One-shot and few-round federated learning (FL) reduce communication burden by constructing a global model within one or a few communication rounds, but often achieve lower performance than conventional multi-round FL. Without frequent synchronization, client models may drift apart, causing neurons that learn similar features to occupy different positions across clients. At the same time, local data heterogeneity can cause corresponding parameters to differ in their importance to each client's predictions. Together, these challenges cause direct averaging to combine mismatched neurons and assign equal weight to parameters despite differences in their importance. We propose FedFiOT, a Fisher-weighted optimal transport framework for one-shot and few-round FL that leverages Fisher information to quantify parameter importance and guide neuron alignment and model aggregation. FedFiOT jointly optimizes neuron correspondences and global model parameters through alternating minimization of a shared Fisher-weighted objective. Theoretically, we show that FedFiOT's optimization procedure monotonically decreases the layer-wise merging objective and establish a stationarity bound that quantifies the effects of client heterogeneity and nonuniform Fisher weighting.Experiments across multiple datasets demonstrate consistent improvements over competing baselines in both one-shot and few-round federated learning settings.

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