Learning paradigms for large language models (LLMs)  currently tend to fall within either in-context learning (ICL)  or full fine-tuning. Each of these comes with their own trade-offs based on available data, model size, compute cost, ease-of-use, and final quality with neither solution performing well across-the-board. In this article, we first describe ICL and fine-tuning paradigms in a way that highlights their natural connections. Based on these connections, we propose a new learning paradigm calledFiat111We derive the nameFiatfromFusing Learning Paradigms withInstructionAcceleratedTuning.that fuses222Fiatfuses not only the learning paradigms but the models themselves.the best of these paradigms together, enabling prompt-engineered instructions and chain-of-thought reasoning with the verylargest modelswhile also using similar methods to perform parameter updates on amodestly-sized LLMwith parameter-efficient tuning. We evaluateFiat’s effectiveness on a variety of multilingual tasks333We say that these tasks arenaturallylow-data because no additional data is available for such languages and it’s non-trivial to obtain more; we contrast this with artificially low-data scenarios where large data exists, but is ignored.and observe thatFiatperforms better than both ICL and fine-tuning at scales ranging from 100–10,000 training examples. We hope thatFiatprovides a practical way of harnessing the full potential of LLMs without needing to make a hard choice between learning paradigms.