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Threshold characterization of distribution shift for in-context learning robustness in Transformers

Derive and prove a threshold condition on covariate shift severity under which Transformer models retain in-context learning capability, without relying on the Neural Tangent Kernel framework, by adapting the covariate-shift analyses of Pathak et al. (2022) and Ma et al. (2023) to the in-context learning setting for kernel-regressor views of large language models.

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Background

The survey highlights empirical findings that Transformers exhibit robustness to mild distribution shifts in in-context learning (ICL), but this robustness degrades under severe shifts. It frames the problem of determining the fundamental limit of shift severity beyond which ICL fails.

It points to recent theoretical treatments of covariate shift in nonparametric regression (Pathak et al., 2022; Ma et al., 2023) and a kernel-regression perspective on ICL (Han et al., 2023), and conjectures that these tools could yield a quantitative threshold for shift tolerance in ICL. A rigorous threshold would inform when ICL generalization guarantees hold under distribution shifts.

References

Without using the NTK framework, there is a recent work which studied in-context learning of LLMs in the context of kernel regressors, we conjecture that the theoretical analysis used in can be utilized for obtaining the threshold limit.

— A Survey on Statistical Theory of Deep Learning: Approximation, Training Dynamics, and Generative Models (2401.07187 - Suh et al., 14 Jan 2024) in Section 6, Distribution Shift and Robustness (Q2)