A mean-field kinetic theory derivation produces a closed-form U-shaped token retrieval profile that explains the lost-in-the-middle phenomenon in Transformers.
A duality method for mean-field limits with singular interactions
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
citation-role summary
background 1
method 1
citation-polarity summary
fields
math.AP 3years
2026 3representative citing papers
Empirical measures from Kac's particle system converge to the Boltzmann equation solution for very soft potentials, proving propagation of chaos for all kernel classes.
Duality-based analysis yields fluctuation-scale O(N^{-1/2}) mean-field convergence for L2 interactions and optimal O(N^{-1}) rates plus correlation bounds under higher regularity via iterative dual cumulants.
citing papers explorer
-
Kinetic theory for Transformers and the lost-in-the-middle phenomenon
A mean-field kinetic theory derivation produces a closed-form U-shaped token retrieval profile that explains the lost-in-the-middle phenomenon in Transformers.
-
Propagation of chaos for the Boltzmann equation with very soft potentials
Empirical measures from Kac's particle system converge to the Boltzmann equation solution for very soft potentials, proving propagation of chaos for all kernel classes.
-
Quantitative Estimates for Mean-Field Limits and Correlation Functions through a Duality Framework
Duality-based analysis yields fluctuation-scale O(N^{-1/2}) mean-field convergence for L2 interactions and optimal O(N^{-1}) rates plus correlation bounds under higher regularity via iterative dual cumulants.