Transformer residual layers are approximated as an explicit Euler scheme for a controlled hidden-state flow whose mean-field limit is a first-order transport control problem with Pontryagin terminal condition given by the softmax residual.
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Characterizes the distributional mean-field limit of co-evolving latent space networks with feedback, including empirical measures and graphon convergence, via a conditional propagation of chaos result.
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A First-Order Mean Field Control Analysis of Transformer Layers under Cross-Entropy Training
Transformer residual layers are approximated as an explicit Euler scheme for a controlled hidden-state flow whose mean-field limit is a first-order transport control problem with Pontryagin terminal condition given by the softmax residual.
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Mean-Field Analysis of Latent Variable Process Models on Dynamically Evolving Graphs with Feedback Effects
Characterizes the distributional mean-field limit of co-evolving latent space networks with feedback, including empirical measures and graphon convergence, via a conditional propagation of chaos result.