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In-Context Learning (ICL) ability has been found efficient across a wide range of applications, where the Large Language Models (LLM) learn to complete the tasks from the examples in the prompt without tuning the parameters. In this work, we conduct a comprehensive study to understand ICL from a statistical perspective. First, we show that the perfectly pretrained LLMs perform Bayesian Model Averaging (BMA) for ICL under a dynamic model of examples in the prompt. The average error analysis for ICL is then built for the perfectly pretrained LLMs with the analysis of BMA. Second, we demonstrate how the attention structure boosts the BMA implementation. With sufficient examples in the prompt, attention is proven to perform BMA under the Gaussian linear ICL model, which also motivates the explicit construction of the hidden concepts from the attention heads' values. Finally, we analyze the pretraining behavior of LLMs. The pretraining error is decomposed as the generalization error and the approximation error. The generalization error is upper bounded via the PAC-Bayes framework. Then the ICL average error of the pretrained LLMs is shown to be the sum of O(T^{-1}) and the pretraining error. In addition, we analyze the ICL performance of the pretrained LLMs with misspecified examples.
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PRODIGY: Enabling In-context Learning Over Graphs
In-context learning is the ability of a pretrained model to adapt to novel and diverse downstream tasks by conditioning on prompt examples, without optimizing any parameters. While large language models have demonstrated this ability, how in-context learning could be performed over graphs is unexplored. In this paper, we develop Pretraining Over Diverse In-Context Graph Systems (PRODIGY), the first pretraining framework that enables in-context learning over graphs. The key idea of our framework is to formulate in-context learning over graphs with a novel prompt graph representation, which connects prompt examples and queries. We then propose a graph neural network architecture over the prompt graph and a corresponding family of in-context pretraining objectives. With PRODIGY, the pre- trained model can directly perform novel downstream classification tasks on unseen graphs via in-context learning. We provide empirical evidence of the effectiveness of our framework by showcasing its strong in-context learning performance on tasks involving citation networks and knowledge graphs. Our approach outperforms the in-context learning accuracy of contrastive pretraining baselines with hard-coded adaptation by 18% on average across all setups. Moreover, it also outperforms standard finetuning with limited data by 33% on average with in-context learning.
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- PAR ID:
- 10497850
- Publisher / Repository:
- Advances in neural information processing systems
- Date Published:
- Journal Name:
- Advances in neural information processing systems
- ISSN:
- 1049-5258
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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