Big Reasoning with Small Models: Instruction Retrieval at Inference Time

The facts a language model stores are tied to its parameter count, so small models that fit on edge devices fail on expert problems, which need specialized knowledge and follow multi-step procedures. Fine-tuning for a specific domain or task writes the knowledge into the parameters but must be repeated for every model and domain, and a retrieved passage leaves the model to find the relevant fact and apply it on its own. We introduce instruction retrieval, which distills a teacher model's expertise into a corpus of instructions tailored so that a small model can follow. For each cluster of a domain's problems, the teacher writes one instruction with the background knowledge the cluster depends on, a procedure for that kind of problem, and the common mistakes made on it. This reusable corpus needs only to be built once per domain and requires no run-time teacher access. At inference, a frozen small model retrieves the instructions nearest its question and follows them, with no fine-tuning. Across medicine, law, and mathematics benchmarks, we demonstrate the corpus improves over zero-shot on every task and over few-shot prompting, self-consistency, and other retrieved text on medicine and law. On MedQA the corpus raises mean accuracy by 10.6 points, where retrieved textbook passages raise it by 3.9 and few-shot examples from the same teacher lower it. An error analysis shows that only the background knowledge fixes the questions a small model always gets wrong, and that the procedure and common mistakes fix only the questions where it wavers between options. Our results show that automatically retrieved inference-time procedural guidance and domain knowledge can yield substantial gains for small models.