Unified Sequence Labeling that articulates different sequence labeling problems such as Named Entity Recognition, Relation Extraction, Semantic Role Labeling, etc. in a generalized sequence-to-sequence format opens up the opportunity to make the maximum utilization of large language model knowledge toward structured prediction. Unfortunately, this requires formatting them into specialized augmented format unknown to the base pretrained language model (PLMs) necessitating finetuning to the target format. This significantly bounds its usefulness in data-limited settings where finetuning large models cannot properly generalize to the target format. To address this challenge and leverage PLM knowledge effectively, we propose FISH-DIP, a sample-aware dynamic sparse finetuning strategy that selectively focuses on a fraction of parameters, informed by feedback from highly regressing examples, during the fine-tuning process. By leveraging the dynamism of sparsity, our approach mitigates the impact of well-learned samples and prioritizes underperforming instances for improvement in generalization. Across five tasks of sequence labeling, we demonstrate that FISH-DIP can smoothly optimize the model in low resource settings offering upto 40% performance improvements over full fine-tuning depending on target evaluation settings. Also, compared to in-context learning and other parameter-efficient fine-tuning approaches, FISH-DIP performs comparably or better, notably in extreme low-resource settings.

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