Large language models (LLMs) are impressive, but their reasoning abilities often lag behind their human counterparts. Especially with smaller, open-source LLMs, getting them to think logically and solve problems step-by-step has been a challenge. Researchers are constantly working on ways to improve these models, and a new study explores a fascinating technique called 'Fault-Aware Distillation via Peer-Review' (FAIR). Imagine a classroom where students take an exam and then, instead of just getting the correct answers, they receive detailed feedback on *why* their reasoning was flawed, coming not from just one instructor but a whole committee of experts. That's the core idea behind FAIR. The research team used multiple large language models (like GPT-3.5-Turbo, Gemini, and Mixtral) as 'teachers.' These teachers generate correct solutions *and* provide specific feedback on a student LLM's incorrect answers. What’s more, these teacher LLMs participate in a simulated peer-review process. They evaluate each other’s reasoning, and only the most highly-rated explanations make it into the student’s learning material. This ensures the student model learns from the best possible examples. The results? Impressive gains in reasoning ability across various tasks, from mathematics and commonsense to logical problem-solving. By using multiple teachers and the innovative peer-review process, FAIR allows smaller LLMs to mimic the way humans learn: by understanding not just the right answers but also the logic behind their own mistakes. This approach holds promise for making AI more intelligent and its reasoning processes more transparent. While this research focused on a specific set of LLMs, the principles behind FAIR could have wider implications. Imagine applying these techniques to different AI models and across diverse problem domains. Future research could explore adding continuous feedback loops, incorporating more complex learning strategies, and fine-tuning the balance between learning correct answers and understanding mistakes. These advancements might open up new possibilities for creating even more effective AI instructors, leading to the development of much smarter and more reliable AI systems.