Reasoning, Test-Time Compute, and Verifiers

Four different things get called reasoning. They expose different artifacts and require different evaluation.

Single-pass generation produces one answer directly from the prompt and context. It is the lowest-latency baseline. It is enough for routine tasks, it gives the workflow no opportunity to recover, and it is the necessary comparison for any compute added on top of it.

Candidate generation and selection samples several solutions and then ranks or verifies them. The cheapest version has a name: self-consistency. Sample many reasoning paths, then keep the majority answer. Google Research introduced it in 2022 and presented it at ICLR 2023, with sizes attached: “Our extensive empirical evaluation shows that self-consistency boosts the performance of chain-of-thought prompting with a striking margin on a range of popular arithmetic and commonsense reasoning benchmarks, including GSM8K (+17.9%), SVAMP (+11.0%), AQuA (+12.2%), StrategyQA (+6.4%) and ARC-challenge (+3.9%).” Note the spread as well as the size. +17.9% on GSM8K and +3.9% on ARC-challenge are the same method on different tasks. Cost scales with the candidate count. And the selection rule here is the model agreeing with itself, so it inherits whatever the model already believes.

Decomposition and tool use breaks the task into explicit subproblems with external checks. It creates inspectable artifacts and supports calculators, code, and retrieval. It adds orchestration and its own failure modes. It is often the stronger option when constraints have to be satisfied exactly.

Iterative critique and revision asks a model or a reviewer to diagnose and improve a draft. It can catch surface and consistency errors. It may also reinforce misconceptions the critic shares with the author, and it needs stop and regression rules. It works best against concrete criteria rather than a request to make the draft better.

The final answer is more trustworthy when the intermediate artifacts have independent semantics. Restate the contract, clarifying target, constraints, and permitted evidence. Propose candidates: plans, answers, proofs, or tool calls. Create testable artifacts, so that calculations, code, citations, schemas, or subclaims become inspectable on their own terms. Verify independently, using execution, retrieval, formal rules, or qualified human review. Revise or abstain, using failed checks to correct, narrow, or stop. Record the trace, retaining enough evidence to reproduce the decision without exposing hidden private reasoning.

The step that carries the weight is verification. Checking the intermediate steps is worth more than checking only the final answer, and the gap has been measured. Lightman and colleagues at OpenAI compared the two on the MATH dataset in 2023. Feedback on each intermediate step significantly outperformed feedback on the outcome alone. Their abstract states the result and its price in the same breath: “Our process-supervised model solves 78% of problems from a representative subset of the MATH test set. Additionally, we show that active learning significantly improves the efficacy of process supervision. To support related research, we also release PRM800K, the complete dataset of 800,000 step-level human feedback labels used to train our best reward model.”

That is the honest shape of the trade. Checking the steps beat checking the answer. Building the checker took 800,000 human labels on individual steps. Independent semantics for intermediate artifacts is not free, and a workflow that claims it without paying for it has usually just moved the assertion one level down.

These patterns should be included in evaluation suites, because each one consumes budget while producing the appearance of diligence.

Spend more only when the task and the verification path justify it. Classify request difficulty, using observable features or a cheap routing model. Choose a strategy: direct answer, multiple candidates, tools, decomposition, or human review. Set a budget, limiting tokens, candidates, tool calls, retries, and elapsed time. Define verification, specifying executable, source-based, formal, or human checks. Add a stopping rule that ends the process on success, diminishing returns, uncertainty, or budget exhaustion. Compare with the single-pass baseline, measuring quality gain, tail risk, latency, and cost on representative tasks.

The first and third of those are not housekeeping. Conditioning the budget on difficulty has a measured payoff. Snell and colleagues tested allocating test-time compute according to how hard each prompt was, in 2024: “Using this compute-optimal strategy, we can improve the efficiency of test-time compute scaling by more than 4x compared to a best-of-N baseline. Additionally, in a FLOPs-matched evaluation, we find that on problems where a smaller base model attains somewhat non-trivial success rates, test-time compute can be used to outperform a 14x larger model.”

Read that as two separate numbers, because they answer two questions a policy has to settle. More than 4x is what routing was worth against spending the same compute uniformly on every prompt. That is the argument for step 1. The 14x is what the compute was worth against parameters, and it comes with its own precondition: it held on problems where the smaller model already had non-trivial success rates. Extra inference bought progress where there was already partial traction to build on. That is exactly the boundary a difficulty classifier is being asked to find.

Some models and workflows benefit from additional inference effort, especially when tasks admit verification or search. The cleanest demonstration is a task where the answer can be checked by rule. Pure reinforcement learning on verifiable tasks raised DeepSeek-R1-Zero's average pass@1 on AIME 2024 from 15.6% to 77.9%. Sampling more solutions and taking the agreed answer raised it again: “In addition, by leveraging the self-consistency decoding (Wang et al., 2023c), the model's performance can be further improved, achieving an accuracy of 86.7%.”

Those figures come from the peer-reviewed version of DeepSeek's R1 paper, published in Nature in September 2025. The original January 2025 tech report gave 15.6% to 71.0% on the same step, with the same 86.7% under majority voting. The middle number moved between the preprint and the reviewed paper. Which version of a result you cite is a small lesson of its own.

The mechanism should remain separable from the story a model tells about its own process. Long context is the next constraint. More available tokens can supply evidence. But where the evidence sits, what competes with it, and how hard it was compressed determine whether the model uses them well.