Exact equivariance, kept through training, buys zero-shot generalisation across the symmetry group

arXiv:2606.03003v1 Announce Type: new Abstract: A latent world model built from an equivariant encoder $E$ and an equivariant predictor $f$ inherits a provable symmetry of its training loss: when the world's dynamics genuinely carries a group $G$ acting on latents by an orthogonal representation $\rho(g)$, the one-step prediction relMSE is exactly invariant across the whole group, so fitting the dynamics on a restricted slice of orientations mathematically determines it on the entire orbit (j\v{u} y\=i f\v{a}n s\=an). We verify this end-to-end at laptop scale (CPU/MPS, fully seeded). [A] The s

Source: arXiv cs.LG — read the full report at the original publisher.

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