Large Language Models (LLMs) have demonstrated considerable advances, and several claims have been made about their exceeding human performance. However, in real-world tasks, domain knowledge is often required. Low-resource learning methods like Active Learning (AL) have been proposed to tackle the cost of domain expert annotation, raising this question: Can LLMs surpass compact models trained with expert annotations in domain-specific tasks? In this work, we conduct an empirical experiment on four datasets from three different domains comparing SOTA LLMs with small models trained on expert annotations with AL. We found that small models can outperform GPT-3.5 with a few hundreds of labeled data, and they achieve higher or similar performance with GPT-4 despite that they are hundreds time smaller. Based on these findings, we posit that LLM predictions can be used as a warmup method in real-world applications and human experts remain indispensable in tasks involving data annotation driven by domain-specific knowledge.
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