Large language models (LLMs) have exhibited an emergent in-context learning (ICL) ability. However, the ICL models that can solve ordinary cases are hardly extended to solve more complex tasks by processing the demonstration examples once. This single-turn ICL is incoordinate with the decision making process of humans by learning from analogy. In this paper, we propose an effective and efficient two-stage framework to boost ICL in LLMs by exploiting a dual form between Transformer attention and gradient descent-based optimization. Concretely, we divide the ICL process into "Deep-Thinking" and inference stages. The "Deep-Thinking" stage performs iterative forward optimization of demonstrations, which is expected to boost the reasoning abilities of LLMs at test time by "thinking" demonstrations multiple times. It produces accumulated meta-gradients by manipulating the Key-Value matrices in the self-attention modules of the Transformer. Then, the inference stage only takes the test query as input without concatenating demonstrations and applies the learned meta-gradients through attention for output prediction. In this way, demonstrations are not required during the inference stage since they are already learned and stored in the definitive meta-gradients. LLMs can be effectively and efficiently adapted to downstream tasks. Extensive experiments on ten classification and multiple-choice datasets show that our method achieves substantially better performance than standard ICL in terms of both accuracy and efficiency.

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