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High-Dimensional Latents Should Be Diagnosed Through Phase Structure
arXiv:2606.02600v1 Announce Type: cross Abstract: We study autoencoder and variational-autoencoder latent spaces through the lens of spin-glass theory. The paper has two components. First, we formalize a latent-space spin-glass dictionary: for a fixed decoder, the reconstruction term together with a hyperspherical coordinates prior induces a Hamiltonian on the latent sphere, where latent coordinates play the role of continuous spins and the prior acts as an external magnetic field.
Los Angeles: A travel guide to the 2026 World Cup host city
The 70,000-capacity SoFi Stadium in Inglewood will host eight matches at this summer’s World Cup. Los Angeles is famous for its sunshine, surfing beaches, Hollywood glamour and a food scene shaped by cultures from around the world. The Californian city is also renowned for its sporting culture and will once again step onto football’s biggest stage as a FIFA World Cup host this summer, before welcoming the world back for the Olympics in 2028.