DeGMatch: Target-Aware Reasoning Data Selection via Deconfounded Gradient Matching

Overview & Synopsis

Reasoning post-training on long trajectories has substantially improved the reasoning capabilities of large language models, but scaling such training to large datasets is increasingly expensive. We study target-aware reasoning data selection, where a small reference set specifies a target capability and guides the selection of training trajectories for specialization. We find that existing target-aware methods can exhibit limited target discrimination on long reasoning trajectories, while dominant population-level structure in candidate gradients can obscure finer target-dependent variation during gradient matching. To address these limitations, we introduce Deconfounded Gradient Matching (DeGMatch), which first constructs a target-relevance gate and then reranks candidates using model-specific gradients. DeGMatch centers gradients using the candidate-population mean and removes leading principal directions before target matching, reducing the influence of dominant population-level structure and improving target discrimination. Across mathematics, science, and code, DeGMatch outperforms strong heuristic, target-aware, and reasoning-specific data selection baselines, while remaining effective across selection budgets, model families, and scales. Our code is publicly available at https://github.com/CHLee0801/degmatch.