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.

As AI assistants become more integrated into our daily lives, they often need to solve complex problems through back-and-forth conversations. However, when an AI makes a mistake during these chats, it faces a fundamental dilemma: was the user's instruction confusing, or does the AI simply lack the capability to solve it? Previous methods try to improve either the text prompt or the AI's internal programming. But fixing just one often causes the AI to get stuck, or worse, learn the wrong things from messy and vague human feedback. In this paper, we introduce a new framework that improves both at the same time. First, our system acts like a translator, automatically taking noisy or vague user feedback and turning it into a crystal-clear instruction. Second, it uses this clarified instruction to instantly "rewire" and upgrade the AI's internal brain. By clearing up the miscommunication before upgrading the AI's capability, we ensure the AI learns exactly what the user intended rather than memorizing mistakes. Our experiments show this combined approach dramatically boosts the AI's ability to solve difficult math and coding problems, helping it arrive at the correct answer in much fewer steps and making future AI assistants significantly more reliable.