Large language models (LLMs) excel at many tasks, but reasoning over long texts remains a challenge. They can often find the right facts buried within a massive document, but connecting those facts to answer complex questions? That's where they stumble. Instead of relying on expensive human annotations or even larger, more advanced AI models to teach them how to reason, what if LLMs could learn to reason by themselves? New research explores this intriguing possibility with an approach called SEALONG (Self-improving method for rEAsoning over LONG-contexts). The idea is surprisingly simple: generate multiple answers to a question, see which answers agree with each other the most, and then use those 'consensus answers' as a self-generated training signal. This method leverages the insight that correct reasoning paths tend to be more consistent. The results are impressive. SEALONG significantly improved the reasoning performance of several LLMs, including Llama-3.1-8B-Instruct, even surpassing the performance of larger models and models trained on datasets generated by GPT-4. This self-improvement is achieved without relying on external annotation, suggesting that LLMs possess an untapped potential for reasoning that is just waiting to be unlocked. While SEALONG represents a significant step, challenges remain. The current scoring methods aren’t perfect, and there's a need for better prompt datasets to push LLM reasoning abilities even further. However, the success of SEALONG suggests an exciting direction for future research: self-improving LLMs that can learn to reason effectively, independently, and perhaps, in ways that surprise us.