The cheapest-looking way to cut reasoning-model cost is to keep asking a half-finished chain of thought what its answer is so far, and stop once several checks in a row come back the same. This paper registers three cost-and-accuracy targets in advance, sweeps 3,520 versions of that rule over frozen traces from four models, and clears none of them. At the best rule still saving 32% of tokens, one stop in nine lands on an answer the trajectory itself later abandons — and those stops overwhelmingly remove the computation that was about to correct it, 155 corrections cut against 57 answers rescued. Widening the agreement window does not fix it. A rule that reads the model's confidence at a natural break in the reasoning, swept identically, cleared all three targets.
The method under test is simple enough that most teams have already tried a version of it. While the model is thinking, interrupt it every so often and ask for its current answer in a couple of tokens. Keep a window of those answers. Once enough of the window says the same thing, take that answer and stop decoding. Nothing about the model changes; you are just betting that a stable answer is a finished one.
The sweep varies everything you would tune: how many recent checks to look at, what fraction of them must agree, how often to check, how many tokens to let the model think before any stop is allowed, whether to require the check to read as confident. That is 3,520 rules. The three acceptance targets were written down before any of them ran — pick one and see what the best rule in the family actually delivered against it.
The pattern is the same at every target. Ask consensus for an accuracy guarantee and the savings collapse to nothing; ask it for savings and the accuracy goes. The control method — read how confident the model is at a natural break in its reasoning, rather than whether its answers agree — was swept through the identical pipeline and cleared all three.
The obvious fix is to be stricter: wait for more checks to agree before you believe them. It works, in the sense that fewer of the stops are premature. It just takes all the savings with it, and the premature stops never actually go away — the share flattens out around seven percent while the saving falls to eight.
Drag the window. The strip is the trajectory: each cell is a stop that fired, and the red cells are the stops that landed on an answer the model itself later abandoned.
The other column in that table is the one that should end the idea. Of the premature stops at the rule still saving a third of the tokens, more than seven in ten cut off a correction the trajectory would have made; the rest mostly swapped one wrong answer for another. Against that, a small number of stops bank a correct answer from a trajectory that was going to end wrong. The ratio is 155 to 57 — meaning the computation an agreement stop removes is, on average, exactly the computation that was about to fix the answer.
Here is the diagnosis, and it is why no amount of tuning rescues the rule. Asking a partial trajectory for its answer does not read out a conclusion the model has reached; it forces one. Agreement between those forced answers establishes that the answer is stable under a fixed way of asking — not that the reasoning has terminated. The paper calls the difference a consensus–termination gap.
Two pieces of evidence. First, hand-label every wrong stop and ask what was actually there: only a quarter were cases where the model had genuinely settled on a wrong value.
Second, change nothing but the wording of the probe and re-ask at the same frozen points in the same trajectories. Early on, the two wordings disagree about the model's own current answer more than half the time. That number falls as the trajectory runs, which is the tell: the answer is not sitting there waiting to be read, it is being constructed by the question, and only late in the reasoning does it stop depending on how you ask.
Put those together with what happens if you simply stop at the first moment a rule could fire, and the size of the gap is obvious.
The control is a boundary-confidence rule: instead of asking the model for its answer on a fixed grid and watching for agreement, it waits for a natural break in the reasoning and reads how confident the model is in the answer it would give there. Swept through the same preregistered machinery, it cleared every target — around thirty percent of the tokens for roughly a point of accuracy.
The paper then decomposes where that advantage comes from, which is the part worth stealing even if you never implement either method. Moving the read points off a token grid and onto reasoning boundaries is worth a few points of saving. Changing what you read — confidence instead of agreement — is worth nearly four times as much, and it is the only one of the two changes that improves accuracy at a fixed saving.
Set your monthly reasoning volume and pick a rule. The savings and the premature-stop rates are the paper's measurements on competition maths; what they cost you depends on how much a silently wrong answer is worth in your product, which is a number only you have.
The asymmetry to keep hold of: the tokens you save are visible on an invoice at the end of the month, and the answers you truncated mid-correction are not visible anywhere. They arrive as a slightly worse product.