Large language models (LLMs) operate in two fundamental learning modes - fine-tuning (FT) and in-context learning (ICL) - raising key questions about which mode yields greater language proficiency and whether they differ in their inductive biases. Prior studies comparing FT and ICL have yielded mixed and inconclusive results due to inconsistent experimental setups. To enable a rigorous comparison, we propose a formal language learning task - offering precise language boundaries, controlled string sampling, and no data contamination - and introduce a discriminative test for language proficiency, where an LLM succeeds if it assigns higher generation probability to in-language strings than to out-of-language strings. Empirically, we find that: (a) FT has greater language proficiency than ICL on in-distribution generalization, but both perform equally well on out-of-distribution generalization. (b) Their inductive biases, measured by the correlation in string generation probabilities, are similar when both modes partially learn the language but diverge at higher proficiency levels. (c) Unlike FT, ICL performance differs substantially across models of varying sizes and families and is sensitive to the token vocabulary of the language. Thus, our work demonstrates the promise of formal languages as a controlled testbed for evaluating LLMs, behaviors that are difficult to isolate in natural language datasets. Our source code is available at https://github.com/bishwamittra/formallm.
Instruction following is a critical ability for Large Language Models to be used directly by humans. This often requires supervised fine-tuning on curated instruction datasets, sometimes complemented with an alignment step. However, in multilingual scenarios, obtaining high-quality data for these stages remains challenging, motivating the exploration of In-Context Learning (ICL) as a possible alternative. In this work, we study whether ICL can serve as a substitute for Instruction Tuning in multilingual language models, while also examining how the comparison changes with model scale. Our results indicate that a gap remains between ICL and Instruction Tuning, motivating further research to reduce it.
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.
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.