is agreement at the top of the lattice, whereas its evidence comes from neighbor overlap, a criterion near the bottom. The Aristotelian Representation Hypothesis (ARH) restricts convergence to local neighborhoods because calibration keeps the growth of neighbor overlap with model size but largely removes that of centered kernel alignment. We show that this removal can come from calibrating a maximum over layers, so global convergence remains open. Back into Plato's Cave (BPC) infers coarse shared structure from the collapse of neighbor overlap on larger evaluation sets, whereas we trace it at least partly to a fixed number of neighbors covering shorter distances. We show that the spanning-tree overlap used by Structure over Geometry (SOG) mostly repeats one-nearest-neighbor overlap. The LRH also extends to independently trained models, whose training procedure and objective decide the criteria met reliably across runs. We prove this claim for the training procedure in a linear autoencoder and for the objective in a finite contrastive Gibbs model. Experiments on dozens of pretrained vision and language models and thousands of runs of both theoretical models support these conclusions. We hope this work paves the way toward a general theory of representation hypotheses, with a framework to analyze them and compare their evidence. Project page: https://eethanshi.github.io/LRH
ER -