World-Model Gate
The page starts where the theorem starts: world state, observation, encoder, alignment, Gaussian regularization, then the only question that matters.
The hard bar in this episode is not probe accuracy. It is linear identifiability: one fixed global map must recover the hidden state well enough that planning and compositional generalization survive in latent space.
The page starts where the theorem starts: world state, observation, encoder, alignment, Gaussian regularization, then the only question that matters.
Hot cells mean the representation passes the stricter recovery test, not just a task-specific probe.
The lower-right trap is real: a representation can help downstream tasks while still scrambling the latent state.
Toggle the latent law. In the Gaussian regime the learned coordinates collapse to a rotation; outside it, nonlinear warps can remain objective-compatible.
The Gaussian proof uses spectral structure to make the linear component dominate; the heatmap shows how sharply that pressure changes with the latent law.
Mocked from the episode’s summary of the paper: SIGReg and VICReg stay near-perfect, while fixed-width InfoNCE degrades as latent dimension grows.
The Gaussian point is not just convenient. It is the sharp peak.
The paper’s cleanest guarantees live in synthetic worlds. The robot bridge is still useful, but it is where assumptions start leaking.
Theorem 4 only covers costs that are invariant to orthogonal transforms. Switch the cost geometry and the latent plan stops matching the oracle.
Pixels → CNN → latent → one linear state map → planner. The bridge is practical evidence, not the theorem itself.
ArXiv-linked papers used to anchor the visual story, plus prior AI Post Transformers episodes for context.