Imagine an AI that not only solves problems but learns from its mistakes, getting smarter with each attempt. Researchers have developed a new technique called RISE (Recursive Introspection) that allows language models to do just that. Unlike traditional AI that receives static training, RISE-trained models treat problem-solving as a multi-turn process. They start with an initial attempt, then analyze their own work, identifying errors and refining their approach. This recursive process, inspired by how humans learn, allows the AI to improve its performance over multiple tries. The key to RISE lies in how it structures this learning process. It converts single-turn problems, like math questions, into a multi-turn sequence. After each attempt, the AI either consults a 'teacher' model for the correct answer or uses a clever self-distillation method where it generates multiple answers and selects the best one. This feedback is used to fine-tune the model, essentially teaching it how to learn from its mistakes. Initial results are promising. LLMs trained with RISE demonstrated significant improvement on math reasoning tasks, outperforming traditional training methods. What’s even more exciting is that RISE-trained models can also tackle new, unseen problems more effectively, suggesting the learned self-improvement strategy generalizes well. This ability for AI to learn and improve on its own could have far-reaching implications, from more efficient problem-solving to the development of truly autonomous learning agents. While challenges remain, like scaling the technique for more complex tasks and refining the self-distillation process, RISE offers a glimpse into a future where AI can not just solve, but also learn.