Trajectory-Aware Information Matching for Multi-Step Gradient Inversion in Federated Learning

Federated learning (FL) enables multiple data holders to train machine learning models collaboratively without centralizing raw data, making it useful in privacy sensitive domains such as healthcare and institutional data sharing. FL keeps data local to clients while communicating only model updates, such as gradients or model deltas. Nevertheless, these updates can expose private client data through gradient inversion attacks (GIAs). We study this risk for tabular FL under an honest-but-curious server threat model across FL protocols, client batch sizes, training stages, attacker assumptions, model architectures, and binary classification, multiclass classification, and regression tasks. We use MIMIC-IV and complementary benchmark datasets. Our evaluation distinguishes numerical and categorical recovery, baseline recoverability, feature level recovery, and exact match rate (EMR). We evaluate FedSGD gradients and FedAvg model deltas with an exposure aligned protocol, comparing attacked models after matched client data exposure rather than matched communication rounds. We compare multilayer perceptron (MLP), ResNet, and FT-Transformer models, and isolate architecture effects through an MLP grid over width, depth, activation, normalization, and dropout. The results show that small client batches and updates representing few distinct records are most vulnerable. Larger local batches and stronger aggregation reduce reconstruction but do not eliminate leakage. FT-Transformer is consistently harder to invert than one-hot baselines, while reconstructability also varies substantially within the MLP family. These findings identify architecture as a practical privacy variable in tabular FL. We also show that aggregate reconstruction accuracy can overstate complete record recovery in sparse data, making EMR and baseline comparisons essential.

Gradient inversion attacks threaten client privacy in federated learning by reconstructing training samples from clients' shared gradients. Gradients aggregate contributions from multiple records and existing attacks may fail to disentangle them, yielding incorrect reconstructions with no intrinsic way to certify success. In vision and language, attackers may fall back on human inspection to judge reconstruction plausibility, but this is far less feasible for numerical tabular records, fueling the impression that tabular data is less vulnerable. We challenge this perception by proposing a verifiable gradient inversion attack (VGIA) that provides an explicit certificate of correctness for reconstructed samples. Our method adopts a geometric view of ReLU leakage: the activation boundary of a fully connected layer defines a hyperplane in input space. VGIA introduces an algebraic, subspace-based verification test that detects when a hyperplane-delimited region contains exactly one record. Once isolation is certified, VGIA recovers the corresponding feature vector analytically and reconstructs the target via a lightweight optimization step. Experiments on tabular benchmarks with large batch sizes demonstrate exact record and target recovery in regimes where existing state-of-the-art attacks either fail or cannot assess reconstruction fidelity. Compared to prior geometric approaches, VGIA allocates hyperplane queries more effectively, yielding faster reconstructions with fewer attack rounds.

Federated learning shares model updates rather than raw data, yet these updates can be inverted to reconstruct the clients' training data. Analytic reconstruction attacks, which invert a gradient in closed form, degrade as the batch grows: prior single-round attacks recover only about half of a batch of size $100$ even when the attacker fully controls the network parameters, and known upper bounds limit what any such method can recover. We establish a connection between gradient inversion and the theory of erasure-correcting codes, and use it to construct attacks that exceed these bounds. Our attacks recover batches exactly, together with every sample's label, from a single FedSGD round, and certify each recovery without ground-truth data. On eight image and tabular benchmarks they outperform prior single-round attacks by a wide margin. Even a passive attacker who only observes an honestly trained network recovers $94$--$100\%$ of ImageNet batches at sizes up to $128$, more than prior single-round attacks achieve even with active manipulation of the model, and in the active setting more than $90\%$ is recovered at batch sizes of several hundred. These results show that the privacy leakage of federated learning has been underestimated.