Given the high cost of expert annotation and limited fine-tuning resources, effective data selection from large unlabeled pools under strict budgets has become a crucial step in adapting LLMs to specialized domains. Existing label-dependent methods risk distorted selection when using pseudo-labels, while traditional active learning methods do not explicitly characterize instruction-tuning dynamics. To address these limitations, we propose Hidden Cartographer (HC), a two-stage framework that uses hidden states to guide annotation and exact training dynamics to select the final training subset. The first stage is Progressive Candidate Expansion, which utilizes the proxy to iteratively select top unlabeled candidates for expert annotation, merging them to recompute training dynamics and update the proxy until the annotation budget is exhausted; the second stage is Exact Cartography Pruning, which ranks these annotated candidates by their exact dynamics scores to isolate a compact subset under the final training budget. Experiments across the medical, legal, and financial domains demonstrate that HC achieves the highest average accuracy among all budgeted baselines, requiring annotation for only 20--30% of the original pool and fine-tuning on just 10--15%.

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