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.

Low-Rank Adaptation (LoRA) has emerged as a parameter-efficient approach for fine-tuning large language models. However, conventional LoRA adapters are typically trained for a single task, limiting their applicability in real-world settings, where inputs may span multiple, diverse task domains. At inference time, existing methods can combine multiple LoRAs to improve cross-task performance, but they require additional labeled data or task-specific training, which is expensive at scale.In this work, we introduce LoRA on the Go (LoGo), a training-free framework that dynamically selects and merges adapters at the instance level without any additional requirements. LoGo leverages signals extracted from a single forward pass through LoRA adapters, to identify the most relevant adapters and determine their contributions on-the-fly. Across 5 NLP benchmarks, 27 datasets, and 3 model families, LoGo outperforms training-based baselines on some tasks upto a margin of 3.6% while remaining competitive on other tasks and maintaining inference throughput, highlighting its effectiveness and practicality.