New paper links gradient descent to implicit EM in neural networks

A new paper proposes that gradient descent in certain neural network objectives functions as an implicit Expectation-Maximization (EM) algorithm. The research demonstrates that for objectives involving log-sum-exp structures over distances or energies, the gradient with respect to each distance is precisely the negative posterior responsibility of the corresponding component. This algebraic identity, a specialization of Fisher's identity, means that standard neural network training implicitly performs generalized EM without explicit auxiliary variables. The findings unify unsupervised mixture modeling, attention mechanisms, and cross-entropy classification, explaining phenomena like soft clustering and Bayesian uncertainty tracking observed in models such as transformers. AI

IMPACT Provides a theoretical framework that could lead to more efficient and interpretable neural network training.

RANK_REASON The cluster contains a single academic paper detailing a new theoretical insight into neural network training dynamics. [lever_c_demoted from research: ic=1 ai=1.0]

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• Alan Oursland
• alphaXiv
• arXiv
• CatalyzeX
• DagsHub
• Fisher's identity
• Gotit.pub
• Hugging Face
• ScienceCast
• transformers

• paper
• model release

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