Search Over Thoughts

Instead of one chain of reasoning, explore a tree of them: generate several possible next steps, evaluate which look promising, expand those, and abandon the rest. It turns reasoning from generation into search, and the classical search machinery — breadth, depth, backtracking, an evaluation function — applies directly.

The evaluation function is where this lives or dies. Search only helps if partial states can be scored better than at random, and a model asked to rate its own half-finished reasoning is a weak evaluator on exactly the problems where search would help most. That is the same dependency Monte Carlo Tree Search has on its value function, arriving in a domain with no simulator to ground it — so the branching gets narrow and shallow in practice, far short of what the framing suggests.

Cost is the branching factor to the power of the depth, which is why nothing runs deep. At branching 5 and depth 4 that is 625 model calls for one answer, against one — so the interesting comparison is never search versus greedy but search versus spending the same 625 calls on independent samples with a verifier. Flat sampling wins more often than the tree framing suggests, and it wins because it needs no evaluation of partial states at all.