Words & Weights: Streamlining Multi-Turn Interactions via Co-Adaptation

Test-time policy adaptation for multi-turn interactions (T$^2$PAM) is essential for aligning Large Language Models (LLMs) with dynamic user needs. However, existing paradigms typically treat adaptation as a single-axis problem by either purely refining instructions or solely updating weights. This bifurcated approach overlooks the fact that interaction failures arise from a coupled mixture of context ambiguity and model incapacity. To address this, we propose ROSA2, a framework that reformulates T$^2$PAM as a joint optimization problem over the heterogeneous space of Words and Weights. Within this framework, the semantic stream acts as a feedback normalizer that transforms noisy or ambiguous user feedback into actionable instructions, ensuring that parametric adaptation is performed on semantically clarified trajectories. Theoretically, we prove that this semantic pre-conditioning strictly reduces the required parameter shift for convergence. Empirically, ROSA2 consistently outperforms state-of-the-art baselines across diverse mathematical, general reasoning, and coding benchmarks. It achieves up to a 37.8% accuracy improvement while reducing average interaction turns by 40%, demonstrating that ROSA2 unlocks the true potential of parameter updates.