Large language models (LLMs) have demonstrated remarkable abilities in various natural language processing areas, but they demand high computation resources which limits their deployment in real-world. Distillation is one technique to solve this problem through either knowledge distillation or task distillation. Both distillation approaches train small models to imitate specific features of LLMs, but they all neglect basic reading education for small models on generic texts that are unrelated to downstream tasks. In this paper, we propose basic reading distillation (BRD) which educates a small model to imitate LLMs basic reading behaviors, such as named entity recognition, question raising and answering, on each sentence. After such basic education, we apply the small model on various tasks including language inference benchmarks and BIG-bench tasks. It shows that the small model can outperform or perform comparable to over 20x bigger LLMs. Analysis reveals that BRD effectively influences the probability distribution of the small model, and has orthogonality to either knowledge distillation or task distillation.

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, including mathematical reasoning. However, the current evaluation mostly focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing or contradictory conditions, known as ill-defined problems. To further study this problem, we develop a large-scale benchmark called Problems with Missing and Contradictory conditions (PMC) containing over 5,000 validated ill-defined mathematical problems. Our preliminary experiments through PMC reveal two challenges about existing methods: (1) traditional methods exhibit a trade-off between solving accuracy and rejection capabilities, and (2) formal methods struggle with modeling complex problems. To address these challenges, We develop Variable-Constraint Search (VCSearch), a training-free framework that leverages formal language to detect ill-defined problems, where a variable-constraint pair search strategy is incorporated to improve the modeling capability of formal language. Extensive experiments demonstrate that VCSearch improves the accuracy of identifying unsolvable problems by at least 12% across different LLMs, thus achieving stronger robust mathematical reasoning ability.