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Mean-Field

Feb 2, 2026 ML Math Derivations 14 min read

Machine Learning Mathematical Derivations (14): Variational Inference and Variational EM

A first-principles derivation of variational inference. From the ELBO identity and the mean-field assumption to the CAVI updates, variational EM, and the reparameterization trick that powers VAEs.

May 31, 2024 PDE and Machine Learning 17 min read

PDE and Machine Learning (3): Variational Principles and Optimization

What is the essence of neural-network training? When we run gradient descent in a high-dimensional parameter space, is there a deeper continuous-time dynamics at work? As the network width tends to …