Reinforcement learning encourages artificial intelligence models to generate longer chains of thought to improve accuracy, yet forcing a single chain to run longer at inference time eventually harms results. Reasoning is effectively pathfinding through token space from a prompt toward an answer, where reinforcement learning optimizes the total likelihood of reaching a verified outcome. Systems can raise their success rate by discovering multiple low-probability routes or reinforcing a single high-probability sequence. Techniques such as best-of-$k$ sampling generate multiple paths until a verifier confirms an accurate result.
Key points
Model reasoning functions as pathfinding through token space rather than a guaranteed con…: Model reasoning functions as pathfinding through token space rather than a guaranteed convergence toward an optimal solution.
Implementing best-of-$k$ sampling helps identify successful answers by generating several…: Implementing best-of-$k$ sampling helps identify successful answers by generating several distinct paths for a verifier to evaluate.
The pathfinding framework provides a clear explanation for persistent issues like reward…: The pathfinding framework provides a clear explanation for persistent issues like reward hacking and unfaithful reasoning chains.
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There’s an intuitive but simplified picture of reasoning: let a model think for longer, and it’ll be more likely to be correct. This aligns well with our human intuition: spend more time and effort on thinking and it’s more likely that we’ll arrive at a correct answer.
But this picture doesn’t seem to explain everything. During RL training, models learn to write longer chains of thought, and they get more accurate as they do. Yet if you take a trained model and force any one chain to run longer, it helps for a while, then stops helping.1 Sometimes the answer even gets worse, as if it’s overthinking.2 If a chain of thought were truly converging toward some optimum, more steps shouldn’t make it worse. So is it really the length of each chain that helps at inference time? Or is it something more subtle?
This post is my attempt to clarify this confusion (mostly for myself) by looking at reasoning as pathfinding through token space. We’ll see that RL maximizes the probability of finding a path from $x$ to $\Scal_x$,…
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