MAGIA: Sensing Per-Image Signals from Single-Round Averaged Gradients for Label-Inference-Free Gradient Inversion

Abstract

We study gradient inversion in the challenging single round averaged gradient SAG regime where per sample cues are entangled within a single batch mean gradient. We introduce MAGIA a momentum based adaptive correction on gradient inversion attack a novel label inference free framework that senses latent per image signals by probing random data subsets. MAGIA objective integrates two core innovations 1 a closed form combinatorial rescaling that creates a provably tighter optimization bound and 2 a momentum based mixing of whole batch and subset losses to ensure reconstruction robustness. Extensive experiments demonstrate that MAGIA significantly outperforms advanced methods achieving high fidelity multi image reconstruction in large batch scenarios where prior works fail. This is all accomplished with a computational footprint comparable to standard solvers and without requiring any auxiliary information.