In-context learning (ICL) has emerged as a central capability of pretrained language models, yet its theoretical analysis has focused primarily on causal language models trained by left-to-right autoregressive prediction, such as GPT-style models. Masked language models instead recover masked tokens from bidirectional context, and their role in ICL remains less understood. We develop a statistical learning framework that represents the context examples by their empirical measure and models prediction as a function of the context and the query. This formulation places autoregressive and masked pretraining objectives within a common excess-risk analysis. Under Wasserstein-type regularity conditions, we relate pretraining with T tasks and N samples per task to k-shot excess risk at inference, obtaining same-order upper bounds for masked and autoregressive objectives. We also study task-distribution shift, where pretraining tasks are sampled from P and inference tasks from Q; the resulting bound contains an additional term controlled by the lifted Wasserstein distance between P and Q. The bounds further imply an order-optimal allocation under a fixed pretraining data budget and refined rates under intrinsic low-dimensional structure. Experiments on controlled function-learning tasks show that the Masked Pair Encoder (MPE) can achieve performance comparable to GPT-2-style causal Transformers, suggesting that ICL behavior is not specific to causal language models.
The factors driving the performance of in-context learning (ICL) in large language models (LLMs) remain poorly understood despite ICL's surprising effectiveness, enabling models to adapt to new tasks from only a handful of examples. To clarify and improve these capabilities, we characterize how the statistical properties of the pretraining distribution (e.g., tail behavior, coverage) shape ICL. We develop a theoretical framework that encompasses generalization and task selection and show how distributional properties govern sample efficiency, task retrieval, and robustness. To this end, we generalize existing concentration results to heavy-tailed priors and dependent sequences, better reflecting the structure of LLM pretraining data. Our framework reveals a fundamental design trade-off: heavy-tailed pretraining distributions facilitate robust task selection under distribution shifts but are detrimental to generalization, especially in low-data regimes. We then empirically evaluate our predictions by studying how ICL performance varies with the pretraining distribution on challenging tasks such as stochastic differential equations and stochastic processes with memory. Together, these findings suggest that controlling key statistical properties of the pretraining distribution is essential for building ICL-capable and reliable LLMs.
In-context learning (ICL) is an emerging paradigm that employs the semantic information inherent in large language models (LLMs) for generating answers to user queries. While the remarkable performance of ICL has been widely known, a general modeling and a rigorous theoretical analysis of this paradigm are still lacking. This work presents a probabilistic model for ICL and derives the performance of ICL for both general parametric distributions and exponential families. Based on the derived results, the work explains the impact of multiple factors such as the number of demonstrations, the sensitivity of the probabilistic model to the variation of its parameters, as well as the similarity between the demonstrations and the query on the performance of ICL.
In-context learning (ICL) derives its power from enabling Large Language Models to adapt to new tasks via prompt-based reasoning alone, entirely bypassing the need for parameter updates. Existing theories primarily study ICL in single-task settings, while real-world prompts often contain sequences of heterogeneous tasks, leaving a gap in understanding whether Large Language Models implicitly perform continual learning during inference. To bridge this gap, we propose the first theoretical framework for in-context continual learning, modeling how a pretrained Transformer processes multiple sequential tasks within a single prompt through shared attention mechanisms. Focusing on linear and masked linear self-attention, we derive error expressions for model predictions under sequential task prompts and analyze their generalization and forgetting behavior. Our results reveal that standard attention mechanisms inevitably induce intertask interference by uniformly or causally aggregating historical contexts, leading to systematic bias. We further provide a bias-variance-interference decomposition of prediction error, characterizing when historical in-context information yields positive transfer or provable negative transfer. This analysis exposes fundamental limits of attention-based continual inference and offers theoretical explanations for order sensitivity and performance degradation in long prompts.