Is a Linear Probe Evidence of a Linear Representation?

Nadir Kutluozen, Christian Internò, David Klindt

The linear representation hypothesis holds that pretrained vision models encode generative factors as linearly decodable directions in feature space, and comes with a standard methodology: train a linear probe, declare a factor represented if accuracy is high. We show this test is too permissive. Asymptotically, any sufficiently rich feature map, including a random one, admits a linear readout, so high probe accuracy is consistent with two very different geometries: a true linear world model, where the latent-aligned subspace dominates the representation, or a kernel machine, where the latents lie linearly inside a much larger curved manifold. This distinction matters because the curved structure orthogonal to the probe is relevant for out-of-distribution generalization, robustness, and compositional transfer. We propose three asymmetric diagnostics that distinguish the two cases: reverse predictivity, spectral concentration, and out-of-distribution generalization. We validate them in a fully observed simulation where ground truth is known. Applied to six pretrained vision transformers on SVG-World, our deterministic generative benchmark with paired visual styles, and to two of…