Don't move the whole RL update: keeping one dominant direction lifts Qwen visual math by 8.55 points

Reasoning transfer between models now moves the parameter change produced during reinforcement learning alone, rather than the whole difference between a language model and a vision-language model. Endpoint-based transfer builds a donor-recipient displacement directly, and that displacement mixes differences that predate reinforcement learning with changes acquired during it. On Qwen3-VL-8B-Instruct, interpolation retaining the dominant reinforcement-learning direction reaches 81.00 on MathVista, while full-update interpolation over the same parameter support reaches 76.70.

Transfer keeps only the single strongest singular direction of each eligible language-layer matrix, then rescales it to the magnitude of the original matrix update. The complete update was optimized for the source language model, so its directions need not be equally useful to a multimodal recipient, and retaining more of them is not necessarily better. On Qwen3-VL-8B-Instruct MathVista, accuracy falls from 81.00 to 78.30 as rank grows from one to sixteen; ten matched random directions average below the untouched receiver, and the trailing direction reaches 73.10.

The gains repeat across three model families, but not on every benchmark. Earlier comparisons lacked a control that separates the reinforcement-learning-stage update from initialization displacement and compares direction choices at matched magnitude. Twelve of fifteen backbone-benchmark comparisons beat full-update interpolation; LLaVA-NeXT-LLaMA3-8B improves on four tasks but loses on MMStar, and Idefics2-8B improves on MathVista, MathVerse and DynaMath while declining on MathVision and MMStar.

The method is validated on three multimodal recipients, Qwen3-VL-8B-Instruct, LLaVA-NeXT-LLaMA3-8B and Idefics2-8B, with donors obtained by DAPO-style post-training on DAPO-Math-17K. Transfer support is limited to seven attention and MLP projections, while visual modules, embeddings, output heads, LayerNorm parameters and biases stay fixed. Evaluation covers MathVista, MathVerse, MathVision, DynaMath and MMStar, with additional results on TextVQA, MMMU, OCRBench and POPE. Construction is offline, and the merged checkpoint remains a standard dense vision-language model with no added inference-time module.

Gains are not uniform: LLaVA-NeXT-LLaMA3-8B declines on MMStar relative to full-update interpolation, and Idefics2-8B declines on MathVision and MMStar. Rank one is described as a fixed empirical rule rather than an assumption that a single direction constitutes reasoning capability, and accuracy falls steadily as rank grows from one to sixteen. Source-model reconstruction and recipient improvement are explicitly treated as separate measurements, with rank-one reconstruction recovering 97.18 percent of the donor's MATH gain over its pre-reinforcement-learning state. Offline SFT, offline distillation and on-policy distillation also raise MathVista, so the effect is not exclusive to reinforcement learning. In the generation analysis, some Selective-only MathVista successes correspond to full-update repetition, truncation or extraction pathology, while the rest correspond to ordinary reasoning or perception errors, and mechanism attribution still requires separate analysis.