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Introduces in-span learning, a method to adapt reduced-order models by streaming the model's own predictions through an incremental singular-value decomposition, reweighting and realigning the basis without changing the subspace. The approach is demonstrated on several dynamical systems and proposed as a computational-science analogue of in-context learning.
FuRA introduces a full-rank parameter-efficient fine-tuning method using spectral preconditioning via block tensor-train decomposition, achieving higher accuracy than full fine-tuning with LoRA-level efficiency. It outperforms LoRA and full FT on LLM and VLM tasks.