Function graph transformers use graph measures to provide a measure-theoretic framework where standard transformer components universally approximate operators between function spaces while preserving single-valued function outputs.
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Global well-posedness and quantitative flocking are shown for Lagrangian p-alignment dynamics; Eulerian variables are constructed via pushforward and disintegration, with defect terms vanishing asymptotically under heavy-tailed kernels to give mono-kinetic closure and mean-field convergence.
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Function graph transformers universally approximate operators between function spaces
Function graph transformers use graph measures to provide a measure-theoretic framework where standard transformer components universally approximate operators between function spaces while preserving single-valued function outputs.
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Lagrangian formulation and Eulerian closure in alignment dynamics
Global well-posedness and quantitative flocking are shown for Lagrangian p-alignment dynamics; Eulerian variables are constructed via pushforward and disintegration, with defect terms vanishing asymptotically under heavy-tailed kernels to give mono-kinetic closure and mean-field convergence.