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arXiv

PI-SME reconstructs FedAvg multi-step gradient updates via Gauss–Legendre quadrature along a learnable Bézier path, surpassing the strongest surrogate baseline on CIFAR-100 and FEMNIST

The work proposes the Path-Integral Surrogate Model Extension (PI-SME), which treats the accumulated multi-step update in FedAvg as a path integral of the gradient field along the client trajectory and approximates it by Gauss–Legendre quadrature over several nodes along a learnable Bézier path; on CIFAR-100 and FEMNIST images, PI-SME reconstructs private inputs more faithfully than the strongest surrogate baseline NL-SME on several inversion metrics and the matching loss, with the largest gains on long trajectories and class-restricted batches.