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Low-rank adaptation (LoRA) provides a parameter-efficient approach to continual learning, but its nominal rank can conceal a loss of effective adaptation capacity. We identify \emph{spectral plasticity collapse}: during sequential adaptation, update energy becomes concentrated in a small subset of singular modes, leavi...
Adaptive preconditioners accelerate model training, but heterogeneous client geometries can bias federated updates even when gradients are evaluated at the same model. Round-start synchronization alone cannot prevent this mismatch from reappearing during local training. We propose \texttt{FedMIX-P}, which mixes shared...
Federated training of foundation models is constrained by client memory and communication costs. LoRA-based methods reduce these costs through low-rank adapters, but their fixed rank budget can limit adaptation. Gradient low-rank optimization offers greater flexibility, yet independently chosen client subspaces create...
The analysis isolates a testable trade-off: extending the prediction path provides more forward-looking gradient information but increases its displacement bias, which is a testable trade-off in the case of full-participation FedAvg-M.
Experiments on vision and language tasks across multiple privacy budgets show that DP-Merging consistently improves private merged-model performance while preserving the privacy guarantees of the underlying DP fine-tuning procedures.
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