Selective Transfer of RL Updates for Visual Reasoning

Model merging provides a training-free way to transfer reasoning capabilities from language models to vision-language models (VLMs), but endpoint-based transfer can conflate pre-existing model differences with changes acquired during reasoning post-training. We instead formulate capability transfer around the training-stage update, isolating the parameter changes induced by reinforcement learning (RL). Yet transferring this update in full remains suboptimal: we find that its components differ substantially in cross-model transferability, with dominant directions transferring more effectively than the complete update. Based on this finding, we introduce Selective-RL, which isolates the RL-stage update, retains its dominant matrix-wise directions with magnitude preservation, and transfers them to the language modules of a VLM. Across three model families and five visual-reasoning benchmarks, Selective-RL improves full-update interpolation in 12 of 15 comparisons, including an 8.55 percentage-point MathVision gain on the Qwen recipient. Matched controls show that update magnitude or arbitrary low rank alone does not reproduce these gains. These results highlight a distinction between what is acquired during post-training and what remains transferable across models, providing a training-stage perspective on cross-model capability transfer. Code is available at https://anonymous.4open.science/r/selective-rl.