Towards Better Understanding of In-Context Learning Ability from In-Context Uncertainty Quantification

• URL: http://arxiv.org/abs/2405.15115v1
• Date: Fri, 24 May 2024 00:08:55 GMT
• Title: Towards Better Understanding of In-Context Learning Ability from In-Context Uncertainty Quantification
• Authors: Shang Liu, Zhongze Cai, Guanting Chen, Xiaocheng Li,
• Abstract summary: We consider a bi-objective prediction task of predicting both the conditional expectation $mathbbE[Y|X]$ and the conditional variance Var$(Y|X)$. Theoretically, we show that the trained Transformer reaches near Bayes-optimum, suggesting the usage of the information of the training distribution.
• Score: 7.869708570399577
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Predicting simple function classes has been widely used as a testbed for developing theory and understanding of the trained Transformer's in-context learning (ICL) ability. In this paper, we revisit the training of Transformers on linear regression tasks, and different from all the existing literature, we consider a bi-objective prediction task of predicting both the conditional expectation $\mathbb{E}[Y|X]$ and the conditional variance Var$(Y|X)$. This additional uncertainty quantification objective provides a handle to (i) better design out-of-distribution experiments to distinguish ICL from in-weight learning (IWL) and (ii) make a better separation between the algorithms with and without using the prior information of the training distribution. Theoretically, we show that the trained Transformer reaches near Bayes-optimum, suggesting the usage of the information of the training distribution. Our method can be extended to other cases. Specifically, with the Transformer's context window $S$, we prove a generalization bound of $\tilde{\mathcal{O}}(\sqrt{\min\{S, T\}/(n T)})$ on $n$ tasks with sequences of length $T$, providing sharper analysis compared to previous results of $\tilde{\mathcal{O}}(\sqrt{1/n})$. Empirically, we illustrate that while the trained Transformer behaves as the Bayes-optimal solution as a natural consequence of supervised training in distribution, it does not necessarily perform a Bayesian inference when facing task shifts, in contrast to the \textit{equivalence} between these two proposed in many existing literature. We also demonstrate the trained Transformer's ICL ability over covariates shift and prompt-length shift and interpret them as a generalization over a meta distribution.

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