Large language models (LLMs) process entire input contexts indiscriminately, which is inefficient when the information required to answer a query is localized within the context. We present dynamic context cutoff, a novel method enabling LLMs to self-terminate processing upon acquiring sufficient task-relevant information. Through analysis of model internals, we discover that specific attention heads inherently encode "sufficiency signals" -- detectable through lightweight classifiers -- that predict when critical information has been processed. This reveals a new efficiency paradigm: models' internal understanding naturally dictates processing needs rather than external compression heuristics. Comprehensive experiments across six QA datasets (up to 40K tokens) with three model families (LLaMA/Qwen/Mistral, 1B-70B) demonstrate 3.4% accuracy improvement while achieving 1.33x token reduction on average. Furthermore, our method demonstrates superior performance compared to other context efficiency methods at equivalent token reduction rates. Additionally, we observe an emergent scaling phenomenon: while smaller models require probing for sufficiency detection, larger models exhibit intrinsic self-assessment capabilities through prompting.

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