Is There a Platonic Tree? Calibrating Latent Hyperbolicity in Foundation Models

Hyperbolic representation learning rests on a premise we call latent hyperbolicity: standard models are already tree-like because their class geometry scores a low Gromov $\delta$, a measure of tree-likeness that is zero for a tree. That low value is also what a random cloud of the same dimension and spread scores. We introduce a calibrated framework that reads tree-likeness as its excess over such structureless clouds, together with a second test, whose power we measure, designed to distinguish hierarchical organization from simple clustering. We apply it to 12 vision backbones, 6 datasets and 15 text models. On image features, where the premise is read, the calibrated reading is indistinguishable from a random cloud in most model-dataset cells and small elsewhere. Class centroids do carry structure that a random cloud of the same shape does not, in 44 of 72 cells, but so does a star of clusters. The second test finds no detectable hierarchy among superclasses in the 9 of 12 backbones where it detects a planted one. What it finds in 4 of them is how each cluster is oriented, which disappears when clusters are rotated at random. MERU, trained in hyperbolic space, shows the same structure as its Euclidean twin in a space that stays nearly flat. In text, the result depends on the model's training recipe and size. Across models, the trees agree on which classes group together well above chance, though less than two resampled versions of the same model, and not on distances; the self-supervised models organize classes by direction rather than by distance, which a comparison by distance misses. Read correctly, foundation models organize classes into clusters that they partly share and show no detectable hierarchy among the superclasses where the test has power. Their raw tree-likeness is not evidence for hyperbolic geometry.