Platonic representation of foundation machine learning interatomic potentials

Abstract

Foundation machine learning interatomic potentials (MLIPs) have emerged as powerful tools for atomistic simulation, yet different models encode chemical environments in incompatible latent spaces, limiting direct comparison and interoperability. The platonic representation hypothesis suggests that sufficiently capable models converge towards a shared statistical representation of reality. Here, motivated by this hypothesis, we show that independently developed MLIPs exhibit statistically consistent geometric organization of atomic environments. By projecting embeddings relative to a set of atomic anchors, we unify the latent spaces of seven MLIPs—spanning equivariant, non-equivariant, conservative and non-conservative architectures—into a common latent space that preserves chemical periodicity and structural invariants. This unified framework enables cross-model optimal transport, interpretable embedding arithmetic and the detection of representational biases. Furthermore, we show that deviation in this space provides a ground-truth-free measure for atypical structures, and signals physical prediction failures. Our results suggest that the platonic representation offers a practical route towards interoperable, comparable and interpretable foundation models for materials science.