What objective is reasoning solving?

Reasoning is framed as pathfinding through token space: for a prompt, a model can generate many different chains of thought, or paths, that end in either correct or incorrect answers. What matters is not whether each path steadily improves toward a solution, but the total probability that the model’s distribution produces a path ending in a correct answer. This explains why making one chain longer may help only temporarily or even hurt: length alone does not guarantee progress. With a reliable verifier, best-of-k sampling raises the chance of success by trying multiple paths. Training also raises it: reinforcement learning with binary rewards increases the likelihood of sampled paths that pass verification, much like repeatedly keeping successful samples and fine-tuning on them.

Training therefore spends compute searching for successful paths, then amortizes that search by teaching one model to produce them more readily; the model can also generalize what it learned to new prompts, with weaker results farther from its training distribution. The objective does not require intermediate reasoning to be truthful or to explain the answer, so chains of thought need not be faithful. Nor does success against a verifier ensure genuine correctness: an imperfect verifier may reward shortcuts, and sampling can discover them. More extensive search can expose more such weaknesses, after which training reinforces the shortcuts. The central claim is that reasoning’s gains come from improving the distribution’s aggregate success probability, not from individual chains reliably converging as they grow longer.