An Information-Geometric View of the Platonic Hypothesis

The Platonic Representation Hypothesis suggests that diverse, large-scale neural networks trained on similar data learn aligned internal representations. This work provides a theoretical justification for this phenomenon from an information-geometric and Bayesian perspective. We demonstrate that representation alignment is a direct consequence of posterior concentration in Bayesian learning. As the dataset size grows, the posterior distribution over model parameters concentrates on those that best approximate the true data distribution. For sufficiently expressive models (i.e., large capacity), this forces them to learn the same underlying function, resulting in aligned representations. We formalize this convergence and also prove a "disunion theorem," showing that models with different approximation capabilities will learn provably distinct representations, with a separation that grows exponentially with dataset size.