arXiv AI By Zegu Zhang, Jian Zhang

A Simplex Witness Certificate and Escape Force for Constant Collapse in Variational Autoencoders

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arXiv:2605. 18224v4 Announce Type: replace-cross Abstract: We study exact constant collapse in variational autoencoders: the deterministic encoder mean becomes independent of the input.

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arXiv AI
Jun 3

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

arXiv:2606. 03003v1 Announce Type: cross 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).

By Hongbo Wang (Stony Brook University)