Autoencoders in Function Space
Read the original on arXiv Machine Learning →The paper introduces function‑space versions of autoencoders (FAE) and variational autoencoders (FVAE), analysing their theoretical properties and practical deployment. It highlights that the FVAE objective is well‑defined only when the data distribution aligns with the generative model, a restriction often met when data come from stochastic differential equations. In contrast, the FAE objective remains well‑defined in many cases where FVAE fails, and both can be paired with neural operator architectures to enable tasks such as inpainting, super‑resolution, and generative modelling of scientific data.
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