# Beyond Correctness: Compute-Responsive Data Selection for Reasoning Model Post-Training

arXiv: https://arxiv.org/abs/2610.20057 · HTML: https://mlsanity.com/paper/2610.20057/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 25 of its 30 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 25 of 25)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [Confident Adaptive Language Modeling](https://mlsanity.com/paper/2207.07061/) (2022)
- [Generating Sequences by Learning to Self-Correct](https://mlsanity.com/paper/2211.00053/) (2022)
- [FastBERT: a Self-distilling BERT with Adaptive Inference Time](https://mlsanity.com/paper/2004.02178/) (2020)
- [The Right Tool for the Job: Matching Model and Instance Complexities](https://mlsanity.com/paper/2004.07453/) (2020)
- [Not All Errors Are Equal: Consequence-Aware Reasoning Compute Allocation](https://mlsanity.com/paper/2606.04402/) (2026)

## Abstract (arXiv)

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.