REER, or Reverse-Engineered Reasoning, is a new way to teach AI models how to think deeply and step-by-step for open-ended tasks like writing stories or essays. Unlike traditional methods that build reasoning from scratch, REER starts with a high-quality final answer and works backward to uncover the hidden thinking process that could have led to it. This creates useful "reasoning trajectories"—detailed paths of thought—for training AI to handle creative, unstructured problems.
Backward synthesis flips the process: instead of guessing thoughts to reach an answer, you start with a known good answer (like a well-written essay) and reverse-engineer the reasoning that might explain it. Using computation, you iteratively build a chain of thoughts—planning, exploring ideas, and self-correcting—that makes the final answer feel logical and natural when "simulated" by the AI. This is done without gradients (no heavy math training), making it efficient and scalable for creating training data.