Learning to Reason in 13 Parameters

This research introduces TinyLoRA, a breakthrough method for fine-tuning large language models that scales down to as few as one trainable parameter. While traditional techniques like LoRA require millions of updates, the authors demonstrate that models can achieve over 90% accuracy on complex math benchmarks using just 13 parameters. The study reveals that Reinforcement Learning (RL) is far more effective than Supervised Fine-Tuning (SFT) in this ultra-low parameter regime because RL provides a cleaner, more task-relevant signal. Experiments on Qwen2.5 and Llama-3 show that larger models are increasingly "programmable," requiring fewer absolute updates to reach peak performance. Ultimately, the paper suggests that the knowledge for reasoning already exists within pre-trained models, needing only a minimal stylistic shift to be unlocked.