上下文學習的能力是使大型語言模型能夠泛化在各種任務上的關鍵，只需要透過提示詞，模型不需要重新訓練也能夠正確預測未曾看過的題目，然而，這種泛化能力卻沒有體現在長度上，上下文學習的能力很可能在長度過長時消失，導致生成的文字產生錯誤。為了研究這個問題，我們提出了使用上下文函數類的資料集來理解 Transformer 模型在上下文學習和長度泛化性上運作模式，我們使用了回歸函數和布林函數生成資料，並使用元學習的方式讓模型具有上下文學習的能力，實驗結果顯示，位置編碼能夠很好地克服長度泛化性的問題，最好的位置編碼能將最大長度外推到原有訓練長度的八倍以上。接著，透過分析實驗，我們還發現了位置編碼雖然提升了長度泛化性，卻相對地犧牲了模型原有的能力，導致資料泛化性下降，比如歸納問題的能力。整體而言，我們的研究說明位置編碼對長度泛化性具有顯著的正向效果，但需要小心權衡資料泛化性的損失。

The capability of In-Context Learning (ICL) is crucial for large language models to generalize across a wide range of tasks. By utilizing prompts, these models can accurately predict outcomes for previously unseen tasks without necessitating retraining. However, this generalization ability does not extend to the length of the inputs; the effectiveness of ICL likely diminishes with excessively long inputs, resulting in errors in the generated text. To investigate this issue, we propose a study using a dataset of In-Context functions to understand the operational mechanisms of Transformer models in ICL and length generalization. We generated data using regression and Boolean functions and employed meta-learning techniques to endow the model with ICL capabilities. Our experimental results indicate that position encodings can significantly mitigate length generalization issues, with the most effective encoding extending the maximum input length to over eight times that of the original training length. However, further analysis revealed that while position encoding enhances length generalization, it compromises the model's inherent capabilities, such as its ability to generalize across different data types. Overall, our research illustrates that position encodings have a pronounced positive effect on length generalization, though it necessitates a careful trade-off with data generalization performance.

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