Interaction Scaling: Grounding the Third Axis of Test-Time Compute

As language model (LM) outputs get more and more natural, it is becoming more difficult than ever to evaluate their quality. Simultaneously, increasing LMs' "thinking" time through scaling test-time compute has proven an effective technique to solve challenging problems in domains such as math and code. This raises a natural question: can an LM's evaluation capability also be improved by spending more test-time compute? To answer this, we investigate employing reasoning models-LMs that natively generate long chain-of-thought reasoning-as evaluators. Specifically, we examine methods to leverage more test-time compute by (1) using reasoning models, and (2) prompting these models to evaluate not only the response as a whole (i.e., outcome evaluation) but also assess each step in the response separately (i.e., process evaluation). In experiments, we observe that the evaluator's performance improves monotonically when generating more reasoning tokens, similar to the trends observed in LM-based generation. Furthermore, we use these more accurate evaluators to rerank multiple generations, and demonstrate that spending more compute at evaluation time can be as effective as using more compute at generation time in improving an LM's problem-solving capability.

Large language models can solve harder reasoning problems with more inference-time compute. The term "test-time scaling," however, covers several inference algorithms: extending deliberation along one trajectory, sampling completed candidates and aggregating them by voting or verification, and searching over partial states. These algorithms differ in statistical structure, compute requirements, and failure modes. Treating them as interchangeable under a scalar "budget," or reporting accuracy without specifying the inference protocol, makes results difficult to compare across studies. We study test-time scaling along three axes. First, we formalize it as budgeted inference over the implicit prefix tree of an autoregressive model and distinguish single-trajectory sequential scaling, leaf-level scaling with terminal reduction, and prefix-level scaling. Second, we treat the full inference system as the evaluated object and separate end-to-end performance from candidate-bank diagnostics. We introduce an evaluation profile whose coordinates and simple functionals recover or bound common repeated-sampling metrics, and require compute accounting and uncertainty estimates that match the protocol. Third, we distinguish exact replay from distributional reproducibility and state the requirements for each. We also organize open-weight reasoning models by model-side and interface mechanisms. Our empirical study covers broad knowledge, symbolic reasoning, and competition mathematics, and we publicly release 1,403,520 sampled model attempts. The project website is available at https://mohsenhariri.github.io/scorio/tts. The released datasets are Trace (https://huggingface.co/datasets/harimo/scorio-trace), Lite (https://huggingface.co/datasets/harimo/scorio-lite), Math (https://huggingface.co/buckets/harimo/scorio-math), and SuperGPQA (https://huggingface.co/buckets/harimo/scorio-gpqa).

Large Reasoning Models (LRMs) achieve strong performance on mathematical reasoning tasks but remain unreliable on challenging instances. Existing test-time scaling methods, such as repeated sampling, self-correction, and tree search, improve performance at the cost of increased computation, yet often exhibit diminishing returns on hard problems. We observe that output disagreement is strongly correlated with instance difficulty and prediction correctness, providing a useful signal for guiding instance-level strategy selection at test time. Based on this insight, we propose a training-free framework that formulates test-time scaling as an instance-level routing problem, rather than allocating more computation within a single strategy, dynamically selecting among different scaling strategies based on output disagreement. The framework applies lightweight resolution for consistent cases, majority voting for moderate disagreement, and rewriting-based reformulation for highly ambiguous instances. Experiments on seven mathematical benchmarks and three models show that our method improves accuracy by 3% - 7% while reducing sampling cost compared to existing approaches.