Beyond Correctness: Compute-Responsive Data Selection for Reasoning Model Post-Training
Most research on test-time compute treats the model as fixed and asks how to allocate extra inference tokens. This paper instead asks whether a model can be post-trained to use a given compute budget more effectively. The authors identify compute-responsive (CR) problems—those that flip from complete failure to success under additional blind re-solving or audit-based revision—and show that supervised fine-tuning on these examples shifts the compute–accuracy frontier across budgets from 512 to 4,096 tokens and generalizes across model families.
The paper presents a well-motivated and cleanly isolated data-selection principle for reasoning post-training. The distinction between compute allocation and compute utilization is conceptually sharp, and the matched-control experimental design strengthens causal claims. However, the absolute gains are modest—a 1.2 point overall accuracy lift on the mixed test set and a 4.7 point recovery advantage over an already-solved baseline—and the reliance on a small, model-specific corpus of 853 training examples limits clear scalability to broader settings.
The conceptual framing and methodological care are the strongest aspects. The authors rigorously separate genuine reasoning recovery from mere completion responsiveness and formatting artifacts by enforcing complete initial failures, answer normalization, and sampled multi-trajectory audits. Their controlled SFT design—holding fixed the model, LoRA configuration, and training budget while varying only data selection—credibly isolates the CR signal, and the extension to on-policy distillation and cross-model reconstruction on Llama-3.1-8B supports the claim that compute responsiveness is a general behavioral signal rather than a quirk of Qwen3-8B.
The overall effect size is small and comes with retention costs. On the mixed generalization set, CR training only lifts overall accuracy from 50.6% to 51.8%, while accuracy on already-solved problems drops from 100.0% to 86.3%, indicating a capacity reallocation rather than uniform improvement.
More fundamentally, the method leans on a tiny model-specific corpus—1,065 unique CR problems, of which only 616 have clean blind-success trajectories for SFT—constructed from over 12,000 evaluated examples. This raises serious questions about whether the gains will hold under full fine-tuning, at larger scale, or outside mathematics where reliable automatic verification is scarce.
The evidence supports the narrow claim that CR-selected data improves recovery of CR-classified failures better than the matched random and already-solved controls. However, the comparison to related work is shallow: the paper does not benchmark CRDS against stronger adaptive data-selection baselines such as difficulty-based filtering, uncertainty sampling, or confidence-weighted curation, which are standard in the data-selection literature. The matched controls are fair for isolating signal, but because they are intentionally weak, the gap to more sophisticated selection strategies remains unknown. The stratified test results also show that most of the gain is concentrated on the CR stratum itself, with unresolved problems remaining nearly flat.
The appendices provide unusually thorough documentation of prompts, normalization rules, data schema, and training configurations, which aids reproduction. Nevertheless, practical barriers are substantial. Constructing the CR corpus is expensive and model-dependent: the protocol requires up to four additional trajectories per complete initial failure, and the final corpus aggregates evaluation over 12,831 problems. The paper also reports sensitive, stack-specific evaluation details—such as batch-size-1 deterministic decoding to avoid batching-dependent generation differences—that may not transfer cleanly to other inference engines. Finally, the authors state that anonymous supplementary materials contain code and scripts, but these were not available for inspection, leaving critical hyperparameters and implementation subtleties unverified.
Reasoning language models increasingly rely on test-time compute scaling, yet most existing work studies how to allocate inference computation while treating the model itself as fixed. We ask a complementary question: can reasoning models be post-trained to make better use of a given amount of test-time compute, and which examples are most useful for this goal? Our key observation is that reasoning problems differ substantially in their response to additional computation. Some are already solved under limited compute, others remain unresolved even after further reasoning, while a distinct subset changes from complete initial failure to success when additional reasoning is provided. We call these compute-responsive (CR) examples and introduce Compute-Responsive Data Selection (CRDS), a post-training data-selection principle that prioritizes examples with empirically demonstrated marginal utility from additional reasoning. On Qwen3-8B, SFT on CR examples recovers 45.3\% of held-out low-compute failures, compared with 40.6\% when training on already-solved examples. The advantage extends beyond the selected CR split: SFT-CR reaches 51.8\% overall accuracy on an independently sampled test distribution, with the gain concentrated on compute-responsive problems. CR training also shifts the compute--accuracy frontier across inference budgets from 512 to 4,096 tokens, outperforming matched non-CR training throughout and reaching 48.1\% recovery at the largest budget. The same pattern is supported across multiple data sources, remains visible under on-policy distillation, and extends to Llama-3.1-8B-Instruct when CR sets are reconstructed separately for that model. Better test-time compute utilization can therefore be learned through post-training, with recoverable responses to additional reasoning providing a particularly informative signal for selecting training examples.
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